Morse-Smale Systems and Machine Learning

Recurrent Neural Networks (RNNs) are seen as a powerful tool in dealing with time series data generated by physical systems with dynamics because RNNs have their own internal dynamics. However, they are limited in the tasks they can perform and are often difficult to train. Since RNNs effectively simulate a dynamical system, some of their inherent drawbacks are due to their heavily constrained energy landscape. We introduce and explore an alternative, non-neuron based learning method using a broader class of dynamical systems called Morse-Smale systems. The extra freedom in the complexity of the energy landscape allows for a more efficient use of dimensions, leading to significant learning even in two dimensions. In this talk, we will show that Morse-Smale systems have significant advantages over conventional neural networks in classifying time series data, which show up across condensed matter physics. This shows how dynamical systems can improve algorithms, which are in turn used to analyze dynamical data from physical systems.