Zexin Sun

Zexin Sun, Mingyu Chen, John Baillieul

Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and invariably unmodeled dynamics present challenges in making precise predictions. In this paper, we present a novel data-driven linear estimator based on Koopman operator theory to extract meaningful finite-dimensional representations of complex non-linear systems. The Koopman model is used together with deep reinforcement networks that learn the optimal stepwise actions to predict future states of nonlinear systems. Our estimator is also adaptive to a diffeomorphic transformation of the estimated nonlinear system, which enables it to compute optimal state estimates without re-learning.

Zexin Sun, John Baillieul

Building on our recent research on neural heuristic quantization systems, results on learning quantized motions and resilience to channel dropouts are reported. We propose a general emulation problem consistent with the neuromimetic paradigm. This optimal quantization problem can be solved by model predictive control (MPC), but because the optimization step involves integer programming, the approach suffers from combinatorial complexity when the number of input channels becomes large. Even if we collect data points to train a neural network simultaneously, collection of training data and the training itself are still time-consuming. Therefore, we propose a general Deep Q Network (DQN) algorithm that can not only learn the trajectory but also exhibit the advantages of resilience to channel dropout. Furthermore, to transfer the model to other emulation problems, a mapping-based transfer learning approach can be used directly on the current model to obtain the optimal direction for the new emulation problems.