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

TL;DR

GeoWarp presents a differentiable, implicit MPM framework for geomechanics built on NVIDIA Warp, enabling automatic Jacobian construction via reverse-mode AD to support Newton solvers without manual tangent derivations. A key contribution is a sparse Jacobian construction that leverages the localized particle-grid coupling in MPM, reducing the number of backward AD passes to a small, problem-size–independent count and delivering strong scalability on GPUs. The paper verifies forward and inverse capabilities across large-deformation elastoplasticity and poromechanics, demonstrating accurate constitutive response, convergence, and gradient-based inversion, with open-source release to foster reproducibility. This work enables robust, differentiable, large-scale MPM simulations in geomechanics, with potential for parameter identification, optimization, and learning-guided modeling on modern heterogeneous hardware.

Abstract

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.

Figures (26)

• Figure 1: MPM update procedure.
• Figure 2: Illustration of the associated grid nodes for a particle in the 1D GIMP formulation. The particle (shown as a gray rectangle) interacts with at most three neighboring grid nodes (marked as red dots) through its shape function support.
• Figure 3: Overlapping influence domains of neighboring particles around Node 3. Rectangles represent three neighboring particles, and their shaded regions represent the respective influence zones.
• Figure 4: Two algorithms for Jacobian construction in implicit MPM. Solid dots indicate the active degrees of freedom. (a) Dense differentiation requires one reverse-mode AD pass per degree of freedom, resulting in high computational cost. (b) Sparse differentiation exploits the locality of particle--grid interactions by partitioning the background grid into independent blocks, enabling multiple Jacobian rows to be computed simultaneously in a single backward pass. Numbers indicate the corresponding local_x and local_y indices.
• Figure 5: Stress-point triaxial compression: problem setup. The axial stress ($\sigma_a$) increases with loading, while the radial stress ($\sigma_r$) is kept constant.