Unveiling Multi-regime Patterns in SciML: Distinct Failure Modes and Regime-specific Optimization

2026-05-27

AI Summary

This work addresses the heterogeneous training behaviors and failure modes of scientific machine learning (SciML) models across hyperparameter settings, which stem from a lack of unified mechanistic understanding. To bridge this gap, the authors propose a mechanism-aware diagnostic framework that integrates performance metrics, training dynamics, and geometric characteristics of the loss landscape to systematically uncover three prevalent optimization mechanisms in SciML. The framework reveals that optimizer efficacy is highly mechanism-dependent and enables the identification of fine-grained failure modes often invisible to conventional loss landscape analyses. Extensive experiments on prominent SciML architectures—including physics-informed neural networks, neural operators, and neural ordinary differential equations—demonstrate the universality of this tripartite mechanistic structure, offering mechanism-guided design principles for robust SciML optimization.

Abstract

Neural networks trained under different hyperparameter settings can fall into distinct training "regimes," with consistent behavior within regimes and qualitative differences across regimes. In this paper, we study such multi-regime behavior in scientific machine learning (SciML) models through a regime-aware diagnostic framework that jointly analyzes performance, training dynamics, and loss-landscape geometry. We identify three key findings: (i) a consistent three-regime structure emerges across many standard SciML models, different constraint enforcements, and various optimizer designs; (ii) optimization effectiveness is regime-specific, with no single method performing well across all regimes; and (iii) SciML models can exhibit fine-grained failure modes that can challenge conventional interpretations of standard loss-landscape metrics. Our results provide an approach to establish a unified, task-oblivious perspective on failure modes in SciML and to inform regime-aware guidance for improving robustness. We validate these findings across widely-used SciML models, including physics-informed neural networks, neural operators, and neural ordinary differential equations, on benchmarks spanning representative ordinary and partial differential equations.

Problem

• scientific machine learning
• training regimes
• failure modes
• loss landscape
• optimization

Innovation

• multi-regime behavior
• regime-aware optimization
• failure modes
• loss-landscape geometry
• scientific machine learning