Solving Partial Differential Equations

Another field in which deep learning, in general, and generative learning, in particular, has led to recent breakthroughs is the solution of partial differential equations (PDEs), a mathematical model used for diverse applications, including fluid dynamics, weather prediction, and understanding the behavior of physical systems.

More formally, a PDE imposes some condition on the partial derivatives of a function, and the problem is to find a function that fulfills this condition. Usually, some set of initial or boundary conditions are placed on the function to limit the search space within a particular grid. As an example, consider Burger’s equationCameron, Maria. n.d. “NOTES on BURGERS’S EQUATION.” https://www.math.umd.edu/~mariakc/burgers.pdf., which governs phenomena such as the speed of a fluid at a given position and time.

Burger’s equation