| Abstract: |
| Many phenomena in science and engineering are observable but not explainable. That is, we can observe solution data generated from many physical systems, but the actual physics, e.g. an ordinary or partial differential equation model, are unknown. In this case, developing a deep neural network based model that replicates the system`s behavior is desirable. Hence in this talk, we will explore how to learn the time evolution of unknown ODE and PDE systems from their solution data using deep neural networks. The specific network architectures used are grounded in numerical methods for solving ODEs and PDEs. We also considering the case of partially observing the solution vector, where a time history of the observed variables are required. |
|