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arXiv · 2606.09001

JAX-AMG: A GPU-Accelerated Differentiable Sparse Linear Solver Library for JAX

Yi Liu·Xiantao Fan·Jian-Xun Wang
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Abstract

Sparse linear systems from PDE discretizations are central to scientific computing, yet no existing JAX-ecosystem solver simultaneously provides GPU-accelerated algebraic multigrid (AMG), automatic differentiation (AD), and distributed multi-GPU execution. JAX-AMG fills this gap by wrapping the NVIDIA AmgX solver suite as a native JAX primitive, exposing AMG and Krylov methods with configurable preconditioners through a unified interface compatible with JIT compilation, reverse-mode AD via adjoint methods, batched solves, and MPI-based distributed execution. Solver caching amortizes setup costs across repeated solves, making JAX-AMG practical for PDE-constrained optimization and inverse problems. The result is a robust, scalable sparse linear algebra layer that integrates seamlessly into differentiable simulation and scientific machine learning pipelines.

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Yi Liu, Xiantao Fan, Jian-Xun Wang. 2026-06-08. JAX-AMG: A GPU-Accelerated Differentiable Sparse Linear Solver Library for JAX. https://doi.org/10.1016/j.softx.2026.102966

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