用多预处理LBFGS加速物理神经网络训练，收敛更快更准。
Multi-Preconditioned LBFGS for Training Finite-Basis PINNs
- 基于子域分解的局部拟牛顿修正，支持并行计算。
- 相比标准LBFGS，收敛速度提升且模型精度更高。
- 适合大规模物理信息神经网络的高效训练场景。
本文提出一种用于有限基物理信息神经网络（FBPINNs）训练的多预处理变体拟牛顿法（MP-LBFGS）。该方法受非线性加性Schwarz方法启发，利用FBPINNs中定义在子域上的局部神经网络所具有的加性结构，将网络表示局部化。在此基础上，在对应局部架构上构建并行的子域局部拟牛顿修正。其核心是新型非线性多预处理机制，通过求解低维子空间最小化问题，最优组合各子域修正。数值实验表明，相较于标准LBFGS，MP-LBFGS在保持更低通信开销的同时，显著提升了收敛速度与模型精度。
原文摘要 · Abstract (English)
A multi-preconditioned LBFGS (MP-LBFGS) algorithm is introduced for training finite-basis physics-informed neural networks (FBPINNs). The algorithm is motivated by the nonlinear additive Schwarz method and exploits the domain-decomposition-inspired additive architecture of FBPINNs, in which local neural networks are defined on subdomains, thereby localizing the network representation. Parallel, subdomain-local quasi-Newton corrections are then constructed on the corresponding local parts of the architecture. A key feature is a novel nonlinear multi-preconditioning mechanism, in which subdomain corrections are optimally combined through the solution of a low-dimensional subspace minimization problem. Numerical experiments indicate that MP-LBFGS can improve convergence speed, as well as model accuracy over standard LBFGS while incurring lower communication overhead.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。