NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia
Author(s)
Pal, Avik
Holtorf, Flemming
Larsson, Axel
Loman, Torkel
Rajput, Utkarsh
Sch?fer, Frank
Qu, Qingyu
Edelman, Alan
Rackauckas, Chris
Date Issued
December 1, 2025
Journal
ACM Transactions on Mathematical Software
Publisher
ACM
Citation
Avik Pal, Flemming Holtorf, Axel Larsson, Torkel Loman, Utkarsh, Frank Schäfer, Qingyu Qu, Alan Edelman, and Chris Rackauckas. 2025. NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia. ACM Trans. Math. Softw. (December 2025).
Version
Final published version
Abstract
Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for challenging system models remains a challenge. This paper presents NonlinearSolve.jl -- a suite of high-performance open-source nonlinear equation solvers implemented natively in the Julia programming language. NonlinearSolve.jl distinguishes itself by offering a unified API that accommodates a diverse range of solver specifications alongside features such as automatic algorithm selection based on runtime analysis, support for static array kernels for improved GPU computation on smaller problems, and the utilization of sparse automatic differentiation and Jacobian-free Krylov methods for large-scale problem-solving. Through rigorous comparison with established tools such as PETSc SNES, Sundials KINSOL, and MINPACK, NonlinearSolve.jl demonstrates robustness and efficiency, achieving significant advancements in solving nonlinear equations while being implemented in a high-level programming language. The capabilities of NonlinearSolve.jl unlock new potentials in modeling and simulation across various domains, making it a valuable addition to the computational toolkit of researchers and practitioners alike.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Chemical Engineering
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/3779117
