# GeoWarp: An automatically differentiable and GPU-accelerated implicit MPM framework for geomechanics based on NVIDIA Warp

arXiv: https://arxiv.org/abs/2507.09435 · HTML: https://mlsanity.com/paper/2507.09435/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2025.

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

- [Size Doesn't Matter: Material-State Reinforcement Learning for Excavator Transferable Soil Manipulation](https://mlsanity.com/paper/2609.12677/) (2026)

## Abstract (arXiv)

The material point method (MPM), a hybrid Lagrangian-Eulerian particle method, is increasingly used to simulate large-deformation and history-dependent behavior of geomaterials. While explicit time integration dominates current MPM implementations due to its algorithmic simplicity, such schemes are unsuitable for quasi-static and long-term processes typical in geomechanics. Implicit MPM formulations are free of these limitations but remain less adopted, largely due to the difficulty of computing the Jacobian matrix required for Newton-type solvers, especially when consistent tangent operators should be derived for complex constitutive models. In this paper, we introduce GeoWarp -- an implicit MPM framework for geomechanics built on NVIDIA Warp -- that exploits GPU parallelism and reverse-mode automatic differentiation to compute Jacobians without manual derivation. To enhance efficiency, we develop a sparse Jacobian construction algorithm that leverages the localized particle-grid interactions intrinsic to MPM. The framework is verified through forward and inverse examples in large-deformation elastoplasticity and coupled poromechanics. Results demonstrate that GeoWarp provides a robust, scalable, and extensible platform for differentiable implicit MPM simulation in computational geomechanics.