Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

Understand

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations.

• In this two part treatise, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations.
• Depending on the nature and arrangement of the available data, we devise two distinct classes of algorithms, namely continuous time and discrete time models.
• The resulting neural networks form a new class of data-efficient universal function approximators that naturally encode any underlying physical laws as prior information.