Physics-informed neural networks for PDE-constrained optimization and control
This addresses the challenge of PDE-constrained optimization and control in science and engineering, offering a novel one-stage approach that could improve efficiency over prior two-stage methods.
The paper tackles the problem of designing optimal control policies for physical systems by proposing Control Physics-Informed Neural Networks (Control PINNs), which solve for system states and optimal control signals in a one-stage framework, demonstrating success on analytical, one-dimensional heat equation, and two-dimensional predator-prey problems.
A fundamental problem in science and engineering is designing optimal control policies that steer a given system towards a desired outcome. This work proposes Control Physics-Informed Neural Networks (Control PINNs) that simultaneously solve for a given system state, and for the optimal control signal, in a one-stage framework that conforms to the underlying physical laws. Prior approaches use a two-stage framework that first models and then controls a system in sequential order. In contrast, a Control PINN incorporates the required optimality conditions in its architecture and in its loss function. The success of Control PINNs is demonstrated by solving the following open-loop optimal control problems: (i) an analytical problem, (ii) a one-dimensional heat equation, and (iii) a two-dimensional predator-prey problem.