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JAX-MPM: a learning-augmented differentiable meshfree framework for GPU-accelerated Lagrangian simulation and geophysical inverse modeling.

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Title: JAX-MPM: a learning-augmented differentiable meshfree framework for GPU-accelerated Lagrangian simulation and geophysical inverse modeling.
Authors: Du, Honghui1 (AUTHOR), He, QiZhi1 (AUTHOR) qzhe@umn.edu
Source: Engineering with Computers. Jun2026, Vol. 42 Issue 3, p1-25. 25p.
Subjects: Material point method, Meshfree methods, Automatic differentiation, Graphics processing units, Lagrange equations, Inversion (Geophysics), Machine learning, Benchmarking (Management), Deep learning
Abstract: Differentiable programming has emerged as a powerful paradigm in scientific computing, enabling automatic differentiation through simulation pipelines and naturally supporting both forward and inverse modeling. We present JAX-MPM, a general-purpose differentiable meshfree solver based on the material point method (MPM) and implemented in the modern JAX ecosystem. The framework adopts a hybrid Eulerian–Lagrangian formulation to capture large deformations, frictional contact, and inelastic material behavior, with emphasis on geomechanics and geophysical hazard applications. Leveraging GPU acceleration and automatic differentiation, JAX-MPM enables efficient gradient-based optimization directly through its time-stepping solvers and supports joint training of physical models with deep learning to infer unknown system conditions and uncover hidden constitutive parameters. We validate JAX-MPM through a series of 2D and 3D benchmark simulations, including dam-break and granular collapse problems, demonstrating both numerical accuracy and GPU-accelerated performance. Results show that a high-resolution 3D granular cylinder collapse with 2.7 million particles completes 1000 time steps in approximately 22 s (single precision) and 98 s (double precision) on a single GPU. Beyond high-fidelity forward modeling, we demonstrate the framework's inverse modeling capabilities through tasks such as velocity field reconstruction and the estimation of spatially varying friction from sparse data. In particular, JAX-MPM introduces a differentiable observation layer that unifies data assimilation from both Lagrangian (particle-based) and Eulerian (region-based) observations, and can be seamlessly coupled with neural network representations. These results establish JAX-MPM as a unified and scalable differentiable meshfree platform that advances fast physical simulation and data assimilation for complex solid and geophysical systems. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Differentiable programming has emerged as a powerful paradigm in scientific computing, enabling automatic differentiation through simulation pipelines and naturally supporting both forward and inverse modeling. We present JAX-MPM, a general-purpose differentiable meshfree solver based on the material point method (MPM) and implemented in the modern JAX ecosystem. The framework adopts a hybrid Eulerian–Lagrangian formulation to capture large deformations, frictional contact, and inelastic material behavior, with emphasis on geomechanics and geophysical hazard applications. Leveraging GPU acceleration and automatic differentiation, JAX-MPM enables efficient gradient-based optimization directly through its time-stepping solvers and supports joint training of physical models with deep learning to infer unknown system conditions and uncover hidden constitutive parameters. We validate JAX-MPM through a series of 2D and 3D benchmark simulations, including dam-break and granular collapse problems, demonstrating both numerical accuracy and GPU-accelerated performance. Results show that a high-resolution 3D granular cylinder collapse with 2.7 million particles completes 1000 time steps in approximately 22 s (single precision) and 98 s (double precision) on a single GPU. Beyond high-fidelity forward modeling, we demonstrate the framework's inverse modeling capabilities through tasks such as velocity field reconstruction and the estimation of spatially varying friction from sparse data. In particular, JAX-MPM introduces a differentiable observation layer that unifies data assimilation from both Lagrangian (particle-based) and Eulerian (region-based) observations, and can be seamlessly coupled with neural network representations. These results establish JAX-MPM as a unified and scalable differentiable meshfree platform that advances fast physical simulation and data assimilation for complex solid and geophysical systems. [ABSTRACT FROM AUTHOR]
ISSN:01770667
DOI:10.1007/s00366-026-02320-6