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| Title | Learning to Approximate Controlled Systems |
| Time | Tuesday 27th November 2018 - 10:35 to 11:05 |
| Venue | Seminar Room 1, Isaac Newton Institute (INI), University of Cambridge |
| Content | In this talk, we consider the regression problem where the input variable X is a continuous path from a non-parametric function class and the output response Y is the solution to the fixed but unknown controlled differential equation driven by the input X. It has a wide range of applications including time series forecasting and video classification. The difficulty in tackling this regression problem comes from the function type of the input variable, which leads to the infinite dimensionality of the input space and potential overfitting issue if not treated properly. Motivated by the numerical approximation theory of the stochastic differential equations, we propose an efficient algorithm based on the rough paths theory and neural network to learn the unknown solution map from data. The proposed model has the universality while exhibiting the better efficiency and robustness compared with RNN with raw data by several numerical examples. |
| URL | Page Link |