Characterization of PINN Sub-Network Loss-Landscape Features

Characterize which observed loss-landscape features—condition-number trajectories, negative spectral mass, and degrees of off-diagonal curvature coupling—are exhibited by each sub-network in the cascaded physics-informed neural network architecture.

Background

The paper evaluates a cascaded physics-informed neural network composed of separate vacancy-concentration, electrostatic-potential, carrier-concentration, and current sub-networks. Empirical analyses show that these sub-networks have distinct optimization behavior, including different condition-number trajectories, amounts of negative Hessian spectral mass, and degrees of off-diagonal curvature coupling.

Although the paper reports that these features differ across sub-networks, it does not identify which specific features characterize each sub-network. Establishing this mapping would inform the selection and development of sub-network-specific optimization strategies, including dynamic spectral and cubic-regularized methods.

References

We have not yet characterized which of these features each PINN sub-network falls into. This analysis is left for future work.

— Physics-Informed Neural Network Surrogate for Oxygen Vacancy Dynamics in epitaxial $\mathrm{SrTiO_3}$ on Si memristors via Dynamic Spectral Optimization  (2609.02966 - Podorozhny et al., 2 Sep 2026) in Section 6.1, “Pretraining and Loss Landscape Analysis” (subsection of Section 6, Evaluation, Validation Metrics, and Performance Analysis)