# Vertex Block Descent

arXiv: https://arxiv.org/abs/2403.06321 · HTML: https://mlsanity.com/paper/2403.06321/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2024.

## Built on by (most cited first, 6 of 6)

- [InternData-A1: Pioneering High-Fidelity Synthetic Data for Pre-training Generalist Policy](https://mlsanity.com/paper/2511.16651/) (2025)
- [Physically Valid Biomolecular Interaction Modeling with Gauss-Seidel Projection](https://mlsanity.com/paper/2510.08946/) (2025)
- [SIM1: Physics-Aligned Simulator as Zero-Shot Data Scaler in Deformable Worlds](https://mlsanity.com/paper/2604.08544/) (2026)
- [Differentiate the Solver, Not the Equation: Reverse-Sweep Adjoints for Block Implicit Simulation](https://mlsanity.com/paper/2608.08559/) (2026)
- [DiT-Garment: Garment Dynamics with Diffusion Transformers](https://mlsanity.com/paper/2609.18510/) (2026)
- [RoboSimStudio: An Interactive Toolkit for Human and Agent Rapid Real2Sim of Robot Manipulation Tasks](https://mlsanity.com/paper/2610.18835/) (2026)

## Abstract (arXiv)

We introduce vertex block descent, a block coordinate descent solution for the variational form of implicit Euler through vertex-level Gauss-Seidel iterations. It operates with local vertex position updates that achieve reductions in global variational energy with maximized parallelism. This forms a physics solver that can achieve numerical convergence with unconditional stability and exceptional computation performance. It can also fit in a given computation budget by simply limiting the iteration count while maintaining its stability and superior convergence rate. We present and evaluate our method in the context of elastic body dynamics, providing details of all essential components and showing that it outperforms alternative techniques. In addition, we discuss and show examples of how our method can be used for other simulation systems, including particle-based simulations and rigid bodies.