Controlling the nonlinear configuration space of mechanical and dynamical systems

From decision making in neural systems to cooperativity in proteins, soft and biological systems exhibit an extraordinarily diverse yet carefully crafted complexity. The specific interactions between constituent elements such as neurons and amino acids enforce dynamical and mechanical constraints, thereby enabling these systems to evolve according to the precise algorithms that govern biological functions such as neural representations and enzyme catalysis. To control these functions, we require knowledge of both the forward map from known interactions to their corresponding dynamical and mechanical functions, and the inverse map from the desired functions to the interactions that evoke them. However, knowledge of these maps is made difficult due to the nonlinearities in both the interactions and the functions. In this talk, I will discuss several strategies for how to obtain these maps to wield control over the nonlinear configuration space. For dynamical systems, I will demonstrate how to embed nonlinear and controllable dynamics into a recurrent neural network (RNN) via its connectivity weights, and how to decode the dynamics learned by trained RNNs. For mechanical systems, I will demonstrate how to control the nonlinear sequence and geometry of conformational shape change in mechanical linkages.