Identifiability and experimental design for inverse physics-informed engineering models

Abstract

An inverse physics-informed neural network can minimize its objective accurately while returning nonunique or weakly  constrained material and operating parameters. This review explains why optimization success must be separated from parameter identifiability. Exact examples from heat conduction, pressure-driven flow, and axial deformation show how observations can determine a parameter combination without determining its individual components. Local sensitivity matrices, dimensionless scaling, nuisance parameters, and profile objectives are then used to organize practical diagnostics. Published flow and viscoplastic PINN studies provide context for representation and constitutive modeling, while inverse-problem analysis supplies qualified stability results. A proposed experimental-design workflow links sensor placement and loading choices to the engineering parameter of interest.