论文标题
关于动态系统在培训物理信息神经网络中的固定点的作用
On the Role of Fixed Points of Dynamical Systems in Training Physics-Informed Neural Networks
论文作者
论文摘要
本文从经验上研究了在动态系统上通常观察到物理信息神经网络（PINN）的训练困难。我们的结果表明，这些系统固有的固定点在PINNS嵌入物理损耗函数的优化中起关键作用。我们观察到，损失景观表现出由固定点的存在所塑造的局部优势。我们发现，这些局部最佳选择有助于物理损失优化的复杂性，这可以解释常见的训练困难和导致的非物理预测。在某些设置（例如，接近固定点或较长仿真时间的初始条件）下，我们表明这些最佳选择甚至可以比所需解决方案更好。
This paper empirically studies commonly observed training difficulties of Physics-Informed Neural Networks (PINNs) on dynamical systems. Our results indicate that fixed points which are inherent to these systems play a key role in the optimization of the in PINNs embedded physics loss function. We observe that the loss landscape exhibits local optima that are shaped by the presence of fixed points. We find that these local optima contribute to the complexity of the physics loss optimization which can explain common training difficulties and resulting nonphysical predictions. Under certain settings, e.g., initial conditions close to fixed points or long simulations times, we show that those optima can even become better than that of the desired solution.
