# Neural Modular Physics for Elastic Simulation

arXiv: https://arxiv.org/abs/2512.15083 · HTML: https://mlsanity.com/paper/2512.15083/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 48 references that are in the map.
- First posted on arXiv 17 Dec 2025.

## Builds on (most cited first, 29 of 29)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Neural Module Networks](https://mlsanity.com/paper/1511.02799/) (2015)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [An Expert's Guide to Training Physics-informed Neural Networks](https://mlsanity.com/paper/2308.08468/) (2023)
- [ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics](https://mlsanity.com/paper/1810.01054/) (2018)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling](https://mlsanity.com/paper/2207.02338/) (2022)
- [DiffCloth: Differentiable Cloth Simulation with Dry Frictional Contact](https://mlsanity.com/paper/2106.05306/) (2021)
- [SPNets: Differentiable Fluid Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1806.06094/) (2018)
- [Modular Networks: Learning to Decompose Neural Computation](https://mlsanity.com/paper/1811.05249/) (2018)
- [DiffPD: Differentiable Projective Dynamics](https://mlsanity.com/paper/2101.05917/) (2021)
- [Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics](https://mlsanity.com/paper/2304.14369/) (2023)
- [An End-to-End Differentiable Framework for Contact-Aware Robot Design](https://mlsanity.com/paper/2107.07501/) (2021)
- [DiffAvatar: Simulation-Ready Garment Optimization with Differentiable Simulation](https://mlsanity.com/paper/2311.12194/) (2023)
- [Equivariant Graph Neural Operator for Modeling 3D Dynamics](https://mlsanity.com/paper/2401.11037/) (2024)
- [Is a Modular Architecture Enough?](https://mlsanity.com/paper/2206.02713/) (2022)
- [RoPINN: Region Optimized Physics-Informed Neural Networks](https://mlsanity.com/paper/2405.14369/) (2024)
- [On The Specialization of Neural Modules](https://mlsanity.com/paper/2409.14981/) (2024)
- [Quaffure: Real-Time Quasi-Static Neural Hair Simulation](https://mlsanity.com/paper/2412.10061/) (2024)
- [PhysGraph: Physics-Based Integration Using Graph Neural Networks](https://mlsanity.com/paper/2301.11841/) (2023)

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

- [GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training](https://mlsanity.com/paper/2602.20399/) (2026)

## Abstract (arXiv)

Learning-based methods have made significant progress in physics simulation, typically approximating dynamics with a monolithic end-to-end optimized neural network. Although these models offer an effective way to simulation, they may lose essential features compared to traditional numerical simulators, such as physical interpretability and reliability. Drawing inspiration from classical simulators that operate in a modular fashion, this paper presents Neural Modular Physics (NMP) for elastic simulation, which combines the approximation capacity of neural networks with the physical reliability of traditional simulators. Beyond the previous monolithic learning paradigm, NMP enables direct supervision of intermediate quantities and physical constraints by decomposing elastic dynamics into physically meaningful neural modules connected through intermediate physical quantities. With a specialized architecture and training strategy, our method transforms the numerical computation flow into a modular neural simulator, achieving improved physical consistency and generalizability. Experimentally, NMP demonstrates superior generalization to unseen initial conditions and resolutions, stable long-horizon simulation, better preservation of physical properties compared to other neural simulators, and greater feasibility in scenarios with unknown underlying dynamics than traditional simulators.