用神经网络模拟物理反问题的复杂损失曲面，加速优化收敛。
Optimization Landscapes Learned: Proxy Networks Boost Convergence in Physics-based Inverse Problems
- 用神经网络学习物理反问题的时空轨迹，复现混沌损失曲面。
- 在多个难题上，新方法比BFGS等优化器收敛更快更稳定。
- 适合需要快速求解复杂反问题的研究者，如科学计算与工程建模。
物理反问题求解是理解复杂系统和推动各领域技术发展的核心。迭代优化算法常因过度依赖局部信息，陷入局部极小值、混沌或梯度为零区域，这源于由偏微分方程（PDEs）决定的高度混沌的反问题损失曲面。本文表明，深度神经网络可通过时空轨迹输入成功复现此类复杂损失曲面，并在训练中通过不同正则化方法调控其内在复杂性。实验显示，在网络平滑后的损失曲面上优化，相比传统基于动量的优化器（如BFGS），在多个挑战性问题上显著提升逆参数预测的收敛性能。
原文摘要 · Abstract (English)
Solving inverse problems in physics is central to understanding complex systems and advancing technologies in various fields. Iterative optimization algorithms, commonly used to solve these problems, often encounter local minima, chaos, or regions with zero gradients. This is due to their overreliance on local information and highly chaotic inverse loss landscapes governed by underlying partial differential equations (PDEs). In this work, we show that deep neural networks successfully replicate such complex loss landscapes through spatio-temporal trajectory inputs. They also offer the potential to control the underlying complexity of these chaotic loss landscapes during training through various regularization methods. We show that optimizing on network-smoothened loss landscapes leads to improved convergence in predicting optimum inverse parameters over conventional momentum-based optimizers such as BFGS on multiple challenging problems.
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