Towards Fast Coarse-graining and Equation Discovery with Foundation Inference Models
This work addresses the challenge of fast and reusable coarse-graining pipelines for dynamical systems analysis, but it appears incremental as it builds on existing FIMs with a proof-of-concept application.
The paper tackled the problem of identifying latent dynamics in high-dimensional recordings by decoupling coarse-grained variable discovery and equation fitting using Foundation Inference Models (FIMs), resulting in a stable representation learning method demonstrated on a stochastic double-well system.
High-dimensional recordings of dynamical processes are often characterized by a much smaller set of effective variables, evolving on low-dimensional manifolds. Identifying these latent dynamics requires solving two intertwined problems: discovering appropriate coarse-grained variables and simultaneously fitting the governing equations. Most machine learning approaches tackle these tasks jointly by training autoencoders together with models that enforce dynamical consistency. We propose to decouple the two problems by leveraging the recently introduced Foundation Inference Models (FIMs). FIMs are pretrained models that estimate the infinitesimal generators of dynamical systems (e.g., the drift and diffusion of a stochastic differential equation) in zero-shot mode. By amortizing the inference of the dynamics through a FIM with frozen weights, and training only the encoder-decoder map, we define a simple, simulation-consistent loss that stabilizes representation learning. A proof of concept on a stochastic double-well system with semicircle diffusion, embedded into synthetic video data, illustrates the potential of this approach for fast and reusable coarse-graining pipelines.