MINDS Seminar Series | Jihun Han (Dartmouth college) - A Derivative-Free Loss Method for Solving Elliptic and Parabolic PDEs with Deep Neural Networks
| Date |
2021-12-07 ~ 2021-12-07 |
Time |
17:00:00 ~ 18:00:00 |
| Speaker |
Jihun Han |
Affiliation |
Dartmouth college |
| Place |
Math Bldg 104 & Online streaming (Zoom) |
Streaming link |
ID : 823 9618 0997 /
PW : 54321 |
| Topic |
A Derivative-Free Loss Method for Solving Elliptic and Parabolic PDEs with Deep Neural Networks |
| Contents |
We introduce a deep neural network based method for solving a class of elliptic and parabolic partial differential equations. We approximate the solution of the PDE with a deep neural network which is trained under the guidance of a probabilistic representation of the PDE in the spirit of the Feynman-Kac formula. The solution is given by an expectation of a martingale process driven by a Brownian motion. As Brownian walkers explore the domain, the deep neural network is iteratively trained using a form of reinforcement learning. Our method is a ‘Derivative-Free Loss Method’ since it does not require the explicit calculation of the derivatives of the neural network with respect to the input neurons in order to compute the training loss. The advantages of our method are showcased in a series of test problems. This is joint work with M. Nica and A. Stinchcombe. |