# Accelerate Neural Subspace-Based Reduced-Order Solver of Deformable Simulation by Lipschitz Optimization

arXiv: https://arxiv.org/abs/2409.03807 · HTML: https://mlsanity.com/paper/2409.03807/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 51 references that are in the map.
- First posted on arXiv 5 Sep 2024.

## Builds on (most cited first, 18 of 18)

- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Robustness via curvature regularization, and vice versa](https://mlsanity.com/paper/1811.09716/) (2018)
- [DeepMimic: Example-Guided Deep Reinforcement Learning of Physics-Based Character Skills](https://mlsanity.com/paper/1804.02717/) (2018)
- [Adversarial Robustness through Local Linearization](https://mlsanity.com/paper/1907.02610/) (2019)
- [Robust Learning with Jacobian Regularization](https://mlsanity.com/paper/1908.02729/) (2019)
- [Improving DNN Robustness to Adversarial Attacks using Jacobian Regularization](https://mlsanity.com/paper/1803.08680/) (2018)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [High-order Differentiable Autoencoder for Nonlinear Model Reduction](https://mlsanity.com/paper/2102.11026/) (2021)
- [Adversarial Lipschitz Regularization](https://mlsanity.com/paper/1907.05681/) (2019)
- [Neural Stress Fields for Reduced-order Elastoplasticity and Fracture](https://mlsanity.com/paper/2310.17790/) (2023)
- [Data-Free Learning of Reduced-Order Kinematics](https://mlsanity.com/paper/2305.03846/) (2023)
- [Fast Complementary Dynamics via Skinning Eigenmodes](https://mlsanity.com/paper/2303.11886/) (2023)
- [Model reduction for the material point method via an implicit neural representation of the deformation map](https://mlsanity.com/paper/2109.12390/) (2021)
- [Anderson Acceleration for Geometry Optimization and Physics Simulation](https://mlsanity.com/paper/1805.05715/) (2018)
- [Fast GPU-Based Two-Way Continuous Collision Handling](https://mlsanity.com/paper/2211.04045/) (2022)

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

- [Neuralocks: Real-Time Dynamic Neural Hair Simulation](https://mlsanity.com/paper/2507.05191/) (2025)
- [FreeForm: Reduced-Order Deformable Simulation from Particle-Based Skinning Eigenmodes](https://mlsanity.com/paper/2605.29318/) (2026)
- [PhysSkin: Real-Time and Generalizable Physics-Based Animation via Self-Supervised Neural Skinning](https://mlsanity.com/paper/2603.23194/) (2026)
- [Reduced-order Neural Modeling with Differentiable Simulation for High-Detail Tactile Perception](https://mlsanity.com/paper/2605.05053/) (2026)
- [RealSimLoop: Online Real-to-Sim Adaptation via Differentiable Reduced-Order Simulation with Vision Feedback](https://mlsanity.com/paper/2609.09828/) (2026)

## Abstract (arXiv)

Reduced-order simulation is an emerging method for accelerating physical simulations with high DOFs, and recently developed neural-network-based methods with nonlinear subspaces have been proven effective in diverse applications as more concise subspaces can be detected. However, the complexity and landscape of simulation objectives within the subspace have not been optimized, which leaves room for enhancement of the convergence speed. This work focuses on this point by proposing a general method for finding optimized subspace mappings, enabling further acceleration of neural reduced-order simulations while capturing comprehensive representations of the configuration manifolds. We achieve this by optimizing the Lipschitz energy of the elasticity term in the simulation objective, and incorporating the cubature approximation into the training process to manage the high memory and time demands associated with optimizing the newly introduced energy. Our method is versatile and applicable to both supervised and unsupervised settings for optimizing the parameterizations of the configuration manifolds. We demonstrate the effectiveness of our approach through general cases in both quasi-static and dynamics simulations. Our method achieves acceleration factors of up to 6.83 while consistently preserving comparable simulation accuracy in various cases, including large twisting, bending, and rotational deformations with collision handling. This novel approach offers significant potential for accelerating physical simulations, and can be a good add-on to existing neural-network-based solutions in modeling complex deformable objects.