NOWS
Neural Operator Warm Starts for accelerating iterative solvers
Abstract
Partial differential equations (PDEs) underpin quantitative descriptions across the physical sciences and engineering, yet high-fidelity simulation remains a major computational bottleneck for many-query, real-time, and design tasks. Data-driven surrogates can be strikingly fast but are often unreliable when applied outside their training distribution. Here we introduce Neural Operator Warm Starts (NOWS), a hybrid strategy that harnesses learned solution operators to accelerate classical iterative solvers by producing high-quality initial guesses for Krylov methods such as conjugate gradient and GMRES. NOWS leaves existing discretizations and solver infrastructures intact, integrating seamlessly with finite-difference, finite-element, isogeometric analysis, finite volume method, etc. Across our benchmarks, the learned initialization consistently reduces iteration counts and end-to-end runtime, resulting in a reduction of the computational time of up to 90%, while preserving the stability and convergence guarantees of the underlying numerical algorithms. By combining the rapid inference of neural operators with the rigor of traditional solvers, NOWS provides a practical and trustworthy approach to accelerate high-fidelity PDE simulations.
Details
- Organisation(s)
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Institute of Photonics
- External Organisation(s)
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Tsinghua University
Bauhaus-Universität Weimar
- Type
- Article
- Journal
- Computer Methods in Applied Mechanics and Engineering
- Volume
- 458
- ISSN
- 0045-7825
- Publication date
- 15.05.2026
- Publication status
- E-pub ahead of print
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
- Electronic version(s)
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https://doi.org/10.1016/j.cma.2026.118989 (Access:
Open
)
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Details in the research portal "Research@Leibniz University"
