JAX-MPM: A Learning-Augmented Differentiable Meshfree Framework for GPU-Accelerated Lagrangian Simulation and Geophysical Inverse Modeling

Differentiable programming that enables automatic differentiation through simulation pipelines has emerged as a powerful paradigm in scientific computing, supporting both forward and inverse modeling and facilitating integration with deep learning frameworks. We present JAX-MPM, a general-purpose differentiable meshfree solver within a hybrid Lagrangian-Eulerian framework, tailored for simulating complex continuum mechanics involving large deformations, frictional contact, and inelastic material behavior, with emphasis on geomechanics and geophysical hazard applications. Built on the material point method (MPM) and implemented using the JAX computing framework, JAX-MPM is fully differentiable and GPU-accelerated, enabling efficient gradient-based optimization directly through time-stepping solvers. It supports joint training of physical models and neural networks, allowing the learning of embedded closures and neural constitutive models. We validate JAX-MPM on several 2D and 3D benchmarks, including dam-breaks and granular collapses, demonstrating its accuracy and performance. A high-resolution 3D granular cylinder collapse with 2.7 million particles completes 1000 steps in ~22 seconds (single precision) and ~98 seconds (double precision) on a single GPU. Beyond forward modeling, we demonstrate inverse modeling capabilities such as velocity field reconstruction and spatially varying friction estimation. These results establish JAX-MPM as a unified, scalable platform for differentiable meshfree simulation and data-driven geomechanical inference.