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

• URL: http://arxiv.org/abs/2512.13708v1
• Date: Sat, 06 Dec 2025 08:16:32 GMT
• Title: Variational Physics-Informed Ansatz for Reconstructing Hidden Interaction Networks from Steady States
• Abstract summary: We propose a Variational Physics-Informed Ansatz (VPIA) that infers general interaction operators directly from heterogeneous steady-state data.<n>VPIA embeds the steady-state constraints of the dynamics into a differentiable variational representation.<n>It reconstructs the underlying couplings by minimizing a physics-derived steady-state residual.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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