Problem
Research questions and friction points this paper is trying to address.
Inverse PINNs
Parameter identification error
Post-training diagnosis
Field accuracy
Residual metric
Beyond Field Accuracy: Two-Axis Diagnosis of Inverse-PINN Parameter Error
🤖 AI Summary
This study addresses the discrepancy between accurate field reconstruction and biased parameter estimation in inverse Physics-Informed Neural Networks (PINNs) by proposing a dual-axis post-training diagnostic framework. The method decouples errors into two complementary dimensions: finite sample resolution and parametric sign preference. By integrating matched forward estimation, frozen-field residual analysis, and endpoint consistency checks, the framework precisely localizes error sources. Experimental results demonstrate that the proposed approach achieves a correlation coefficient of 0.994 for parameter error prediction and exceeds 98% accuracy in directional judgment. These findings effectively elucidate the intrinsic mechanisms underlying the field-parameter performance inconsistency in inverse problems, providing precise, complementary diagnostic coordinates to guide subsequent model optimization.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Inverse-PINNs
Two-axis diagnosis
Parameter error
Residual profile
Post-training analysis
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