Learning equations of motion for coupled spatio-temporal processes

我们将开发和验证学习与合金中微观结构生长相关的运动方程的方法。这些过程由耦合的偏微分运动方程描述，每个方程描述一种组分的局部浓度或结晶度。理论上提出的方程变得越来越复杂，使得解释和验证变得具有挑战性。通过使用数据驱动的方法来学习方程，我们希望证明机器学习的方法可以补充更传统的方法来开发时空过程的理论描述。

We will develop and validate methods for learning the equations of motion associated with microstructure growth in alloys. Such processes are described by coupled partial differential equations of motion, each describing the local concentration or degree of crystallinity of one of the components. The equations proposed theoretically have become increasingly complex, making interpretation and validation challenging. By using a data driven approach to learning the equations, we hope to demonstrate that the methods of machine learning can complement more traditional approaches to developing theoretical descriptions of spatio-temporal processes.