FLARE Discovers Hidden Dynamics in Forced Physical Systems

Understanding complex physical systems often requires identifying their underlying governing equations, which can be obscured within high-dimensional measurement data. This challenge is particularly acute for "forced systems," where responses are influenced by both intrinsic dynamics and time-varying external inputs. Researchers have introduced FLARE (Forced Latent Autoencoder for Response Equations), a novel framework designed to uncover these hidden dynamics. FLARE operates by learning compact, interpretable response coordinates, identifying sparse latent dynamics that depend on inputs, and then decoding these learned dynamics back into full system responses. A key innovation is its ability to estimate latent dimension directly from data and to decouple state estimation from external forcing. This separation allows FLARE to initialize forecasts from past responses and drive them with future inputs not seen during training. The system has been validated across various known dynamical systems, application-scale forced responses, and visual observations. FLARE successfully recovers compact forced dynamics and delivers accurate long-horizon predictions of high-dimensional responses, even with novel inputs, providing a pathway for more interpretable modeling and prediction in complex forced dynamical systems.