2.1. The Powder Lifecycle as a Traceable Data System

In powder-based manufacturing, powder is better regarded as an evolving material state than as a passive starting input. Its condition changes through production, sampling, storage, handling, spreading or compaction, thermal exposure, reuse, reconditioning, post-processing, and final inspection. As a result, the same nominal alloy, and even the same nominal powder specification, may behave differently across batches when particle-size distribution, morphology, surface chemistry, moisture level, contamination, flowability, oxygen content, or reuse history changes. These variations affect powder packing, energy absorption, melt-pool stability, densification, defect formation, and the final microstructure and properties^{[4, 6, 7, 22]}. This lifecycle view is important because powder-manufacturing data are generated in separate but connected stages. Before processing, powder characterization provides descriptors such as particle size, morphology, chemistry, apparent density, tap density, flowability, and spreadability. During processing, powder is converted into an intermediate state, such as a powder bed, green compact, melt pool, or sintering body. After consolidation and post-processing, the same material history is evaluated through density, porosity, microstructure, surface roughness, hardness, tensile properties, fatigue response, or wear behavior. These data layers differ in format, scale, cost, and uncertainty, but they describe the same powder-to-part route. If the data layers are not connected, a measured property change cannot be assigned confidently to the feedstock, processing route, machine condition, post-processing step, or their combined effect^{[6, 7, 22]}.

Powder characterization is therefore more than feedstock acceptance. Particle-level descriptors such as size, shape, surface texture, internal porosity, and chemistry must be considered together with bulk-level behavior such as flowability, apparent density, tap density, rheology, and spreadability^{[4, 6]}. Many standard powder tests remain useful, but they do not always reproduce the stress state, spreading mechanism, environmental exposure, or machine-specific conditions experienced during PBF. This is why a powder may pass common specification checks and still produce unstable layers under a given recoating condition. Powder-evaluation methods are most useful when selected in relation to the powder lifecycle, alloy system, machine configuration, and intended process route^6]. The same logic also applies to pressed powder metallurgy routes. A powder that shows acceptable flowability or apparent density may still produce different green density, density gradients, crack susceptibility, or sintering shrinkage when compaction pressure, die geometry, lubrication, or particle morphology changes. For ML, green-density measurements, compaction signals, and sintered-density labels should therefore be treated as linked processing data rather than isolated tabular values^{[26– 29]}.

The powder-spreading step illustrates this point clearly. In PBF, the powder layer is not simply a geometric input of prescribed thickness. It is a process state shaped by powder cohesion, particle-size distribution, particle morphology, recoater type, recoating speed, layer thickness, dosing condition, and machine-specific mechanisms^{[6, 7]}. Layer quality can be quantified through descriptors such as layer-thickness deviation, surface coverage, surface roughness, and packing density. For example, recent discrete element method (DEM)-based work suggests that skewness and kurtosis of the layer surface profile can serve as useful indicators of layer-quality variation^[30]. For ML, these metrics matter because powder-bed images or recoating metrics should not be treated as generic image data. They are process signatures that sit between powder descriptors and final defects.

Powder reuse further strengthens the need for lifecycle tracking. Reused powder carries a processing history that may include thermal exposure, spatter contamination, oxidation, sieving, blending, storage, and repeated contact with the machine environment^{[10, 11]}. These processes can alter particle morphology, surface chemistry, particle-size distribution, flow behavior, packing response, and oxygen or nitrogen content. Different reuse strategies also create different levels of history reconstruction. Single-batch and collective-ageing approaches preserve clearer powder provenance, whereas top-up and refreshing methods may preserve usability while making the exact exposure history more difficult to reconstruct^[10]. As a representative example, recent work on reused AlSi10Mg shows that recycling count can interact with process parameters such as laser power and deposition thickness, affecting void nucleation, indentation modulus, and wear behavior^[17]. Reuse state needs to be recorded as a material-history variable, not treated as background information.

Traceability remains equally important after consolidation. Final labels used for ML, including density, porosity, microstructure, surface roughness, hardness, tensile strength, fatigue life, and wear rate, are not direct outputs of a single process parameter. They are outcomes of the full powder-to-part route. Heat treatment, HIP, debinding, sintering, stress relief, machining, and surface finishing can all change the relationship between the as-processed state and the final measured response^[22]. Moreover, not all labels have the same fidelity. In laser powder bed fusion (LPBF) density assessment, Archimedes measurements are relatively accessible and scalable, but they provide bulk estimates and can be affected by sample geometry or measurement conditions. Micrographic or computed tomography (CT)-based observations provide more spatially resolved information on porosity and defects, but they are more labor-intensive and harder to collect at scale^[23]. This label hierarchy should be made explicit when training, comparing, or interpreting ML models. The main bottleneck is therefore not only that powder-manufacturing datasets are small. The more difficult problem is that powder qualification reports, machine logs, in-situ monitoring files, post-processing records, and final testing results are often stored as separate records. Multimodal sensor fusion is useful only when different signals are linked to the same physical location, layer, specimen, or build history. A representative powder-based AM example is the multimodal sensor-fusion study of Petrich et al., where optical images, acoustic emission, multispectral emission, scan-vector information, and machine logs were linked to CT-based flaw labels at the voxel level^[20]. In that workflow, the value of sensor fusion came from registration between sensor features and post-build defect labels, not simply from using many sensors. The same traceability logic applies to pressed powder metallurgy, where press-force or displacement signals are useful for crack or compact-quality assessment only when the signal history is connected to compact identity, tooling condition, sintering route, and final inspection result.

A lifecycle dataset should preserve both material provenance and process provenance. At minimum, this includes identifiers for powder origin and condition, machine and sensor configuration, process parameters, post-processing history, and final characterization^[6]. This does not mean that every study must measure every variable. Rather, unmeasured variables should be recognized as missing parts of the manufacturing history. Missing metadata are not neutral omissions. Missing powder, process, sensor, or post-processing records define the boundary within which an ML model can be interpreted, validated, or transferred^{[6, 11, 20]}. The lifecycle view provides the basis for the ML discussion in the following section. Classification, regression, spatiotemporal modeling, and optimization do not operate on isolated datasets; they use different portions of the same lifecycle record. When this record is incomplete, model accuracy may reflect dataset-specific correlations rather than transferable process–structure–property relationships. When the record is traceable, ML can be used more defensibly to screen powder quality, identify process windows, connect in-situ signatures with defects, and support decisions about reuse or post-processing. The goal is therefore not only to apply more complex algorithms, but to build datasets in which the physical meaning of each input and label is retained.

2.2. ML Task Types Across the Powder-Manufacturing Data Thread

The lifecycle view in Section 2.1 can be translated into four practical ML task types: classification, regression, sequence or spatiotemporal modeling, and optimization or inverse design. These task types appear across powder metallurgy, binder jetting, powder bed fusion, directed energy deposition, and related powder-processing routes. The task categories are not restricted to additive manufacturing. Conventional powder metallurgy also uses classification for quality screening, regression for density or sintering prediction, time-dependent signals for compaction or process monitoring, and optimization for composition, compaction, sintering, or post-processing design. The common feature is that each task extracts a different type of decision from powder state, processing conditions, monitoring signals, post-processing records, and final quality measurements^{[12– 16, 27– 29]}. Figure 2 organizes these task types within the powder-manufacturing data thread. Powder descriptors, process variables, images, sensor signals, simulation outputs, and property measurements can support different ML objectives, but the usefulness of each objective depends on whether the input data and output labels remain traceable to the same powder batch, specimen, build, layer, compact, or processing history.

Fig. 2. Major ML task categories in powder-manufacturing applications

For the powder-manufacturing data thread to support ML, powder descriptors, process parameters, layer-level or compact-level monitoring signals, and ex-situ measurements must be connected through common identifiers. These identifiers may include powder lot, reuse cycle, build number, layer number, compact number, specimen location, tooling condition, heat-treatment route, or measurement position. Without such links, traceability remains a documentation concept rather than a usable structure for ML. This issue is important in powder-based manufacturing because powder lot, reuse history, recoating condition, compaction state, machine configuration, and post-processing route can all influence the same final quality label^{[4, 6, 11, 15, 20, 21]}.

One important use of ML is screening and state recognition. In powder-processing applications, this task is usually formulated as classification, where the output is a discrete label rather than a continuous value. Classification includes anomaly detection, defect detection, powder-layer assessment, powder quality screening, compact-quality classification, swelling or shrinkage classification, crack detection, and pass/fail evaluation. The input data may be powder-bed images, optical or thermal signals, acoustic signals, photodiode traces, press-force signals, or tabular powder descriptors. The output may indicate a nominal or abnormal layer, defective or non-defective region, cracked or non-cracked compact, swelling or shrinkage behavior, or acceptable or unacceptable powder condition^{[5, 20, 27, 31– 33]}.

The main limitation of classification is label reliability. In powder-based manufacturing, a defect label is rarely caused by a single factor. A region marked as defective may result from powder spreading, local energy input, powder reuse, contamination, atmosphere, tooling condition, geometry, or post-processing. Rare defect occurrence, class imbalance, subjective annotation, and inconsistent inspection thresholds can make a classifier appear accurate within one dataset while failing on another powder lot, build, compact, or machine. Classification outputs should therefore be treated as process-state indicators unless the class labels are linked to objective validation such as CT, metallography, dimensional inspection, mechanical testing, or other final quality measurements^{[20, 31– 33]}. A warning label becomes more useful when the warning can be traced back to the powder and process conditions that produced it.

A second group of ML applications aims to predict continuous responses. These applications are usually formulated as regression problems. Typical regression targets include density, porosity, melt-pool width or depth, surface roughness, hardness, tensile strength, fatigue response, wear rate, sintering shrinkage, green density, and other property-related quantities^{[26, 27, 29, 34, 35]}. In PM and powder-based AM, regression inputs may include powder composition, particle-size distribution, mass fraction, morphology, green density, compaction pressure, laser power, scan speed, hatch spacing, layer thickness, sintering temperature, heat-treatment condition, or HIP condition. Regression is attractive because many powder-processing studies generate tabular datasets with measurable process variables and numerical quality responses. The same tabular structure can also make regression misleading. Many powder-processing datasets are small, highly correlated, and sparse in the true process space. For example, laser power and scan speed are often varied together; powder morphology and flowability are coupled; reuse history can change both chemistry and spreading behavior; and post-processing can mask or amplify differences formed earlier in the process. A regression model trained under these conditions can report low error while learning experimental bias or dataset-specific correlations^{[13, 15, 22, 34, 35]}. Regression predictions should therefore be checked not only by statistical metrics, but also by physical consistency within the process–structure–property relationship. When regression is used for transfer, extrapolation, or process recommendation, the predicted response should be compared with micrographs, CT observations, powder-bed data, compact-quality measurements, or known processing trends^{[22, 27, 29, 34– 36]}.

Forward and inverse modeling provide a useful distinction within prediction- and optimization-oriented ML. Forward models predict process signatures, microstructure, build quality, properties, or performance from powder and processing inputs. Inverse models start from a target response and search for powder conditions or process parameters that may achieve it^[13]. The inverse task is attractive because practical process development often requires a window of acceptable conditions rather than a single prediction. However, inverse outputs should be interpreted with care. If the training data come from one alloy, powder lot, machine, geometry, or post-processing condition, the recommended conditions may not remain valid after any of these factors changes^[13].

A third class of ML applications deals with process evolution. Sequence and spatiotemporal modeling become important when the data describe how a process changes over time or across location rather than a single static state. Acoustic signals, emission spectroscopy, photodiode traces, melt-pool videos, thermal histories, layerwise images, scan-vector trajectories, press-force histories, and displacement signals can contain time- or location-dependent information about powder spreading, compaction, melt-pool instability, plume fluctuation, recoating disturbance, crack formation, and process drift^{[20, 31, 32, 37, 38]}. These data are valuable because defects often develop through a sequence of local events rather than appearing instantaneously in the final part or compact. A temporal or spatiotemporal model can detect signatures of instability before the defect becomes visible as porosity, distortion, cracking, or mechanical degradation. The difficulty is data alignment. Sensors measure different physical phenomena at different sampling rates, resolutions, and fields of view. A signal anomaly does not automatically correspond to a defect unless the signal is registered to the correct layer, coordinate, scan path, compact, specimen, and post-build inspection result. Multimodal monitoring should therefore be treated as a data-alignment problem, not only as a model-architecture problem^{[17, 28, 33, 34]}. Time shifts, delayed responses, missing frames, sensor drift, and rare abnormal events all weaken model transferability. In practice, the bottleneck is often not the amount of sensor data, but the reliability with which sensor data are connected to ground truth from CT, metallography, dimensional inspection, crack inspection, or mechanical testing^{[20, 31, 36, 38]}.

Optimization-oriented ML extends prediction into decision support. Instead of asking what output will result from known inputs, optimization searches for powder-production settings, process parameters, powder conditions, alloy compositions, or post-processing routes that are likely to meet target properties under constraints^{[13, 39– 41]}. In this review, inverse design refers to decision-oriented search over feasible powder, process, or post-processing conditions, rather than only the mathematical inversion of a predictive model. Bayesian optimization is particularly attractive because it can guide expensive experiments by using a surrogate model and uncertainty estimate to decide which condition should be tested next^{[2, 41, 42]}. Recent examples include multi-objective Bayesian optimization of LPBF Ti6Al4V processing conditions and multi-response optimization of powder-based DED parameters, both showing that process optimization in metal AM must balance density, surface quality, defect formation, melt-pool geometry, and mechanical response rather than optimize a single metric alone^{[40, 43]}. This is valuable in powder-based manufacturing, where process-window development, powder reuse qualification, and composition screening often require costly builds and destructive characterization.

Most optimization workflows depend on a surrogate model, and their recommendations are only as reliable as the data, assumptions, and constraints behind that surrogate. The search space, feasible processing limits, powder-state variables, measurement fidelity, and uncertainty estimates must be stated explicitly^{[13, 15, 21, 42]}. Optimization recommendations are most defensible when they guide the next round of experiments, narrow the parameter window, or rank candidate conditions. The same recommendations are less defensible when presented as final process recipes without experimental confirmation. For this reason, inverse design should be viewed as constrained decision support under uncertainty rather than as a black-box replacement for process qualification^{[26, 39]}. Data-efficient strategies extend these four task types rather than replacing them. Transfer learning can reduce target-domain labeling when related materials, machines, sensors, or simulations provide useful source information. Multi-fidelity modeling can combine lower-cost measurements or simulations with fewer high-fidelity labels. Physics-informed and hybrid learning can use physical priors, simulations, or mechanistic descriptors to improve plausibility under sparse-data conditions. These three strategy families are discussed in Section 3 because their usefulness depends on source–target similarity, fidelity hierarchy, physical validity, and lifecycle traceability^{[15, 16, 23– 25, 42, 44– 46]}.

The four task types should be viewed as complementary operations on the same powder-manufacturing data system. Classification is strongest for rapid screening and state recognition. Regression is strongest for continuous property or process-response prediction. Sequence and spatiotemporal models are strongest for tracking process evolution. Optimization and inverse design are strongest for constrained decision-making and experimental planning. In practice, the task types also interact: classification outputs may become inputs to regression, sequence features may support defect prediction, and optimization usually depends on a surrogate predictive model. From a materials-science perspective, the central issue is not only predictive accuracy. The central issue is whether powder history, process evolution, and final validation remain connected through a traceable, physically interpretable, and transferable data chain.

2.3. Representative ML Applications Across the Powder-Processing Workflow

The task categories discussed above become more meaningful when they are placed back into the manufacturing workflow. In powder-based manufacturing, ML is not applied at a single point. It appears at the feedstock stage, during layer formation or densification, in process monitoring, after post-processing, and finally in property evaluation or process optimization. These applications differ in input format and modeling objective, but they share a common requirement: predictions must remain traceable to the powder and process history from which the data were generated.

At the feedstock stage, ML can be used to model and optimize powder production itself. Powder yield, particle-size distribution, sphericity, satellite formation, and morphology are not only powder-supplier concerns; they define the starting condition for spreading, packing, melting, sintering, and final property development^{[4, 6]}. Tamura et al. studied gas-atomized Ni–Co-based superalloy powders for turbine-disk applications and used a Gaussian-process surrogate model with Bayesian optimization to select melt temperature and gas pressure^[41]. Starting from three initial experiments and three optimization cycles, the study reported a qualified powder fraction of 77.85% for particles smaller than 53 μm, together with an estimated production-cost reduction of about 72% relative to commercial powder^[41]. The modeled target was not a final part property, but the powder state itself. This places ML upstream in the powder lifecycle, before spreading, melting, sintering, or post-processing begins. A different set of applications begins once the powder is spread, compacted, or otherwise converted into a process state. Powder delivery is also an important process-state variable in powder-fed directed energy deposition. Jung et al. showed that variations in powder line density altered bead geometry, grain morphology, anisotropy, and mechanical properties in L-DED-fabricated STS316L, even under comparable energy-density conditions^[47]. In laser powder bed fusion (LPBF), the powder layer is often treated as if it were defined only by nominal layer thickness, but actual layer quality depends on particle cohesion, size distribution, recoater motion, surface coverage, surface roughness, and packing density^{[6, 7]}. Discrete element method (DEM)-based studies have shown that layer quality can be described using measurable descriptors such as layer-thickness deviation, surface coverage ratio, root-mean-square roughness, packing density, skewness, and kurtosis^[30]. These descriptors turn the powder bed from a visual observation into a measurable process signature. Figure 3 illustrates how layer-wise or powder-bed monitoring data are converted into model inputs and linked to process-state or defect labels. This connection is central to evaluating whether an ML model detects a physically meaningful anomaly or only separates patterns within a specific dataset.

Fig. 3. Example of ML-based in-situ monitoring and anomaly-pattern detection during LPBF ^[5].

Computer-vision methods have been used to extract such signatures directly from powder-bed images. Scime and Beuth proposed an early LPBF monitoring workflow in which post-recoating images were processed to detect and classify powder-bed anomalies^[5]. Their training database contained 2402 labeled image patches covering anomaly-free regions and six anomaly classes^[5]. In that workflow, a powder-bed image was first converted into numerical visual descriptors. Handcrafted visual features are manually designed descriptors, such as intensity, texture, edge, or shape-related information, that represent the appearance of a local image region. A bag-of-visual-words representation treats recurring local visual patterns as “visual words” and summarizes their occurrence in an image as a compact feature vector. Scime and Beuth used k-means clustering as an unsupervised method to group similar local feature descriptors and define the visual-word vocabulary used for anomaly classification^[5]. The resulting feature vectors were then used for powder-bed anomaly classification. This workflow is useful because it shows how recoating defects can be converted from visual observations into trainable layerwise features, rather than being treated only as qualitative images. Later image-based work increased both image resolution and annotation scale. Fischer et al. used more than 45,000 annotated powder-bed anomalies and reported 99.15% classification accuracy with class F1-scores between 97.85% and 99.71% under the best imaging and model conditions^[33]. These results support the use of powder-bed imaging for layer-quality monitoring, but they also define the boundary of the evidence. Performance remains sensitive to image resolution, lighting, anomaly definition, powder reflectivity, and the representativeness of expert labels.

More recent monitoring studies have moved from single-image analysis toward multimodal sensor fusion. Instead of relying on one signal, these workflows combine several records from the same build. Layerwise optical images refer to images captured at individual build layers, typically after powder recoating or after laser exposure, so that local layer disturbances can be linked to a specific layer and build location. These images can be combined with acoustic signals, multispectral emissions, scan-vector information, and machine logs, and then correlated with post-build inspection results such as CT-detected flaws, metallographic porosity, or location-specific quality measurements^{[20, 31, 32]}. Petrich et al. provide a useful scale reference for this type of work: their multimodal sensor-fusion model used 168,574 voxel-level samples, four-fold cross-validation, and reported 98.5% binary flaw/no-flaw classification accuracy against CT-linked labels^[20]. In that workflow, the reported accuracy was meaningful because sensor features were registered to build location, layer number, scan-vector information, and final flaw labels. Without this registration, a sensor feature may still correlate with a defect, but the physical meaning of the prediction becomes difficult to defend.

ML has also been used to predict part quality and mechanical properties from process and material variables. In these cases, the model usually receives structured inputs such as powder composition, particle size, energy input, scan speed, hatch spacing, layer thickness, build orientation, heat-treatment condition, or HIP parameters, and then predicts density, porosity, hardness, tensile strength, elongation, fatigue life, or wear behavior^{[13– 15, 27, 34, 35]}. Destructive characterization is expensive, so validated property-prediction models can reduce the number of experiments needed to screen a process window. Their reliability, however, depends on whether powder lot, reuse state, build location, specimen location, and post-processing condition are recorded. A recent LPBF study on 3.3% Si electrical steel also combined ML and explainable AI to model density, surface roughness, and hardness as functions of laser power, scan speed, and scanning angle, showing that ML-based process optimization can be linked directly to powder-bed-fusion process variables and experimentally measured quality indicators^[48].

Post-processing illustrates this issue particularly well. Final performance is often not determined by the build step alone. Heat treatment, stress relief, and HIP can alter residual stress, microstructure, porosity, surface condition, and mechanical scatter^{[18, 19, 22, 34]}. Yang et al. developed an artificial neural network model for LPBF-fabricated Ti–6Al–4V components in which as-printed properties and HIP parameters were included as inputs for predicting final tensile properties^[34]. The model predicted yield strength and ultimate tensile strength more reliably than elongation: 87.5% of yield-strength predictions and 100% of ultimate-tensile-strength predictions were within 5% error, whereas only 62.1% of elongation predictions were within 10% error^[34]. This uneven performance is important for lifecycle modeling. Strength can often be captured by processing and heat-treatment variables, but elongation is more sensitive to hidden defects, surface condition, residual porosity, and source-study variability. HIP or heat treatment should therefore be modeled as a downstream transformation of the as-built state, not left as background experimental information. Process-window construction is another area where ML has become useful. In LPBF, density is often used as a first indicator of process quality, but density measurements can differ in cost, resolution, uncertainty, and spatial representativeness. Song et al. used multi-fidelity Gaussian-process modeling to combine 60 low-fidelity Archimedes measurements with 25 high-fidelity micrographic observations for constructing a process window for a thin-walled LPBF structure^[23]. Archimedes measurements provided lower-cost bulk-density coverage, whereas micrographic observations supplied more spatially resolved porosity information. The workflow reflects a practical measurement problem in powder processing: the most accessible data are not always sufficient to resolve local defects, while the most spatially informative labels are often too costly to collect at scale.

Powder reuse has recently become another application area where ML can support decision-making. Reuse can change powder state through oxidation, contamination, agglomeration, changes in particle-size distribution or morphology, and altered flow behavior^{[10, 11]}. In an experimental–ML study on reused AlSi10Mg powder in LPBF, laser power, deposition thickness, and reuse count were used to predict void nucleation, indentation modulus, and wear behavior^[17]. The study varied laser power at 280, 380, and 480 W, reuse cycles at 5, 7, and 9 cycles, and deposition thickness at 35, 60, and 85 μm; the reported optimum was 380 W, 35 μm, and 7 reuse cycles, with 1.94% void nucleation, a wear rate of 0.97 × 10^-4 mm³/Nm, and an indentation modulus of 115.15 GPa^[17]. The exact optimum should not be generalized beyond the tested material and machine conditions. The reusable lesson is not the specific parameter set, but the treatment of reuse count as an explicit process-history variable. A model that omits reuse history may assign porosity or mechanical-property changes to laser parameters even when powder aging or contamination contributes to the response.

Across these workflow stages, optimization and inverse design represent the decision-oriented use of ML. Instead of only predicting the consequence of a given condition, these approaches search for powder-production settings, process parameters, compositions, or post-processing routes that are likely to meet a target response^{[13, 15, 21, 39– 41]}. Bayesian optimization is particularly attractive when each experiment is expensive, as in gas atomization, process-window development, and mechanical-property qualification^{[13, 42, 43]}. Digital-twin-oriented frameworks extend this idea by using time-series models and uncertainty-aware optimization to recommend process adjustments during manufacturing^[21]. These outputs should be treated as recommendations for the next experimental step, not as final recipes. Their reliability depends on the surrogate model, the search space, the uncertainty estimate, and the lifecycle data used for training. Viewed along the workflow, these examples show that ML applications in powder-based manufacturing now cover a wider part of the powder-to-part chain. Powder-production optimization, recoating-anomaly detection, multimodal monitoring, property prediction, post-processing analysis, reuse assessment, and process-window construction represent different points along the same data chain. When powder history, process signatures, post-processing records, and final labels are connected, ML can support screening, prediction, and decision-making with a clearer validation boundary. When those links are missing, even a model with strong internal performance may remain difficult to interpret, reproduce, or transfer.

Additional representative cases are summarized in Table 1. The table extends the workflow-based discussion by comparing studies according to workflow stage, data and model type, scale and validation design, reported metric, and main limitation. This structure is intended to show not only where ML has been applied, but also how strongly each result is supported by data scale, label quality, and validation boundary.

3.1. Data Scarcity, Label Fidelity, and Lifecycle Incompleteness

Data scarcity remains a major barrier to reliable ML in powder-based manufacturing. The issue is not only the number of experiments. Available datasets are often sparse, uneven, weakly labeled, and split across different stages of the powder lifecycle. A dataset may contain process parameters without powder history, in-situ monitoring signals without post-build validation, or final mechanical properties without sufficient information about post-processing and specimen location. Under these conditions, a model may learn a local statistical association without capturing the physical route through which powder state, process evolution, and final properties are connected^{[12, 13, 15, 16]}.

The constraint is built into the experimental route. A single labeled data point may require powder preparation, powder characterization, spreading or compaction, melting or sintering, heat treatment, machining, microscopy, CT, or destructive mechanical testing. For high-value alloys, the cost is increased by expensive powder batches, limited machine access, and the difficulty of reproducing failed builds under the same conditions. Many ML studies therefore rely on narrow process windows, simplified geometries, small parameter sets, or data collected on one material and one machine^{[13, 32]}. Such datasets are useful for feasibility studies, but they rarely cover the variability expected in production.

The same limitation appears outside additive manufacturing. In conventional powder metallurgy, sintering outcomes depend on powder characteristics, alloy chemistry, green density, compaction pressure, sintering atmosphere, heating rate, holding time, and sintering temperature. Recent ML studies on sintered bronze and Cu-based powder metallurgy alloys used datasets with a few hundred samples, including 460 data points for bronze/Cu-based density prediction, 211 samples for Cu–Sn swelling or shrinkage classification, and 210 data points for Cu–Al sintered-density prediction^{[27– 29]}. These studies show that useful models can be built from curated experimental and literature-derived datasets. Their transferability, however, remains bounded by the alloy families, powder descriptors, green-density range, and thermal histories represented in the training data. Image-based monitoring shows another form of the data problem: a larger image dataset does not automatically remove label uncertainty. Scime and Beuth used post-recoating LPBF images to detect and classify powder-bed anomalies such as recoater streaking, debris, and part-related failures^[5]. Their database contained 2402 labeled image patches, and the workflow converted powder-bed images into handcrafted visual features and bag-of-visual-words representations for anomaly classification^[5]. Later image-based monitoring work increased the annotation scale to more than 45,000 powder-bed anomalies and reported high classification performance under controlled imaging conditions^[33]. This progression shows that larger labeled image datasets can improve training stability, but the evidence still depends on image resolution, illumination, powder reflectivity, recoater configuration, anomaly definition, and expert-label consistency. A model trained under one imaging setup may therefore require adaptation before being used with another machine, alloy system, powder lot, or recoating condition^{[15, 16, 20, 33]}.

Label scarcity is not limited to images. In-situ monitoring can generate large volumes of acoustic, optical, spectral, thermal, or photodiode data, but supervised learning requires these signals to be linked to trustworthy ground truth. A signal cluster or latent representation should not be interpreted as lack of fusion, keyholing, cracking, or contamination unless the signal is supported by independent evidence from CT, metallography, mechanical testing, or another physically meaningful label^{[20, 31, 32, 37]}. Rare events such as lack-of-fusion pores, keyhole defects, cracks, severe recoating streaks, contamination events, and abnormal powder-layer disturbances may be critical for qualification, but they occur much less frequently than nominal regions. A classifier can therefore show high overall accuracy while missing the events that matter most for safety or reliability. Accuracy should be reported together with class-wise recall, precision, confusion matrices, or defect-specific performance, especially when the positive class represents a rare but critical defect^{[5, 13, 20, 31, 32]}.

A related coverage problem appears in composition-based printability datasets. Roy et al. compiled data for balling and porosity prediction from alloy composition and process descriptors, with 267 data points for balling and 138 data points for porosity^[49]. Such datasets are useful for rapid screening across composition and process space, but their reliability depends on whether rare alloy families, defect modes, powder states, and machine conditions are represented rather than merely interpolated from nearby examples. Label fidelity also varies across measurement methods. Bulk density, visual inspection, or a limited set of tensile tests can provide accessible scalar labels, but they may not resolve local porosity, defect morphology, surface-connected flaws, or microstructural variation. Song et al. addressed this problem in LPBF process-window construction by combining broader-coverage Archimedes density measurements with more labor-intensive micrographic observations through multi-fidelity Gaussian-process modeling^[23]. The example is useful here because it separates label availability from label fidelity. Broader-coverage measurements help map the process space, while spatially resolved observations are needed where local porosity or defect morphology controls the final interpretation. Applicability domains should be treated as part of validation, not as a separate post-analysis. A model trained within a curated dataset can report low error while remaining valid only for a narrow range of compositions, particle sizes, compaction pressures, sintering conditions, or heat-treatment histories. PM sintering studies illustrate this point. Some studies include experimental validation under selected alloy and processing conditions, whereas others use multiple error metrics and leverage-based outlier analysis to identify data outside the model domain^{[27, 29]}. Validation therefore cannot be reduced to a single accuracy or error value. It must also specify where the input features, alloy systems, and processing conditions remain physically meaningful. Random train–test splitting is often too weak for this setting. Specimens from the same build, powder lot, geometry, imaging condition, or experimental campaign can appear in both training and test sets, making the model look more general than it is. Stronger tests include leave-one-build, leave-one-machine, leave-one-powder-lot, grouped experiment splits, or external-dataset validation^{[15, 16, 20]}. These validation designs are harder to satisfy, but they better reflect the way ML models fail in powder-based manufacturing: not by small random errors within one dataset, but by distribution shifts across powder lots, machines, sensors, geometries, and post-processing routes.

History dependence makes the input–output relationship non-unique. The same final density or strength may result from different combinations of powder state, thermal exposure, post-processing, and defect morphology. Conversely, the same nominal process parameters may produce different outcomes when the powder batch, reuse condition, recoating response, atmosphere, or machine state changes^{[10, 20, 21, 46, 51]}. Without lifecycle identifiers, apparent accuracy can appear high because the model has learned batch-specific, geometry-specific, or machine-specific correlations rather than a transferable process–structure–property relationship.

The data-scarcity problem therefore cannot be solved by increasing dataset size alone. Additional data are useful only when they add diversity, improve label fidelity, preserve provenance, and cover relevant powder and process states. Poorly aligned or weakly documented data can increase sample count without improving model reliability. This bottleneck motivates the strategies discussed in the following subsections. Transfer-based methods reuse information from related materials, machines, sensors, or simulations when the target domain has limited labels. Multi-fidelity methods combine lower-cost or broader-coverage measurements with fewer high-fidelity or spatially resolved observations. Physics-informed and hybrid methods constrain learning using prior knowledge from heat transfer, fluid flow, densification, thermodynamics, or process simulation. These strategies improve sample efficiency in different ways, but none removes the need for traceable lifecycle data.

3.2. Domain Shift and Transfer-Based Generalization

The limitations described above lead to a second problem: a model trained on one powder-processing domain rarely moves unchanged to another. Here, a domain refers to the material, powder lot, machine, sensor configuration, geometry, process window, post-processing route, and labeling method that define how the data were generated. Domain shift occurs when one or more of these conditions change. Across powder routes, this shift is common rather than exceptional. A model calibrated on one LPBF machine may not preserve its error level on another machine, even for the same alloy, because gas flow, beam delivery, recoating behavior, chamber geometry, and scan-control implementation are not identical^{[13, 15, 20, 42]}.

Random train–test splits can hide this problem. If samples from the same build campaign, powder batch, or machine appear in both training and test sets, the reported error may describe interpolation within one experimental context rather than generalization to a new context. Domain-aware validation is stricter. It asks whether the model still works when the powder lot, machine, alloy family, specimen geometry, sensor setup, or post-processing route changes. This distinction is central for industrial use because deployment almost always involves a target domain that is not identical to the training domain. Domain-aware validation is therefore a diagnostic step before transfer learning is attempted. It tests whether the model is still reliable after a change in powder lot, machine, alloy family, specimen geometry, sensor setup, or post-processing route, rather than only within a random split of the original dataset^{[13, 15, 42]}. Transfer learning offers one route through this problem. In this review, transfer learning refers to using information from a related source domain to improve modeling in a target domain where labeled data are scarce. The transferred information may be a pretrained representation, a source model, a calibrated simulation prior, or a source dataset that is adjusted using a small number of target-domain measurements. The method is attractive for powder-based manufacturing because target-domain labels are often expensive: tensile tests, CT inspection, metallography, creep tests, and high-temperature validation cannot be generated at the scale required by conventional data-hungry models. Cross-platform LPBF property prediction provides a clear example. Zheng et al. studied active transfer learning for ultimate tensile strength prediction across three LPBF platforms: 265 data points from an EOS M290, 36 from a Renishaw AM250, and 32 from a 3DSystems DMP350^[42]. The model used laser power, scan speed, and hatch distance as inputs, and treated cross-platform differences as prediction errors that could be learned from a small set of target-platform tensile tests. In one AM250 transfer case, the model reached a target RMSE level of approximately 35 MPa with fewer actively selected target samples than random transfer or from-scratch modeling^[42]. The gain is best interpreted as a reduction in target-machine labeling burden, not as proof of universal cross-platform generalization. Each added target label was a tensile-test result from the target platform, and the transferred model still depended on how well the source and target platforms shared the same process–property relationship. The same study also reported large transfer errors near regions associated with severe process defects^[42]. Transfer learning can therefore reduce the number of target-domain experiments when the source and target platforms remain physically comparable. Transfer learning cannot compensate for a source model when the target condition moves into a different regime, such as lack-of-fusion, keyhole instability, or another defect-dominated response.

A second transfer setting appears in computation-to-experiment alloy design. In nickel-based powder-metallurgy superalloy development, Li et al. combined high-throughput calculation, diffusion-multiple experiments, and transfer learning to connect computational microstructure information with sparse experimental data^[50]. Their framework transferred from a high-throughput calculation domain to high-throughput experimental data, and then used the calibrated microstructural predictions as part of downstream property modeling and alloy screening. The reported extrapolation test for topologically close-packed phase classification reached 90.48% accuracy and 95.06% recall, and the γ′ feature regression models reported extrapolation MAPE values of 2.21%, 4.28%, and 5.13%^[50]. The study also screened 10⁵ candidate compositions after calibration with sparse experimental data^[50]. In this case, transfer learning did not simply reuse a model; it used experimental data to correct a broader computational prior. Monitoring models provide another transfer setting. Image, acoustic, thermal, photodiode, or spectrogram-based representations may retain low-level signal features across related materials or machines, but the defect meaning of those features still depends on sensor configuration, process regime, powder condition, and post-build validation. A feature that separates process states in one dataset may not correspond to the same defect class after a change in powder absorptivity, melt-pool stability, recoater behavior, sensor field of view, or labeling procedure^{[20, 31, 32, 37]}.

These examples represent different forms of transfer. The LPBF case transfers across machines that produce the same nominal material, while the PM superalloy case transfers from computation-rich data to experiment-scarce alloy design. Monitoring transfer often lies between these cases because the learned representation may be portable, while the associated defect label may not be. Cross-platform LPBF transfer assumes that source and target machines share enough process physics for calibrated error correction to remain meaningful. Computation-to-experiment transfer assumes that the computational source domain contains useful trends even when it is biased relative to experimental observations. In each case, the target-domain calibration data define the boundary of trust. Negative transfer remains the main risk. It occurs when information from the source domain degrades target-domain prediction. In powder-based manufacturing, negative transfer can arise from changes in powder morphology, oxygen content, reuse history, recoater behavior, melt-pool regime, sintering route, or heat-treatment response. A model transferred across materials may preserve image features while losing defect meaning; a model transferred across machines may preserve parameter trends while shifting absolute property values; a model transferred from simulation may inherit systematic errors in thermodynamics, heat transfer, or densification kinetics. These failures are not always visible from global accuracy alone. A useful transfer study should therefore report more than a target-domain metric. It should specify the source domain, target domain, number of target calibration samples, selection strategy for those samples, validation split, and conditions where transfer fails. For powder-processing applications, applicability-domain analysis is especially useful because the costliest errors occur at the edge of the tested space: new powder lots, new machines, higher reuse cycles, extreme energy densities, unfamiliar geometries, or post-processing histories outside the training record^{[15, 16, 42, 50]}. Transfer learning is best viewed as a way to reduce target-domain labeling burden, not as a substitute for target-domain validation. It is most defensible when the source and target domains share a physically plausible relationship and when the remaining mismatch is measured rather than assumed away. When the difference between data sources is better described primarily as a fidelity hierarchy rather than as a source–target domain shift, multi-fidelity modeling may be the more appropriate framing because it treats lower-cost and higher-fidelity evidence as related but explicitly different evidence streams. That distinction motivates the next subsection^{[23, 42, 50]}.

3.3. Multi-Fidelity Learning for Data-Efficient Modeling

A fidelity hierarchy exists when several data sources describe a related response but differ in cost, resolution, reliability, or physical completeness. Unlike domain shift, which concerns transfer between different data-generating domains, multi-fidelity learning focuses on how lower-cost evidence and higher-fidelity evidence can be combined within a related modeling task. In powder-based manufacturing, this situation appears frequently: bulk density can be measured faster than local porosity, simplified simulations can cover a wider parameter space than experiments, and rapid screening tests can rank candidate conditions before high-cost validation is performed^{[23, 52, 53]}.

Fidelity is target-dependent. A data source should not be called high fidelity in an absolute sense; it is higher fidelity only relative to a specified target, measurement scale, and decision. In this review, fidelity is also used in a measurement-hierarchy sense, not only in a simulation-versus-experiment hierarchy. For example, Archimedes density may be adequate for evaluating bulk densification, but it becomes lower-fidelity information when the target is local pore morphology in a thin wall because it provides low-cost bulk-density data without resolving local defect morphology. Micrographic observation is treated as higher-fidelity information in that context because it provides more spatially resolved defect information, although it requires greater effort and cost^[23]. More generally, multi-fidelity learning can combine lower-cost simulations, reduced-order models, literature-derived data, rapid screening measurements, or lower-resolution experiments with smaller amounts of higher-fidelity experimental evidence^{[23, 52, 53]}. The LPBF process-window study by Song et al. gives a compact example. The study used Archimedes density as the low-fidelity source and micrographic observation as the high-fidelity source for thin-walled LPBF specimens^[23]. The dataset contained 60 Archimedes measurements and 25 micrographic observations for the thin-wall case^[23]. Leave-one-out cross-validation showed the effect of combining the two sources: the reported error was 7.88 for the low-fidelity model, 0.88 for the high-fidelity model, and 0.19 for the multi-fidelity model. The reported measurement cost was also lower: approximately USD 2180 for the mixed LF/HF workflow, compared with about USD 6800 if all measurements were collected at high fidelity^[23].

The technical value of the method lies in how the two sources are linked. In multi-fidelity Gaussian-process modeling, the lower-fidelity model supplies a broad trend across the process window, while the model uses the higher-fidelity data to learn the discrepancy between that trend and the higher-fidelity response. This structure is useful only when the fidelity levels are correlated but not identical. If the lower-fidelity source has no stable relationship with the high-fidelity target, additional low-fidelity data can make the model more confident without making the prediction more reliable^[23]. Analytical models, reduced-order thermal simulations, discrete element method simulations, CALPHAD calculations, and finite-element analyses can explore wider process or composition spaces than experiments. These models should not replace measurement; they are most useful when they provide trends that can be calibrated against higher-fidelity or application-relevant data^{[52, 53]}. A coarse thermal model, for example, may be useful for ranking scan conditions, but it cannot by itself validate local defect morphology or final tensile performance. In the same way, a powder-spreading simulation may identify trends in layer uniformity while still requiring experimental imaging, density measurement, or part-quality inspection before it can support process qualification.

The failure mode is label misalignment. Bulk density, local porosity, CT-detected flaw volume, micrographic area fraction, melt-pool features, and mechanical performance are related, but they are not interchangeable labels. A model may combine them successfully only if the spatial scale, measurement location, specimen identity, build history, and post-processing route are traceable. Without those links, multi-fidelity learning can mix responses from different physical levels of the workflow and produce a process window that looks precise but is difficult to interpret. Multi-fidelity learning also changes how experiments should be allocated. Instead of collecting every label at the highest available fidelity, the model can use broad low-fidelity coverage to locate regions where additional high-fidelity data are most valuable. This connects multi-fidelity modeling with active learning and Bayesian experimental design. The main purpose is to spend high-fidelity measurements where they reduce uncertainty in the response that matters for the decision. High-throughput computation and experiments follow the same logic when they are used carefully. Broad CALPHAD-based calculations, reduced-order simulations, or high-throughput screening experiments can cover large regions of composition or process space, while smaller experimental datasets provide correction and validation. The nickel-based PM superalloy example discussed in Section 3.2 illustrates a neighboring case: broad computational data supplied coverage, while diffusion-multiple experimental data provided calibration for microstructural prediction^[50]. The lesson for multi-fidelity modeling is similar: large imperfect datasets become more useful when their bias is measured against smaller, more reliable observations.

For powder-based manufacturing, multi-fidelity learning is most useful when three conditions are satisfied. First, the fidelity levels must refer to a common target or to targets with a clearly defined mapping. Second, the low-fidelity source must preserve a trend that is relevant to the high-fidelity response. Third, sample identity and process history must remain traceable across fidelity levels. When these conditions are missing, the model may gain data volume but lose physical meaning. Multi-fidelity methods address measurement cost and label scarcity; they do not guarantee physical consistency. If the dominant error comes from violating heat-transfer, melt-pool, densification, or thermodynamic constraints, the next step is not only to combine data sources but to constrain the learning problem itself. That point leads to physics-informed and hybrid modeling.

3.4. Physics-Informed and Hybrid Learning for Physical Consistency

Transfer learning and multi-fidelity modeling improve how limited data are reused and combined, but they do not guarantee physical consistency. A model may still predict a plausible value while violating known process behavior, conservation laws, thermal trends, or microstructure–property relationships. This risk is particularly relevant in powder-based manufacturing because several controlling variables are only partially observed. Powder-bed packing is heterogeneous, heat transfer is transient and geometry-dependent, melt-pool behavior depends on the local powder state, and post-processing can modify defects before final testing. A purely data-driven model may interpolate within a narrow dataset but become unreliable outside the measured process window^[13].

Physics-informed and hybrid learning address this problem by introducing prior physical knowledge into the modeling process. In this review, physics-informed and hybrid learning are used as broad umbrella terms to include PINNs and other physics-informed neural architectures^{[25, 44, 54– 56]}, as well as broader hybrid models that use physical descriptors, simulation priors, architecture constraints, or consistency checks^{[44, 45, 54– 56]}. In practical terms, physical knowledge may enter before training through descriptors, during training through constraints or architecture design, or after prediction through consistency checks. In all cases, prior knowledge narrows, guides, or checks the learned relationship instead of leaving the model to infer the full structure from data alone.

In powder-based manufacturing, the physical knowledge used in such models can take several forms. LPBF thermal models often rely on heat-conduction or thermal-diffusion equations, together with Gaussian, Goldak, or Rosenthal-type descriptions of a moving heat source^{[24, 25, 45]}. Melt-pool models may further involve conservation of mass, momentum, and energy when fluid flow, recoil pressure, or free-surface effects are considered^[25]. In powder metallurgy and post-processing, relevant priors may include Arrhenius-type diffusion relations, sintering or densification kinetics, grain-growth models, phase-transformation models, or precipitation-related models. For example, microstructure–property and precipitation-related priors are particularly relevant in powder-metallurgy superalloy design^[50]. These models do not need to be solved fully inside every ML framework, but they can guide feature design, constrain admissible predictions, or provide consistency checks for learned trends^{[44, 54– 56]}. Physics-informed Bayesian optimization can also incorporate simplified physical priors into the search strategy when experiments or high-fidelity evaluations are costly^[57]. This distinction separates physics-informed and hybrid learning from the multi-fidelity strategy discussed in Section 3.3. Multi-fidelity learning organizes evidence according to cost, resolution, and measurement fidelity. Physics-informed learning organizes the model according to physical constraints and mechanistic structure. The same simulation can support either strategy, but its role is different. In a multi-fidelity workflow, a simulation may act as a lower-cost data source. In a hybrid workflow, it may define descriptors, constrain admissible outputs, or supply a mechanistic prior that shapes the model response.

In powder-based additive manufacturing, many physics-informed studies focus on thermal history and melt-pool evolution because these quantities link process parameters to porosity, residual stress, solidification structure, and mechanical performance. Zhu et al. developed a PINN framework for metal additive manufacturing by embedding governing equations into models for temperature and melt-pool fluid dynamics^[25]. Tiwari et al. later used a PINN for LPBF Inconel 718 by incorporating heat-transfer constraints and a Goldak heat-source description, which represents the spatial distribution of laser-induced heat input, into the learning framework^[24]. Using a 347-sample multi-source dataset, their model reported mean absolute percentage errors of 3.8%, 4.7%, 3.1%, and 1.9% for melt-pool width, melt-pool depth, peak temperature, and relative density, respectively^[24]. Ghungrad et al. followed a different route: an architecture-driven physics-informed deep-learning model in which the network design was inspired by iterative transient-thermal calculations for LPBF temperature prediction^[45]. With 1000 points and an 80:20 split, the model reported a testing mean absolute percentage error of about 2.8% and an R² value of 0.936^[45]. These examples show that “physics-informed” does not refer to a single algorithmic form. Physical knowledge may enter through the loss function, the input representation, the model architecture, the simulation prior, or checks applied to predicted outputs. The relevant question is not whether a model is labeled physics-informed, but which physical assumption is imposed and whether that assumption remains valid for the target process regime.

Hybrid learning is broader than equation-constrained neural networks. In many powder-processing studies, physical knowledge enters through descriptors rather than differential equations. Examples include volumetric energy density, melt-pool geometry, cooling-rate estimates, packing density, powder flowability, oxygen content, reuse count, precipitate volume fraction, and diffusion-related features^{[6, 11, 50]}. Descriptor-driven ML studies in alloy design also show that thermodynamic and electronic descriptors can provide physically meaningful inputs for phase prediction, although such descriptors still require experimental validation before being used for process qualification^[58]. Such descriptors can improve interpretability because they connect input variables to powder, process, or microstructural mechanisms. A physically named descriptor, however, is not physical validation. Volumetric energy density combines laser power, scan speed, hatch spacing, and layer thickness into one scalar, but it can hide differences in beam profile, scan strategy, powder absorption, shielding-gas flow, and local geometry.

The expected advantage of physics-informed learning is better behavior under sparse data, but only along directions where the embedded physics remains valid. A heat-conduction constraint can improve temperature prediction in a conduction-dominated LPBF regime, where heat transport is mainly governed by thermal diffusion. A heat-conduction constraint may be insufficient when non-conduction regimes such as keyhole-mode melting, vaporization-driven spatter, denudation, or powder-bed disruption control the response. A sintering model may transfer across related powder compacts when densification mechanisms are similar. It may fail when liquid-phase sintering, swelling, abnormal grain growth, or phase transformation dominates. Physics narrows the admissible solution space; it does not identify the active mechanism by itself. Validation needs to test both numerical accuracy and physical plausibility.

Predicted temperature fields should follow plausible thermal gradients and cooling trends. Melt-pool dimensions should remain consistent with energy input and known instability regimes. Predicted density or porosity should be checked against metallography, CT, or other defect-sensitive measurements. Property predictions should be evaluated against the microstructure and post-processing route that produced them. If a model is claimed to be physically interpretable, its intermediate variables or learned trends should be compared with known process–structure–property behavior rather than treated as self-evident explanations. Interpretability is related to physical consistency, but it is not the same thing. Hybrid descriptors, Shapley additive explanations (SHAP) analysis, sensitivity analysis, and physically structured models can help identify which variables influence a prediction, but they do not prove causality. Variable-importance rankings may reflect oxygen content, reuse count, scan speed, or precipitate size as important because those variables are correlated with hidden process conditions in the dataset. Interpretation becomes more credible when powder lot, reuse history, machine condition, geometry, post-processing route, and measurement method are recorded well enough to reduce obvious confounding effects^{[6, 10, 11, 22]}. Physics-informed and hybrid learning are most defensible when the relevant mechanism is known well enough to constrain the model without excluding real behavior. The data must also preserve links among inputs, intermediate process states, and final labels, and validation must test both prediction accuracy and physical consistency. Under these conditions, physical priors can improve sample efficiency and reduce nonphysical predictions. Without them, adding physics terms or mechanistic descriptors may create an appearance of rigor without improving reliability.

The three strategies discussed in Section 3 address different parts of the sparse-data problem. Transfer learning relies on testable source–target similarity. Multi-fidelity modeling relies on a meaningful hierarchy between lower-cost and higher-fidelity evidence. Physics-informed learning relies on physical priors that remain valid for the target regime. For powder-based manufacturing, none of these strategies removes the need for lifecycle metadata. Physical constraints can guide learning, but they cannot compensate for missing provenance, weak labels, unmeasured process shifts, or an incorrect assumption about the governing mechanism.