# Towards Fast Coarse-graining and Equation Discovery with Foundation Inference Models

arXiv: https://arxiv.org/abs/2510.12618 · HTML: https://mlsanity.com/paper/2510.12618/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 19 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## Builds on (most cited first, 13 of 13)

- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Efficient and Accurate Gradients for Neural SDEs](https://mlsanity.com/paper/2105.13493/) (2021)
- [ODEFormer: Symbolic Regression of Dynamical Systems with Transformers](https://mlsanity.com/paper/2310.05573/) (2023)
- [Learning interpretable continuous-time models of latent stochastic dynamical systems](https://mlsanity.com/paper/1902.04420/) (2019)
- [Foundation Inference Models for Markov Jump Processes](https://mlsanity.com/paper/2406.06419/) (2024)
- [Neural Markov Jump Processes](https://mlsanity.com/paper/2305.19744/) (2023)
- [Approximate Bayes learning of stochastic differential equations](https://mlsanity.com/paper/1702.05390/) (2017)
- [Variational Gaussian Process Diffusion Processes](https://mlsanity.com/paper/2306.02066/) (2023)
- [In-Context Learning of Temporal Point Processes with Foundation Inference Models](https://mlsanity.com/paper/2509.24762/) (2025)
- [The future is different: Large pre-trained language models fail in prediction tasks](https://mlsanity.com/paper/2211.00384/) (2022)
- [Neural Dynamic Focused Topic Model](https://mlsanity.com/paper/2301.10988/) (2023)
- [In-Context Learning of Stochastic Differential Equations with Foundation Inference Models](https://mlsanity.com/paper/2502.19049/) (2025)

## Built on by (most cited first, 1 of 1)

- [Foundation Inference Models for Ordinary Differential Equations](https://mlsanity.com/paper/2602.08733/) (2026)

## Abstract (arXiv)

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.