mlsanityData to 14 Oct 2026

Beyond Field Accuracy: Two-Axis Diagnosis of Inverse-PINN Parameter Error

arXiv 2608.15373 ↗First posted 15 Aug 2026cs.LG cs.NA math.NAcited by 0

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Abstract (arXiv)

Inverse physics-informed neural networks (PINNs) can reconstruct a field accurately while returning an incorrect physical parameter. We introduce a two-axis post-training diagnosis that separates finite-sample resolution under a specified observation-and-estimation protocol from the signed parameter preference encoded by the final learned field and residual metric. The first axis repeatedly fits noisy observations with a matched forward estimator. At known synthetic truth, the second freezes the field and residual view and computes a local score displacement toward a nearby residual-profile minimum. Endpoint consistency then tests whether joint training delivers that preference under the same final view. Across three synthetic one-dimensional, scalar-parameter PDEs, matched-forward mean absolute relative error ranges from 2.34 percent to 17.46 percent. The displacement tracks frozen-profile minima across locked seeds, architectures, and fresh-noise retraining (r from .945 to .982), and it tracks delivered signed log-error in 240 fresh-noise RBA runs (r = .994; 237/240 correct directions). A coupled two-parameter Darcy check validates the full matrix calculation. The axes are complementary diagnostic coordinates, not additive error components or a deployable oracle-free estimator. Together, they route follow-up work toward observations, residual evidence, or endpoint delivery.

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References · 20

  1. 2020Gradient Surgery for Multi-Task Learningcited by 1,256
  2. 2021Characterizing possible failure modes in physics-informed neural networkscited by 643
  3. 2019DeepXDE: A deep learning library for solving differential equationscited by 619
  4. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 335
  5. 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 170
  6. 2019Variational Physics-Informed Neural Networks For Solving Partial Differential Equationscited by 148
  7. 2023Residual-based attention in physics-informed neural networkscited by 72
  8. 2024ConFIG: Towards Conflict-free Training of Physics Informed Neural Networkscited by 46
  9. 2021Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networkscited by 27
  10. 2022Simulator-Based Inference with Waldo: Confidence Regions by Leveraging Prediction Algorithms and Posterior Estimators for Inverse Problemscited by 15
  11. 2025Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equationscited by 14
  12. 2019Learning Partial Differential Equations from Data Using Neural Networkscited by 8
8 more
  1. 2024BiLO: Bilevel Local Operator Learning for PDE Inverse Problemscited by 8
  2. 2015Application of one-step method to parameter estimation in ODE modelscited by 1
  3. 2019Minimization based formulations of inverse problems and their regularizationcited by 1
  4. 2024PINNfluence: Interpreting PINNs through Influence Functionscited by 1
  5. 2025Uncertainties in Physics-informed Inverse Problems: The Hidden Risk in Scientific AIcited by 1
  6. 2026Loss Landscape Diagnosis for Gradient-Based Gray-Scott System Inversion: Disentangling the Roles of PINN Componentscited by 1
  7. 2026Silent Failures in Physics-Informed Neural Networks: Parameter Poisoning and the Limits of Loss-Based Validationcited by 1
  8. 2026Target-Guided Selective Reweighting for Physics-Informed Neural Network Inverse Problems: A Transfer Learning Approachcited by 1

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