NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers

• URL: http://arxiv.org/abs/2511.02481v3
• Date: Mon, 10 Nov 2025 17:57:10 GMT
• Title: NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers
• Authors: Mohammad Sadegh Eshaghi, Cosmin Anitescu, Navid Valizadeh, Yizheng Wang, Xiaoying Zhuang, Timon Rabczuk,
• Abstract summary: Partial differential equations (PDEs) underpin quantitative descriptions across the physical sciences and engineering.<n>Data-driven surrogates can be strikingly fast but are often unreliable when applied outside their training distribution.<n>Here we introduce Neural Operator Warm Starts (NOWS), a hybrid strategy that harnesses learned solution operators to accelerate classical iterative solvers.
• Score: 1.8117099374299037
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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