JAX-AMG

JAX-AMG brings the power of NVIDIA's AmgX library to the JAX ecosystem, providing high-performance, GPU-accelerated sparse linear solvers with full support for automatic differentiation.

Documentation: https://jx-wang-s-group.github.io/JAX-AMG/

Features

• GPU-Accelerated Solvers: Leverages NVIDIA AmgX for a broad range of GPU-accelerated sparse linear solvers, including algebraic multigrid (AMG), Krylov methods, and various variants, with flexible configuraiton options for solvers, smoothers, and preconditioners.
• Automatic Differentiation: Supports adjoint-based gradient computation and integrates seamlessly with JAX for end-to-end differentiable workflows.
• JIT Compilation: Built as a native JAX primitive, fully compatible with Just-in-Time compilation (jax.jit) for efficient, low-overhead execution.
• MPI Support: Enables distributed linear solves across multiple GPUs, with GPU-aware MPI support.
• Matrix-Free Operators: Beyond explicit matrices, A can be a callable operator. The library recovers the exact sparsity pattern in a single pass by tracing the operator's computation graph, then assembles the matrix the solver needs.

Prerequisites

• Python 3.10+
• JAX 0.5.0+ with CUDA support
• AmgX 2.5.0+
• CUDA Toolkit 12.0+

Additional for Distributed (MPI) Mode:

• MPI library (e.g., OpenMPI, MPICH)
• CUDA-aware MPI (optional, for GPU-direct communication)

Installation

JAX-AMG is installed with pip. It compiles a native extension against a CUDA toolkit and a source build of NVIDIA AmgX, so set CUDA_HOME and AMGX_ROOT first, then run the command for your CUDA version:

pip install "jaxamg[cuda12]"   # or jaxamg[cuda13]

At runtime, add the AmgX and CUDA libraries to your library path:

export LD_LIBRARY_PATH=$AMGX_ROOT/build:$CUDA_HOME/lib64:$LD_LIBRARY_PATH

For distributed (MPI) mode, the install script, conda, or building from source, see the full Installation Guide.

Quick Start

A simple tridiagonal system can be solved as:

import jaxamg
from jaxamg.matrices import tridiagonal_matrix, rhs_ones

# Create a simple tridiagonal system
n = 100
A = tridiagonal_matrix(n, diagonal_value=2.0)
b = rhs_ones(n)

# Solve Ax = b
x, info = jaxamg.solve(A, b)

MPI Distributed Solving

A distributed 2D Poisson system can be solved with GPU-aware MPI as:

from mpi4py import MPI
import jaxamg
from jaxamg.mpi_utils import partition_vector, gather_vector
from jaxamg.matrices import poisson_matrix_distributed, rhs_ones

comm = MPI.COMM_WORLD
rank = comm.Get_rank()
nranks = comm.Get_size()

# Create distributed 2D Poisson matrix
n = 16
A_local, row_start, row_end = poisson_matrix_distributed(n, n, rank, nranks)
b_local, _, _ = partition_vector(rhs_ones(n * n), rank, nranks)

# Solve in distributed mode
x_local, info = jaxamg.solve(
    A_local, b_local,
    comm=comm,
    nglobal=n * n,
    partition_info=(row_start, row_end),
    config={
        "solver": "CG",
        "preconditioner": {"solver": "JACOBI_L1"},
        "communicator": "MPI_DIRECT",
    }
)

# Gather solution at root rank
x_global = gather_vector(x_local, comm, root=0)
if rank == 0: print(x_global)

Citation

If you use JAX-AMG in your work, please consider using the following citation (arXiv:2606.09001):

@misc{jaxamg2026,
      title={JAX-AMG: A GPU-Accelerated Differentiable Sparse Linear Solver Library for JAX},
      author={Yi Liu and Xiantao Fan and Jian-Xun Wang},
      year={2026},
      eprint={2606.09001},
      archivePrefix={arXiv},
      primaryClass={cs.MS},
      url={https://arxiv.org/abs/2606.09001},
}