神经物理模拟器在瞬态动力学展开训练中的可微性
Differentiability in Unrolled Training of Neural Physics Simulators on Transient Dynamics
AI总结：
本文分析了神经物理模拟器展开训练中可微性的影响，发现不可微但展开的训练在校正设置中能显著提升精度，且可微模型表现最佳，这促使在缺乏完全可微性时整合数值模拟器。
摘要：
随时间展开训练轨迹强烈影响神经网络增强的物理模拟器的推理精度。我们在三种训练神经时间步进器的变体中对此进行了分析。除了单步设置和完全可微的展开外，我们还包含了第三种较少使用的变体：无时间梯度的展开。通过比较使用这三种模式训练的网络，我们理清了展开的两个主导效应：训练分布偏移和长期梯度。我们对物理系统、网络规模与架构、训练设置和测试场景进行了详细研究。该研究还包含两种模拟模式：在预测设置中，我们仅依靠神经网络来计算轨迹。相比之下，校正设置包含一个由神经网络辅助的数值求解器。涵盖这些变化，我们的研究为以下主要发现提供了实证基础：在校正设置中，使用数值求解器进行不可微但展开的训练，相比于不利用该求解器的完全可微预测设置，能产生显著的改进。在完全可微设置中训练的模型，其精度与不可微的对应模型相比存在差异。在校正网络和预测设置的对比中，可微模型表现最佳。对于这两者，不可微展开的精度与之接近。此外，我们表明这些行为对于物理系统、网络架构与规模以及数值方案是不变的。这些结果促使我们即使在不具备完全可微性的情况下，也将不可微的数值模拟器集成到训练设置中。我们表明，与数值算法相比，常见架构的收敛速率较低。这促使我们采用结合神经与数值部分的校正设置，以利用两者的优势。
英文摘要：
Unrolling training trajectories over time strongly influences the inference accuracy of neural network-augmented physics simulators. We analyze this in three variants of training neural time-steppers. In addition to one-step setups and fully differentiable unrolling, we include a third, less widely used variant: unrolling without temporal gradients. Comparing networks trained with these three modalities disentangles the two dominant effects of unrolling, training distribution shift and long-term gradients. We present detailed study across physical systems, network sizes and architectures, training setups, and test scenarios. It also encompasses two simulation modes: In prediction setups, we rely solely on neural networks to compute a trajectory. In contrast, correction setups include a numerical solver that is supported by a neural network. Spanning these variations, our study provides the empirical basis for our main findings: Non-differentiable but unrolled training with a numerical solver in a correction setup can yield substantial improvements over a fully differentiable prediction setup not utilizing this solver. The accuracy of models trained in a fully differentiable setup differs compared to their non-differentiable counterparts. Differentiable ones perform best in a comparison among correction networks as well as among prediction setups. For both, the accuracy of non-differentiable unrolling comes close. Furthermore, we show that these behaviors are invariant to the physical system, the network architecture and size, and the numerical scheme. These results motivate integrating non-differentiable numerical simulators into training setups even if full differentiability is unavailable. We show the convergence rate of common architectures to be low compared to numerical algorithms. This motivates correction setups combining neural and numerical parts which utilize benefits of both.
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