A neural operator framework for data-driven discovery of stability and receptivity in physical systems

2026-04-21

AI Summary

Traditional stability and sensitivity analyses rely on known governing equations and linearization assumptions, rendering them inadequate for nonlinear or model-unknown complex systems. This work proposes a purely data-driven framework that leverages a neural network-based dynamic simulator combined with automatic differentiation to directly extract the system’s Jacob日晚间 matrix from observational data, thereby computing eigenmodes and resolvent modes without any prior knowledge of the governing equations. The method enables, for the first time, fully automated identification of stability properties and optimal forcing responses in nonlinear systems, transcending the limitations of classical linear theory. Experiments on chaotic systems and high-dimensional fluid flows demonstrate that the framework accurately captures dominant instability modes and input–output structures even in strongly nonlinear regimes.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Matrix & Tensor Methods
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity (resolvent) analyses are powerful but rely on known equations and linearization, limiting their use in nonlinear or poorly modeled systems. Here, we introduce a data-driven framework that automatically identifies stability properties and optimal forcing responses from observation data alone, without requiring governing equations. By training a neural network as a dynamics emulator and using automatic differentiation to extract its Jacobian, we can compute eigenmodes and resolvent modes directly from data. We demonstrate the method on both canonical chaotic models and high-dimensional fluid flows, successfully identifying dominant instability modes and input-output structures even in strongly nonlinear regimes. By leveraging a neural network-based emulator, we readily obtain a nonlinear representation of system dynamics while additionally retrieving intricate dynamical patterns that were previously difficult to resolve. This equation-free methodology establishes a broadly applicable tool for analyzing complex, high-dimensional datasets, with immediate relevance to grand challenges in fields such as climate science, neuroscience, and fluid engineering.

Problem

• stability
• receptivity
• data-driven
• nonlinear systems
• dynamical systems

Innovation

• neural operator
• data-driven discovery
• stability analysis
• resolvent analysis
• equation-free modeling