Parameter identifiability problem in physics-based neural networks

Summary

This review argues that Physics-Informed Neural Networks (PINNs) can produce non-unique material or operational parameters even when their loss function is reduced to near zero. The article demonstrates, using closed-form examples such as heat conduction, pressure-driven flow, and axial deformation, that data may determine a combination of parameters rather than a single one. It then organizes practical diagnostic tools, including sensitivity matrices, dimensionless scaling, nuisance parameters, and profile-based functions. It also outlines an experimental design workflow that links sensor placement to the target parameter.

Why it matters

PINNs are increasingly used to infer structural or process parameters from sparse field data. However, low training loss is often mistakenly equated with a well-posed inverse problem. By distinguishing optimization success from identifiability, the article provides engineers with a concrete checklist. This checklist helps diagnose when a seemingly 'converged' PINN is actually underdetermined. The proposed sensor placement and loading workflow can reduce the number of costly re-experiments in structural and fluid mechanics applications.

Highlights

• Optimization convergence does not imply parameter identifiability. Exact 1D examples show that data determine parameter combinations, not individual parameters.
• Local sensitivity matrices, dimensionless scaling, and profile-based functions are presented as a structured set of diagnostic tools.
• The proposed experimental design workflow explicitly links sensor placement and loading choices to the target engineering parameter.

Critical take

This single-author review, published on a preprint server without institutional affiliation, largely consists of a reorganization of known inverse problem and scaling arguments. It offers no new empirical evidence. The 'exact examples' are analytical toy cases. Furthermore, the experimental design workflow is provided only as a summary outline, and its practical utility remains untested.