论文标题
物理知识神经网络损失功能的随机缩放
Stochastic Scaling in Loss Functions for Physics-Informed Neural Networks
论文作者
论文摘要
微分方程用于多种学科，描述了物理世界的复杂行为。这些方程式的分析解决方案通常很难求解，这限制了我们目前求解复杂微分方程的能力，并需要将复杂的数值方法近似于解决方案。训练有素的神经网络充当通用函数近似器，能够以新颖的方式求解微分方程。在这项工作中，探索了神经网络算法在数值求解微分方程方面的方法和应用，重点是不同的损失函数和生物应用。传统损失函数和训练参数的变化显示出使神经网络辅助解决方案更有效的希望，从而可以调查更复杂的方程式生物学原理。
Differential equations are used in a wide variety of disciplines, describing the complex behavior of the physical world. Analytic solutions to these equations are often difficult to solve for, limiting our current ability to solve complex differential equations and necessitating sophisticated numerical methods to approximate solutions. Trained neural networks act as universal function approximators, able to numerically solve differential equations in a novel way. In this work, methods and applications of neural network algorithms for numerically solving differential equations are explored, with an emphasis on varying loss functions and biological applications. Variations on traditional loss function and training parameters show promise in making neural network-aided solutions more efficient, allowing for the investigation of more complex equations governing biological principles.
