[2602.09980] Supervised Metric Regularization Through Alternating Optimization for Multi-Regime Physics-Informed Neural Networks

Computer Science > Machine Learning arXiv:2602.09980 (cs) [Submitted on 10 Feb 2026 (v1), last revised 5 Mar 2026 (this version, v2)] Title:Supervised Metric Regularization Through Alternating Optimization for Multi-Regime Physics-Informed Neural Networks Authors:Enzo Nicolas Spotorno, Josafat Ribeiro Leal, Antonio Augusto Frohlich View a PDF of the paper titled Supervised Metric Regularization Through Alternating Optimization for Multi-Regime Physics-Informed Neural Networks, by Enzo Nicolas Spotorno and Josafat Ribeiro Leal and Antonio Augusto Frohlich View PDF HTML (experimental) Abstract:Standard Physics-Informed Neural Networks (PINNs) often face challenges when modeling parameterized dynamical systems with sharp regime transitions, such as bifurcations. In these scenarios, the continuous mapping from parameters to solutions can result in spectral bias or "mode collapse", where the network averages distinct physical behaviors. We propose a Topology-Aware PINN (TAPINN) that aims to mitigate this challenge by structuring the latent space via Supervised Metric Regularization. Unlike standard parametric PINNs that map physical parameters directly to solutions, our method conditions the solver on a latent state optimized to reflect the metric-based separation between regimes, showing ~49% lower physics residual (0.082 vs. 0.160). We train this architecture using a phase-based Alternating Optimization (AO) schedule to manage gradient conflicts between the metric and physics...