论文标题
学会在初始条件下求解微分方程
Learning To Solve Differential Equations Across Initial Conditions
论文作者
论文摘要
最近，人们对使用神经网络来求解部分微分方程引起了人们的极大兴趣。已经制定了许多基于神经网络的偏微分方程求解器，这些方程式求解器提供了相当于经典求解器的性能，在某些情况下甚至具有优越的性能。但是，通常每当偏微分方程的初始条件或域变化时，这些神经求解器通常需要重新训练。在这项工作中，我们提出了一个问题，即在学习条件概率分布的任何任意初始条件中近似固定部分微分方程的解。我们演示了我们在汉堡方程式上的方法的实用性。
Recently, there has been a lot of interest in using neural networks for solving partial differential equations. A number of neural network-based partial differential equation solvers have been formulated which provide performances equivalent, and in some cases even superior, to classical solvers. However, these neural solvers, in general, need to be retrained each time the initial conditions or the domain of the partial differential equation changes. In this work, we posit the problem of approximating the solution of a fixed partial differential equation for any arbitrary initial conditions as learning a conditional probability distribution. We demonstrate the utility of our method on Burger's Equation.
