论文标题
使用深度学习象征性地求解部分微分方程
Symbolically Solving Partial Differential Equations using Deep Learning
论文作者
论文摘要
我们描述了一种基于神经的方法，用于以数学表达式的形式生成针对微分方程的精确解决方案。与其他神经方法不同，我们的系统返回可以直接解释的符号表达式。我们的方法使用神经体系结构来学习数学表达式，以优化可自定义的目标，并且可扩展，紧凑且易于适应各种任务和配置。该系统已被证明可以有效地找到与自然科学中应用的各种微分方程的精确或近似符号解决方案。在这项工作中，我们强调了我们的方法如何应用于多个变量，更复杂的边界和初始值条件上的部分微分方程。
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted directly. Our method uses a neural architecture for learning mathematical expressions to optimize a customizable objective, and is scalable, compact, and easily adaptable for a variety of tasks and configurations. The system has been shown to effectively find exact or approximate symbolic solutions to various differential equations with applications in natural sciences. In this work, we highlight how our method applies to partial differential equations over multiple variables and more complex boundary and initial value conditions.
