SOLIS: Physics-Informed Learning of Interpretable Neural Surrogates for Nonlinear Systems

2026-04-16 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Expert, quick

Summary

SOLIS is a novel framework designed for identifying nonlinear system dynamics, balancing physical interpretability with model flexibility. It addresses limitations of classical methods, which use rigid parametric forms, and Neural ODEs, which are often black-box. Unlike typical Physics-Informed Neural Networks (PINNs) that assume known governing equations, SOLIS models unknown dynamics using a state-conditioned second-order surrogate model. This approach recasts identification as learning a Quasi-Linear Parameter-Varying (Quasi-LPV) representation, enabling the recovery of interpretable natural frequency, damping, and gain without requiring a global equation. SOLIS decouples trajectory reconstruction from parameter estimation and employs a cyclic curriculum and "Local Physics Hints" (windowed ridge-regression anchors) to stabilize training and prevent optimization collapse. Experiments demonstrate accurate parameter-manifold recovery and coherent physical rollouts even with sparse data, outperforming standard inverse methods in challenging regimes.

Key takeaway

For AI Scientists and Research Scientists developing models for complex nonlinear systems, SOLIS offers a robust method to achieve both high expressivity and physical interpretability. Your teams should consider integrating its Quasi-LPV representation and "Local Physics Hints" approach to overcome identifiability issues and improve training stability, especially when dealing with unknown or state-dependent dynamics from sparse datasets. This can lead to more reliable and explainable models for control-relevant applications.

Key insights

SOLIS identifies nonlinear system dynamics by learning a Quasi-LPV representation for interpretable physical parameters.

Principles

• Decouple trajectory reconstruction from parameter estimation.
• Use state-conditioned surrogates for unknown dynamics.
• Employ local physics hints to stabilize training.

Method

SOLIS models unknown dynamics via a state-conditioned second-order surrogate, learning a Quasi-LPV representation. It uses a cyclic curriculum and "Local Physics Hints" (windowed ridge-regression anchors) to stabilize training and mitigate optimization collapse.

In practice

• Recover natural frequency, damping, and gain.
• Identify systems from sparse data.
• Improve identifiability where inverse PINNs fail.

Topics

• SOLIS
• Nonlinear System Identification
• Physics-Informed Neural Networks
• Neural Surrogates
• Quasi-Linear Parameter-Varying

Best for: AI Scientist, Research Scientist, Robotics Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.