JAX-AMG: New GPU-Accelerated Library for Solving Sparse Linear Systems with Automatic Differentiation
Researchers have released JAX-AMG, an open-source library that integrates GPU-accelerated algebraic multigrid (AMG) sparse linear solvers into the JAX scientific computing framework. The library wraps Nvidia's AmgX solver suite as a native JAX primitive, enabling JIT compilation, reverse-mode automatic differentiation, batched solves, and multi-GPU distributed execution in a single unified interface. This fills a notable gap in the JAX ecosystem for PDE-constrained optimization and scientific machine learning workflows that require scalable, differentiable sparse linear algebra.
JAX-AMG, submitted to arXiv on June 8, 2026, addresses a recognized gap in the JAX scientific computing ecosystem: no existing solver simultaneously offered GPU-accelerated algebraic multigrid (AMG), automatic differentiation (AD), and distributed multi-GPU execution. The library achieves this by wrapping Nvidia's AmgX solver suite as a native JAX primitive, exposing both AMG and Krylov iterative methods with configurable preconditioners. It supports JIT compilation, reverse-mode AD through adjoint methods, batched solves, and MPI-based distributed execution across multiple GPUs. A solver caching mechanism amortizes the often-expensive setup costs when the same solver configuration is reused across repeated solves, making the library particularly practical for inverse problems and PDE-constrained optimization. The work targets integration into differentiable simulation and scientific machine learning pipelines, where sparse linear systems arising from PDE discretizations are a computational bottleneck. The library is positioned as a robust and scalable sparse linear algebra layer compatible with modern JAX-based research workflows.
What's missing
As a preprint, the work has not yet undergone formal peer review.
What different sources said
- arXiv physicsCenter
JAX-AMG: A GPU-Accelerated Differentiable Sparse Linear Solver Library for JAX
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