用渐进精化物理求解器，训练速度提升62%且不损失精度。
PRDP: Progressively Refined Differentiable Physics
- 从粗略物理开始，训练中逐步细化，直到满足精度即可停止。
- 在模拟纳维-斯托克斯方程时，训练时间减少62%。
- 适合需要高效训练的科学计算类神经网络任务。
神经网络训练中使用的物理求解器多为迭代式，导致反向传播计算开销巨大。受双层优化研究启发，我们发现网络全精度训练可在远低于完全收敛的粗糙物理条件下实现。为此提出渐进精化可微物理（PRDP）：初始采用粗略物理，训练过程中自适应精细化，达到足够精度即停止。该方法显著降低计算成本，同时保持网络精度。研究聚焦于稀疏离散微分算子的迭代线性求解器，是科学计算核心。PRDP适用于显式与隐式反向传播。在反问题、自回归神经代理模型及基于修正的神经-混合求解器等多种学习场景中验证有效。以模拟纳维-斯托克斯方程为例，训练时间减少62%。
原文摘要 · Abstract (English)
The physics solvers employed for neural network training are primarily iterative, and hence, differentiating through them introduces a severe computational burden as iterations grow large. Inspired by works in bilevel optimization, we show that full accuracy of the network is achievable through physics significantly coarser than fully converged solvers. We propose Progressively Refined Differentiable Physics (PRDP), an approach that identifies the level of physics refinement sufficient for full training accuracy. By beginning with coarse physics, adaptively refining it during training, and stopping refinement at the level adequate for training, it enables significant compute savings without sacrificing network accuracy. Our focus is on differentiating iterative linear solvers for sparsely discretized differential operators, which are fundamental to scientific computing. PRDP is applicable to both unrolled and implicit differentiation. We validate its performance on a variety of learning scenarios involving differentiable physics solvers such as inverse problems, autoregressive neural emulators, and correction-based neural-hybrid solvers. In the challenging example of emulating the Navier-Stokes equations, we reduce training time by 62%.
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