不靠反向传播训练哈密顿神经网络，速度提升百倍以上
Training Hamiltonian neural networks without backpropagation
- 用无需梯度的采样法替代反向传播优化参数
- 在混沌系统中精度比传统方法高四个数量级，速度超100倍
- 适合需快速建模复杂动力系统的科研与工程场景
将数据与物理规律融合的神经网络在建模动态系统方面潜力巨大。然而，传统基于梯度的参数优化计算成本高且收敛慢。本文提出一种无需反向传播的算法，通过数据无关和数据驱动的参数采样方法，加速哈密顿系统神经网络的训练。实验表明，在函数梯度陡峭或输入域宽广的情况下，数据驱动采样优于数据无关采样或传统迭代优化。该方法在CPU上训练速度比传统哈密顿神经网络快逾100倍，并在混沌系统（如Hénon-Heiles系统）中实现超过四个数量级的精度提升。
原文摘要 · Abstract (English)
Neural networks that synergistically integrate data and physical laws offer great promise in modeling dynamical systems. However, iterative gradient-based optimization of network parameters is often computationally expensive and suffers from slow convergence. In this work, we present a backpropagation-free algorithm to accelerate the training of neural networks for approximating Hamiltonian systems through data-agnostic and data-driven algorithms. We empirically show that data-driven sampling of the network parameters outperforms data-agnostic sampling or the traditional gradient-based iterative optimization of the network parameters when approximating functions with steep gradients or wide input domains. We demonstrate that our approach is more than 100 times faster with CPUs than the traditionally trained Hamiltonian Neural Networks using gradient-based iterative optimization and is more than four orders of magnitude accurate in chaotic examples, including the Hénon-Heiles system.
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