| Content | In this talk, motivated by the numerical approximation theory of the stochastic differential equations, we propose an effective algorithm (Logsig-RNN model) to learn the unknown solution map from data by combining the log signature feature set and the recurrent neural network (RNN). The proposed model is proved to have the universality while exhibiting better efficiency compared with RNN with raw data. We validate the effectiveness of the proposed algorithm in both the simulated data and the empirical datasets, i.e. handwritten digit data and gesture recognition data. Those numerical experiments demonstrate superior performance of our algorithm when the sampling frequency of the input data is getting finer and finer. Furthermore, it shows the robustness even for the case the distribution of the driving path in the training set is different from that of the testing set. |