# Learning Stochastic Multiscale Models

arXiv: https://arxiv.org/abs/2506.22655 · HTML: https://mlsanity.com/paper/2506.22655/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 57 references that are in the map.
- First posted on arXiv 27 Jun 2025.

## Builds on (most cited first, 9 of 9)

- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Probabilistic Weather Forecasting with Hierarchical Graph Neural Networks](https://mlsanity.com/paper/2406.04759/) (2024)
- [Amortized Reparametrization: Efficient and Scalable Variational Inference for Latent SDEs](https://mlsanity.com/paper/2312.10550/) (2023)
- [PyDMD: A Python package for robust dynamic mode decomposition](https://mlsanity.com/paper/2402.07463/) (2024)
- [Neural Ideal Large Eddy Simulation: Modeling Turbulence with Neural Stochastic Differential Equations](https://mlsanity.com/paper/2306.01174/) (2023)
- [Mori-Zwanzig latent space Koopman closure for nonlinear autoencoder](https://mlsanity.com/paper/2310.10745/) (2023)
- [ClimSim-Online: A Large Multi-scale Dataset and Framework for Hybrid ML-physics Climate Emulation](https://mlsanity.com/paper/2306.08754/) (2023)
- [Generalized Neural Closure Models with Interpretability](https://mlsanity.com/paper/2301.06198/) (2023)
- [Model Reduction for Large Scale Systems](https://mlsanity.com/paper/2105.01433/) (2021)

## Built on by (most cited first, 3 of 3)

- [SENDAI: A Hierarchical Sparse-measurement, EfficieNt Data AssImilation Framework](https://mlsanity.com/paper/2601.21664/) (2026)
- [Why Does the Future Branch? Identifiable Closure Tests for Stochastic Physical World Models](https://mlsanity.com/paper/2608.00591/) (2026)
- [Learning Continuous Neural Representation of Stochastic Hybrid Systems](https://mlsanity.com/paper/2609.38893/) (2026)

## Abstract (arXiv)

The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at the finest relevant scales, leading to a high-dimensional state space. In this work, we propose an approach to learn stochastic multiscale models in the form of stochastic differential equations directly from observational data. Drawing inspiration from physics-based multiscale modeling approaches, we resolve the macroscale state on a coarse mesh while introducing a microscale latent state to explicitly model unresolved dynamics. We learn the parameters of the multiscale model using a simulator-free amortized variational inference method with a Product of Experts likelihood that enforces scale separation. We present detailed numerical studies to demonstrate that our learned multiscale models achieve superior predictive accuracy compared to under-resolved direct numerical simulation and closure-type models at equivalent resolution, as well as reduced-order modeling approaches.