Controlling Chaos in Van Der Pol Dynamics Using Signal-Encoded Deep Learning

Controlling nonlinear dynamics is a long-standing problem in engineering. Harnessing known physical information to accelerate or constrain stochastic learning pursues new paradigm of scientific machine learning. By linearizing systems, traditional control methods cannot learn features from chaotic data for use control. Here, we introduce Physics-Informed Deep Operator Control (PIDOC), and by encoding the signal initial position into losses physics-informed neural network (PINN), system forced exhibit desired trajectory given signal. PIDOC receives signals as physics commands learns output van der Pol system, where PINN Applied benchmark problem, successfully implements with higher stochasticity higher-order terms. has also been proven be capable converging different trajectories based on case studies. Initial positions slightly affect accuracy at beginning stage yet do not change overall quality. For highly able execute high compared problem. The depth width structure greatly convergence studies systems low nonlinearities. Surprisingly, enlarging does help improve proposed framework can potentially applied many controls.