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.

中文翻译：

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使用深度学习符号求解偏微分方程

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微分方程的精确或近似解。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架构来学习数学表达式以优化可定制的目标，并且具有可扩展性、紧凑性并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各种微分方程的精确或近似符号解，并应用于自然科学。在这项工作中，我们重点介绍了我们的方法如何应用于多个变量以及更复杂的边界和初始值条件的偏微分方程。