论文标题
物理信息网络的神经进化:基准问题和比较结果
Neuroevolution of Physics-Informed Neural Nets: Benchmark Problems and Comparative Results
论文作者
论文摘要
学识渊博的模型对基本科学研究和发现的潜力正在引起全球的越来越多的关注。物理知识的神经网络(PINN),其中损失函数直接嵌入了科学现象的管理方程,是最近进步最前沿的关键技术之一。 PINN通常使用随机梯度下降方法进行训练,类似于他们的深度学习对应物。但是,本文分析表明,Pinn的独特损失制剂会导致高度的复杂性和坚固性,这可能不利于梯度下降。与标准深度学习不同,Pinn培训需要尽可能接近物理定律的全球最佳参数值。必须避免杂乱无章的局部最佳,指示错误的物理学。因此,神经进化算法具有出色的全球搜索能力,可能是PINN相对于梯度下降方法的更好选择。在这里,我们提出了一组带有开源代码的五个基准问题,涵盖了新型神经进化算法开发的各种物理现象。使用此方法,我们将两种神经进化算法与常用的随机梯度下降进行了比较,我们的基线结果支持这样的主张,即神经进化可以超过梯度下降,确保在预测的输出中更好地物理依从性。 %此外,使用JAX实施神经进化会导致相对于标准实现的速度加速。
The potential of learned models for fundamental scientific research and discovery is drawing increasing attention worldwide. Physics-informed neural networks (PINNs), where the loss function directly embeds governing equations of scientific phenomena, is one of the key techniques at the forefront of recent advances. PINNs are typically trained using stochastic gradient descent methods, akin to their deep learning counterparts. However, analysis in this paper shows that PINNs' unique loss formulations lead to a high degree of complexity and ruggedness that may not be conducive for gradient descent. Unlike in standard deep learning, PINN training requires globally optimum parameter values that satisfy physical laws as closely as possible. Spurious local optimum, indicative of erroneous physics, must be avoided. Hence, neuroevolution algorithms, with their superior global search capacity, may be a better choice for PINNs relative to gradient descent methods. Here, we propose a set of five benchmark problems, with open-source codes, spanning diverse physical phenomena for novel neuroevolution algorithm development. Using this, we compare two neuroevolution algorithms against the commonly used stochastic gradient descent, and our baseline results support the claim that neuroevolution can surpass gradient descent, ensuring better physics compliance in the predicted outputs. %Furthermore, implementing neuroevolution with JAX leads to orders of magnitude speedup relative to standard implementations.