NOWS: 用于加速迭代求解器的神经算子预热
NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers
AI总结：
NOWS结合神经算子的快速推理与传统求解器的严谨性，通过生成高质量初始猜测加速迭代求解，显著降低计算时间并保持稳定性。
摘要：
偏微分方程（PDEs）是物理科学和工程中定量描述的基础，但高保真模拟仍是许多查询、实时和设计任务的主要计算瓶颈。数据驱动的代理可以非常快速，但通常在训练分布外不可靠。本文介绍Neural Operator Warm Starts（NOWS），一种混合策略，利用学习的解算子加速经典迭代求解器，通过生成共轭梯度和GMRES等Krylov方法的高质量初始猜测。NOWS保持现有离散化和求解器基础设施不变，无缝集成有限差分、有限元、等几何分析、有限体积法等。在我们的基准测试中，学习的初始化一致减少了迭代次数和端到端运行时间，导致计算时间减少高达90%，同时保持底层数值算法的稳定性和收敛保证。通过结合神经算子的快速推理与传统求解器的严谨性，NOWS提供了一种实用且可信的方法，加速高保真PDE模拟。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
