# M2PDE: Compositional Generative Multiphysics and Multi-component PDE Simulation

arXiv: https://arxiv.org/abs/2412.04134 · HTML: https://mlsanity.com/paper/2412.04134/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2024.

## Built on by (most cited first, 5 of 5)

- [Compositional Generation for Long-Horizon Coupled PDEs](https://mlsanity.com/paper/2510.20141/) (2025)
- [PCGD: Physics-Guided Conditional Graph Diffusion for TCAD Device Simulation](https://mlsanity.com/paper/2606.29272/) (2026)
- [Geometry-aware Latent Autoregressive Generative Model for PDEs in Complex Domains](https://mlsanity.com/paper/2609.00297/) (2026)
- [Learnable composition for neural operators](https://mlsanity.com/paper/2609.03069/) (2026)
- [AutoPDEBench: Benchmarking LLM Auto-Research for Neural PDE Solver Design](https://mlsanity.com/paper/2609.32245/) (2026)

## Abstract (arXiv)

Multiphysics simulation, which models the interactions between multiple physical processes, and multi-component simulation of complex structures are critical in fields like nuclear and aerospace engineering. Previous studies use numerical solvers or ML-based surrogate models for these simulations. However, multiphysics simulations typically require integrating multiple specialized solvers-each for a specific physical process-into a coupled program, which introduces significant development challenges. Furthermore, existing numerical algorithms struggle with highly complex large-scale structures in multi-component simulations. Here we propose compositional Multiphysics and Multi-component PDE Simulation with Diffusion models (M2PDE) to overcome these challenges. During diffusion-based training, M2PDE learns energy functions modeling the conditional probability of one physical process/component conditioned on other processes/components. In inference, M2PDE generates coupled multiphysics and multi-component solutions by sampling from the joint probability distribution. We evaluate M2PDE on two multiphysics tasks-reaction-diffusion and nuclear thermal coupling-where it achieves more accurate predictions than surrogate models in challenging scenarios. We then apply it to a multi-component prismatic fuel element problem, demonstrating that M2PDE scales from single-component training to a 64-component structure and outperforms existing domain-decomposition and graph-based approaches. The code is available at https://github.com/AI4Science-WestlakeU/M2PDE.