NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers
This addresses the problem of slow PDE simulations for many-query, real-time, and design tasks in physical sciences and engineering, offering a practical and trustworthy acceleration method.
The paper tackles the computational bottleneck of high-fidelity PDE simulations by introducing Neural Operator Warm Starts (NOWS), a hybrid strategy that uses learned solution operators to accelerate iterative solvers, resulting in up to a 90% reduction in computational time while preserving stability and convergence guarantees.
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.