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

2025-07-12

AI Summary

Explicit material point method (MPM) struggles with quasi-static or long-term geomechanical simulations involving large deformations and history-dependent behavior, while implicit MPM remains limited by the analytical derivation of Jacobian matrices—especially consistent tangent operators for complex constitutive models. Method: This paper proposes an automatic-differentiation-based implicit MPM framework built on NVIDIA Warp, integrating reverse-mode automatic differentiation (eliminating manual tangent derivation), GPU-accelerated sparse Jacobian assembly, and implicit time integration. The framework supports efficient forward and inverse modeling for elastoplasticity and coupled poromechanics. Contribution/Results: Experiments demonstrate substantial improvements in computational efficiency and scalability without compromising numerical robustness. To our knowledge, this is the first open-source, differentiable, and fully GPU-accelerated implicit MPM implementation for computational geomechanics.

Technology Category

• Machine Learning: Hardware-aware ML
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

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.

Problem

• Develops implicit MPM for geomechanics without manual Jacobian derivation
• Addresses inefficiency in quasi-static and long-term geomechanical processes
• Enables GPU-accelerated differentiable simulation for complex constitutive models

Innovation

• GPU-accelerated implicit MPM framework
• Automatic differentiation for Jacobian computation
• Sparse Jacobian construction algorithm