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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.04192 |
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| _version_ | 1866914060290752512 |
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| author | Du, Honghui He, QiZhi |
| author_facet | Du, Honghui He, QiZhi |
| contents | 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 architecture. The solver adopts a hybrid Eulerian-Lagrangian framework 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 seconds (single precision) and 98 seconds (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 accommodates 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04192 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | JAX-MPM: A Learning-Augmented Differentiable Meshfree Framework for GPU-Accelerated Lagrangian Simulation and Geophysical Inverse Modeling Du, Honghui He, QiZhi Machine Learning 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 architecture. The solver adopts a hybrid Eulerian-Lagrangian framework 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 seconds (single precision) and 98 seconds (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 accommodates 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. |
| title | JAX-MPM: A Learning-Augmented Differentiable Meshfree Framework for GPU-Accelerated Lagrangian Simulation and Geophysical Inverse Modeling |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2507.04192 |