Neural network framework analyzes system stability and sensitivity from observational data

There's a new computational method that helps identify stability characteristics and how systems respond to forces using only observational data, without needing any predefined equations. Basically, it trains a neural network to mimic how a system behaves and then uses automatic differentiation to create the Jacobian matrix. This lets researchers calculate eigenmodes and resolvent modes directly from the data. Unlike traditional stability analyses, which depend on known equations and linearization, this new approach can handle nonlinear or poorly defined systems. It has been successfully applied to chaotic models and complex fluid flows, uncovering important instability modes and input-output relationships. This advancement is a big step in understanding how complex systems react to disturbances in various scientific and engineering domains.