A learned interface-aware neural Newton preconditioner improves convergence on difficult CZM increments while preserving the original discrete solution set and force-displacement response.
NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers
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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.
years
2026 3verdicts
UNVERDICTED 3representative citing papers
HAMNO introduces adaptive gating between local and global operators in a hierarchical setup, with PI-HAMNO adding PDE residual constraints, demonstrating better performance on Allen-Cahn, Cahn-Hilliard, and Swift-Hohenberg equations.
WINO is a weak-form physics-informed neural operator for hyperelasticity on variable domains that uses phi-FEM for geometric flexibility and achieves accuracy below 0.04 while cutting computation time by 50-80% as warm starts for solvers.
citing papers explorer
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Interface-Aware Neural Newton Preconditioning for Robust Cohesive Zone Model Simulations
A learned interface-aware neural Newton preconditioner improves convergence on difficult CZM increments while preserving the original discrete solution set and force-displacement response.
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HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems
HAMNO introduces adaptive gating between local and global operators in a hierarchical setup, with PI-HAMNO adding PDE residual constraints, demonstrating better performance on Allen-Cahn, Cahn-Hilliard, and Swift-Hohenberg equations.