arxiv: 2604.14562 · v1 · submitted 2026-04-16 · 💻 cs.LG · physics.app-ph· physics.comp-ph

Recognition: unknown

Material-Agnostic Zero-Shot Thermal Inference for Metal Additive Manufacturing via a Parametric PINN Framework

Hyeonsu Lee , Jihoon Jeong

Authors on Pith no claims yet

Pith reviewed 2026-05-10 12:08 UTC · model grok-4.3

classification 💻 cs.LG physics.app-phphysics.comp-ph

keywords physics-informed neural networkszero-shot learningadditive manufacturingthermal modelingparametric PINNlaser powder bed fusionmaterial generalization

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The pith

A parametric PINN with decoupled material encoding and Rosenthal scaling achieves zero-shot thermal inference across arbitrary metals in additive manufacturing.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to prove that a single physics-informed neural network can produce accurate temperature fields for metal alloys never seen in training, without any new labeled data or model updates. This would matter because current thermal models in laser powder bed fusion require fresh datasets and retraining whenever the alloy changes, slowing down process development. The approach works by encoding material properties separately from space-time coordinates, fusing them with conditional modulation to respect how material parameters multiply into the heat equation, and then rescaling the network output using an analytical Rosenthal solution. Experiments across in-distribution and out-of-distribution alloys show the method cuts relative L2 error by up to 64.2 percent while matching baseline accuracy after only 4.4 percent of the usual training time. Ablation results indicate the same architectural pieces improve other PINN variants as well.

Core claim

The framework demonstrates that a decoupled parametric PINN architecture, which encodes material properties and spatiotemporal coordinates independently before fusing them through conditional modulation, combined with physics-guided output scaling derived from Rosenthal's analytical solution, produces physically consistent zero-shot predictions for out-of-distribution materials in bare-plate LPBF without labeled data, retraining, or pre-training, while also accelerating convergence relative to standard non-parametric PINNs.

What carries the argument

Decoupled parametric PINN architecture that encodes material properties separately from spatiotemporal coordinates and fuses them via conditional modulation, plus Rosenthal-based output scaling.

If this is right

A single trained model can be deployed for thermal modeling of any metal alloy in LPBF without collecting new data or performing retraining.
Training time drops dramatically, allowing the network to reach better accuracy than baselines after only a small fraction of the usual epochs.
The conditional modulation and Rosenthal scaling steps can be added to other PINN architectures to improve their material generalization.
Process design and optimization in metal AM become more flexible because material changes no longer require rebuilding the entire simulation pipeline.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same separation of material parameters from geometry could be tested on other manufacturing physics problems such as residual stress or microstructure evolution.
If the scaling term remains accurate, the framework might support real-time temperature field estimation when paired with sparse sensor readings during a build.
Extending the conditional modulation to include process parameters alongside material properties could further reduce the need for case-by-case calibration.

Load-bearing premise

That encoding material properties separately and modulating them conditionally will keep the network predictions physically consistent when the new alloy's thermal properties lie well outside the training distribution.

What would settle it

Run the trained model on a new alloy whose thermal conductivity and diffusivity fall far outside the training range, compute the relative L2 error against a high-fidelity reference simulation or experiment, and check whether the error stays below the non-parametric baseline; if it does not, the zero-shot claim is falsified.

Figures

Figures reproduced from arXiv: 2604.14562 by Hyeonsu Lee, Jihoon Jeong.

**Figure 2.** Figure 2: Architectural comparison between a conventional monolithic parametric PINN and the proposed decoupled [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Comparison of output scaling strategies for temperature prediction. (a) Manual output scaling [ [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Ground-truth temperature field snapshots at [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: Visualization of the sampled collocation points used in this study. Sampling points at time t (a) on the boundary (b) in the domain. Reproduced from [20]. Collocation Sampling Strategy To train PINN models using physicsbased residuals, collocation points sampled from the spatiotemporal domain are employed. Although the choice of sampling strategy is critical and constitutes a broad research topic in itse… view at source ↗

**Figure 6.** Figure 6: Comparison of training dynamics between the N-PINN [ [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

**Figure 7.** Figure 7: Thermal history comparison at a probe location along the laser scan path on the top surface for Ti–6Al–4V, [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗

**Figure 8.** Figure 8: Comparison of training dynamics between the P-PINN and the proposed framework. (a)–(c) Evolution of the [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗

**Figure 9.** Figure 9: Thermal history comparison at a probe location along the laser scan path on the top surface for Ti–6Al–4V, [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗

**Figure 10.** Figure 10: Qualitative comparison of temperature fields at [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗

**Figure 11.** Figure 11: Qualitative comparison of temperature fields at [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗

**Figure 12.** Figure 12: Qualitative comparison of temperature fields at [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗

**Figure 13.** Figure 13: Qualitative comparison of temperature fields at [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗

**Figure 14.** Figure 14: Sensitivity analysis of the proposed physics-guided output scaling strategy w.r.t. the scaling factor [PITH_FULL_IMAGE:figures/full_fig_p021_14.png] view at source ↗

**Figure 15.** Figure 15: Comparison of training dynamics between the Adam+L-BFGS and the proposed hybrid training strategy. [PITH_FULL_IMAGE:figures/full_fig_p022_15.png] view at source ↗

read the original abstract

Accurate thermal modeling in metal additive manufacturing (AM) is essential for understanding the process-structure-performance relationship. While prior studies have explored generalization across unseen process conditions, they often require extensive datasets, costly retraining, or pre-training. Generalization across different materials also remains relatively unexplored due to the challenges posed by distinct material-dependent thermal behaviors. This paper introduces a parametric physics-informed neural network (PINN) framework for zero-shot generalization across arbitrary materials without labeled data, retraining, or pre-training. The framework adopts a decoupled parametric PINN architecture that separately encodes material properties and spatiotemporal coordinates, fusing them through conditional modulation to better align with the multiplicative role of material parameters in the governing equation and boundary conditions. Physics-guided output scaling derived from Rosenthal's analytical solution and a hybrid optimization strategy are further incorporated to enhance physical consistency, training stability, and convergence. Experiments on bare plate laser powder bed fusion (LPBF) across diverse metal alloys, including both in-distribution and out-of-distribution cases, demonstrate effective zero-shot generalizability along with superior training efficiency. Specifically, the proposed framework achieved up to a 64.2% reduction in relative L2 error compared to the non-parametric baseline while surpassing its performance within only 4.4% of the baseline training epochs. Ablation studies confirm that the proposed framework's components are broadly applicable to other PINN-based approaches. Overall, the proposed framework provides an efficient and scalable material-agnostic solution for zero-shot thermal modeling, contributing to more flexible and practical deployment in metal AM.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper's decoupled parametric PINN with material encoding, conditional modulation, and Rosenthal scaling delivers zero-shot thermal predictions for new alloys in LPBF with reported error cuts and faster training, but OOD physical consistency hinges on unverified extrapolation.

read the letter

The main takeaway is that this work gives a way to do thermal modeling for new metal alloys in additive manufacturing without collecting data or retraining the model each time. They use a parametric PINN with separate encoding for material properties and coordinates, conditional modulation to match how properties multiply in the equations, plus scaling based on Rosenthal's analytical solution. The hybrid optimization helps convergence too. This setup targets the practical pain of handling arbitrary materials in metal AM simulation. The paper does a good job demonstrating this on bare plate LPBF experiments across several alloys. It reports clear gains: up to 64% less error than the baseline non-parametric PINN and faster convergence, hitting better results in just 4.4% of the epochs. The ablations apparently show the pieces work across other PINN setups too. That's practical for AM where new alloys come up often and data collection is expensive. Where it could be stronger is on the zero-shot physical consistency for out-of-distribution materials. The framework relies on the network learning a map that stays accurate far from the training property values, but neural networks often struggle with that kind of extrapolation. Rosenthal scaling assumes constant thermal properties and a semi-infinite domain, which is an approximation that may not capture phase changes or real part geometries in LPBF. If the out-of-distribution tests don't include materials with properties quite distant or show rising PDE residuals, the performance numbers might overstate the robustness. The abstract presents positive results, so the evidence is there for in-distribution and moderate OOD, but the central claim would benefit from more explicit checks on residual norms for extreme cases. This paper is for people building simulation tools for metal AM who want to avoid material-specific retraining. It would interest readers working on physics-informed models for manufacturing processes. I think it deserves a serious referee. The architecture is thoughtful, the results are quantified, and the problem it targets is real. A review could push for those extra consistency diagnostics but the work is worth the time.

Referee Report

3 major / 3 minor

Summary. The paper introduces a parametric PINN framework for zero-shot thermal field prediction in laser powder bed fusion across arbitrary metal alloys without retraining or target-material data. It decouples material-property encoding from spatiotemporal coordinates, fuses them via conditional modulation to respect the multiplicative structure of the heat equation, applies Rosenthal-derived output scaling, and uses a hybrid optimizer. Experiments on bare-plate LPBF report up to 64.2% relative L2-error reduction versus a non-parametric baseline and convergence within 4.4% of baseline epochs on both in-distribution and out-of-distribution alloys; ablations indicate the components transfer to other PINN architectures.

Significance. If the reported zero-shot generalization and physical consistency hold for OOD materials whose properties lie well outside the training support, the work would meaningfully advance material-agnostic modeling in additive manufacturing by removing the need for per-alloy data collection and retraining. The demonstrated training-speed gains and ablation results are practically useful. However, the significance is tempered by the reliance on Rosenthal scaling (constant properties, semi-infinite domain) whose mismatch with LPBF realities (phase change, finite geometry, temperature-dependent properties) could undermine extrapolation claims.

major comments (3)

The central zero-shot claim rests on the assertion that the learned parametric map yields low PDE residuals for OOD alloys without any optimization or labeled data. No quantitative residual norms (heat-equation, boundary, or initial-condition) are reported for the farthest OOD cases; only L2 field errors versus (presumably simulated) ground truth are shown. If residuals rise sharply outside the training property range, the error reductions cannot be attributed to physically consistent inference.
Rosenthal scaling is applied as a post-hoc multiplier derived under constant-property, semi-infinite assumptions. The manuscript does not quantify how this scaling interacts with the learned network when conductivity, diffusivity, or specific heat deviate substantially from training values, nor does it test sensitivity to the semi-infinite idealization on finite-plate geometries used in the experiments.
The data-split and OOD protocol details are insufficient to verify that the reported 64.2% error reduction and 4.4% epoch comparison are not influenced by post-hoc selection of training alloys or test cases. Explicit leave-one-alloy-out statistics and the exact range of material parameters in the training distribution versus test distribution are needed.

minor comments (3)

Notation for the conditional modulation operator and the precise form of the physics-guided scaling factor should be stated explicitly in the methods section rather than left to the supplementary material.
Figure captions for the temperature-field visualizations should include the specific alloy, laser parameters, and whether the field is a network prediction or reference solution.
The ablation study table would benefit from reporting both mean and standard deviation across multiple random seeds to establish statistical significance of the component contributions.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback on our manuscript. The comments highlight important aspects of physical consistency, methodological transparency, and experimental rigor that we will address in the revision. Below we respond point-by-point to each major comment.

read point-by-point responses

Referee: The central zero-shot claim rests on the assertion that the learned parametric map yields low PDE residuals for OOD alloys without any optimization or labeled data. No quantitative residual norms (heat-equation, boundary, or initial-condition) are reported for the farthest OOD cases; only L2 field errors versus (presumably simulated) ground truth are shown. If residuals rise sharply outside the training property range, the error reductions cannot be attributed to physically consistent inference.

Authors: We agree that reporting PDE residuals would provide direct evidence of physical consistency for the zero-shot predictions. The L2 errors are measured against high-fidelity finite-element simulations that satisfy the governing equations, but this does not substitute for explicit residual evaluation on the network outputs. In the revised manuscript we will add quantitative residual norms (mean squared residuals of the heat equation, boundary conditions, and initial conditions) evaluated over the domain for the farthest OOD alloys. These will be presented in a supplementary table to confirm that residuals remain controlled outside the training support. revision: yes
Referee: Rosenthal scaling is applied as a post-hoc multiplier derived under constant-property, semi-infinite assumptions. The manuscript does not quantify how this scaling interacts with the learned network when conductivity, diffusivity, or specific heat deviate substantially from training values, nor does it test sensitivity to the semi-infinite idealization on finite-plate geometries used in the experiments.

Authors: The scaling is derived from Rosenthal's solution to normalize the output temperature scale and improve training stability across material parameters; the network itself learns the parametric modulation of the solution. We acknowledge that the interaction between this fixed scaling and large property deviations, as well as the semi-infinite assumption on finite plates, merits explicit quantification. In the revision we will add a dedicated analysis section that (i) compares network predictions with and without the scaling for OOD alloys and (ii) discusses the limitations of the semi-infinite idealization relative to the bare-plate geometry and time scales used in the experiments. Full sensitivity sweeps over extreme property deviations would require additional high-fidelity simulations beyond the current scope, but the added analysis will clarify the practical range of validity. revision: partial
Referee: The data-split and OOD protocol details are insufficient to verify that the reported 64.2% error reduction and 4.4% epoch comparison are not influenced by post-hoc selection of training alloys or test cases. Explicit leave-one-alloy-out statistics and the exact range of material parameters in the training distribution versus test distribution are needed.

Authors: The original manuscript describes the set of alloys and the in-distribution versus out-of-distribution split, but we accept that more granular reporting is required for reproducibility. In the revised version we will expand the experimental section to include (i) explicit leave-one-alloy-out cross-validation results with per-alloy relative L2 errors, (ii) the precise numerical ranges of thermal conductivity, diffusivity, and specific heat used for training versus testing, and (iii) confirmation that the OOD alloys lie outside the convex hull of the training parameter distribution. This will eliminate any ambiguity regarding post-hoc selection. revision: yes

Circularity Check

0 steps flagged

No significant circularity; framework uses external Rosenthal scaling and standard PINN components with experimental validation

full rationale

The paper's central framework employs a decoupled parametric PINN with conditional modulation to encode material properties separately from spatiotemporal inputs, plus output scaling drawn from Rosenthal's external analytical solution and a hybrid optimizer. Performance metrics (L2 error reductions, epoch efficiency) are reported from direct experimental comparisons against non-parametric baselines on both in-distribution and out-of-distribution alloys. No quoted equations or steps reduce the zero-shot generalization claim to a fitted parameter by construction, a self-citation chain, or an ansatz smuggled from prior author work. The derivation remains self-contained against external benchmarks and standard physics, consistent with the reader's assessment of score 2.0.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard heat equation and boundary conditions for LPBF plus the validity of Rosenthal's analytical solution as an external scaling reference; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)

domain assumption The governing thermal equations and boundary conditions for laser powder bed fusion remain valid across the tested metal alloys.
Invoked implicitly when claiming the physics-guided scaling and zero-shot generalization will hold for arbitrary materials.
domain assumption Rosenthal's analytical solution provides a suitable scaling reference that improves physical consistency for the neural network output.
Used to derive the physics-guided output scaling component.

pith-pipeline@v0.9.0 · 5585 in / 1368 out tokens · 34679 ms · 2026-05-10T12:08:49.808325+00:00 · methodology

discussion (0)

Reference graph

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