# Differentiable Physics-Neural Models enable Learning of Non-Markovian Closures for Accelerated Coarse-Grained Physics Simulations

arXiv: https://arxiv.org/abs/2511.21369 · HTML: https://mlsanity.com/paper/2511.21369/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 26 Nov 2025.

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

- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Physics-based Deep Learning](https://mlsanity.com/paper/2109.05237/) (2021)
- [LEADS: Learning Dynamical Systems that Generalize Across Environments](https://mlsanity.com/paper/2106.04546/) (2021)
- [On the Benefits of Memory for Modeling Time-Dependent PDEs](https://mlsanity.com/paper/2409.02313/) (2024)
- [Data-driven Discovery of Closure Models](https://mlsanity.com/paper/1803.09318/) (2018)
- [Predicting Effective Diffusivity of Porous Media from Images by Deep Learning](https://mlsanity.com/paper/1912.05532/) (2019)
- [Predicting the temporal dynamics of turbulent channels through deep learning](https://mlsanity.com/paper/2203.00974/) (2022)
- [Generalized Neural Closure Models with Interpretability](https://mlsanity.com/paper/2301.06198/) (2023)

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

- [Mamba-Assisted Non-Markovian Closure for Reduced-Order Modeling](https://mlsanity.com/paper/2606.05371/) (2026)

## Abstract (arXiv)

Numerical simulations provide key insights into many physical, real-world problems. However, while these simulations are solved on a full 3D domain, most analysis only require a reduced set of metrics (e.g. plane-level concentrations). This work presents a hybrid physics-neural model that predicts scalar transport in a complex domain orders of magnitude faster than the 3D simulation (from hours to less than 1 min). This end-to-end differentiable framework jointly learns the physical model parameterization (i.e. orthotropic diffusivity) and a non-Markovian neural closure model to capture unresolved, 'coarse-grained' effects, thereby enabling stable, long time horizon rollouts. This proposed model is data-efficient (learning with 26 training data), and can be flexibly extended to an out-of-distribution scenario (with a moving source), achieving a Spearman correlation coefficient of 0.96 at the final simulation time. Overall results show that this differentiable physics-neural framework enables fast, accurate, and generalizable coarse-grained surrogates for physical phenomena.