Solving Partial Differential Equations
Explore how generative AI applies deep learning to solve partial differential equations by approximating solutions through convolutional networks. Understand boundary conditions, numerical methods, and how models like DiffNet generate PDE solutions more efficiently than traditional methods.
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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
Burger’s equation
Where