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.
翻译:不同的方程式用于各种各样的学科,描述物理世界的复杂行为。这些方程式的分析性解决办法往往难以解决,限制了我们目前解决复杂差异方程式的能力,并需要复杂的数字方法来解决近似的解决办法。受过训练的神经网络是通用功能近似器,能够以新的方式从数字上解决差异方程式。在这项工作中,探索了神经网络算法用于以数字方式解决差异方程式的方法和应用,重点是不同的损失功能和生物应用。传统损失功能和培训参数的变化表明,有可能提高神经网络辅助解决方案的效率,从而能够调查关于生物原理的更复杂的方程式。