Variational Physics-Informed Ansatz for Reconstructing Hidden Interaction Networks from Steady States

TL;DR

The paper introduces VPIA, a novel variational method that reconstructs complex interaction networks from steady-state data without needing dynamic trajectories, handling noise and higher-order couplings.

Contribution

VPIA is a new physics-informed variational approach that infers general interaction operators directly from steady states, enabling scalable reconstruction of complex networks.

Findings

Accurately recovers directed, weighted, and multi-body interactions.

Effective under high noise conditions.

Works across diverse nonlinear systems.

Abstract

The interaction structure of a complex dynamical system governs its collective behavior, yet existing reconstruction methods struggle with nonlinear, heterogeneous, and higher-order couplings, especially when only steady states are observable. We propose a Variational Physics-Informed Ansatz (VPIA) that infers general interaction operators directly from heterogeneous steady-state data. VPIA embeds the steady-state constraints of the dynamics into a differentiable variational representation and reconstructs the underlying couplings by minimizing a physics-derived steady-state residual, without requiring temporal trajectories, derivative estimation, or supervision. Residual sampling combined with natural-gradient optimization enables scalable learning of large and higher-order networks. Across diverse nonlinear systems, VPIA accurately recovers directed, weighted, and multi-body structures under substantial noise, providing a unified and robust framework for physics-constrained inference of complex interaction networks in settings where only snapshot observations are available.