Neural-ODE for PDE Solution Operators

SIAM Student Seminar
Friday, September 29, 2023 - 11:00am for 1 hour (actually 50 minutes)
Skiles 005
Nathan Gaby – Georgia State University –
Biraj Dahal

We consider a numerical method to approximate the solution operator for evolutional partial differential equations (PDEs). By employing a general reduced-order model, such as a deep neural network, we connect the evolution of a model's parameters with trajectories in a corresponding function space. Using the Neural Ordinary Differential Equations (NODE) technique we learn a vector field over the parameter space such that from any initial starting point, the resulting trajectory solves the evolutional PDE. Numerical results are presented for a number of high-dimensional problems where traditional methods fail due to the curse of dimensionality.