Supervised Metric Regularization Through Alternating Optimization for Multi-Regime Physics-Informed Neural Networks
View original at arxiv.org{ "id": "2602.09980v1", "url": "http://arxiv.org/abs/2602.09980v1", "title": "Supervised Metric Regularization Through Alternating Optimization for Multi-Regime Physics-Informed Neural Networks", "summary": "Standard Physics-Informed Neural Networks (PINNs) often face challenges when modeling parameterized dynamical sy…
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TAPINN uses 5x fewer parameters than hypernetwork-based alternative while achieving better physics compliance
80% confidenceLinear probe on latent space achieves prognostics MSE of 3.5×10^-4 for regressing forcing parameter F0, confirming highly structured representation
80% confidenceHyperPINN suffers from memorization pathology, achieving lowest data MSE but high physics residual, overfitting trajectory points without satisfying governing ODE
80% confidenceTAPINN shows approximately 49% lower physics residual compared to baseline (0.082 vs. 0.160)
80% confidenceStandard MLPs struggle to approximate discontinuous or non-smooth parameter dependence due to spectral bias and singular Jacobians at bifurcation points
80% confidenceJoint training without alternating optimization yields significantly higher physics residual (~0.158), performing nearly identically to standard baseline, confirming alternating optimization is critical
80% confidenceMulti-Output baseline with Sobolev training exhibited gradient norms 2.14x higher on average with variance 2.18x larger, suggesting unstructured latent space exacerbates optimization pathologies
80% confidenceStandard PINNs often face challenges when modeling parameterized dynamical systems with sharp regime transitions, such as bifurcations
80% confidenceTAPINN achieves stable convergence with 2.18x lower gradient variance than a multi-output Sobolev Error baseline
80% confidence