Decision-Aware Evaluation of Physics-Informed Surrogates
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Abstract (arXiv)
Physics-informed machine learning is often assessed by curve error, although engineering use depends on downstream decisions: ranking candidates, avoiding infeasible designs and limiting regret. We introduce pinn-gym, an open benchmark for material-conditioned lattice design that couples a transparent reduced-order crush-and-impact oracle with five printable polymer cards, dimensionless force-response targets and a protocol spanning curve fidelity, physical admissibility, top-k retrieval and mass regret. Across per-material, pooled and cross-material settings, low nRMSE is frequently insufficient to identify useful design selections. Physics-informed losses alter trade-offs rather than monotonically improving all metrics, and dimensionless conditioning improves comparability without making transfer symmetric. The benchmark is not a certified material model; within the released oracle, candidate generator and material cards, pinn-gym provides a reproducible testbed for evaluating PIML surrogates as decision systems rather than curve predictors alone.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 14 of its 26 references that are in the map. First posted on arXiv 5 Jun 2026.
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14 of 26 references.
References · 14
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
- 2021Characterizing possible failure modes in physics-informed neural networkscited by 643
- 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
- 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
- 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 413
- 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 170
- 2022Respecting causality is all you need for training physics-informed neural networkscited by 156
- 2023Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behaviorcited by 131
- 2023An Expert's Guide to Training Physics-informed Neural Networkscited by 126
- 2021Multi-Objective Loss Balancing for Physics-Informed Deep Learningcited by 87
- 2022Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Samplingcited by 73
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Citing papers per year: 2026: 1.
1 paper.