Physics-Informed Gaussian Processes with Localized Features for Topology Optimization

We introduce a simultaneous and meshfree topology optimization (TO) framework based on physics-informed Gaussian processes (GPs). In our approach, we parametrize all design and state variables via GP priors which have a shared multi-output mean function. This mean function is represented by a customized deep neural network (DNN) whose parameters are estimated by minimizing a multi-component loss function that depends on the performance metric, design constraints, and the residuals on the state equations. Our TO approach yields well-defined material interfaces and has a built-in continuation nature that promotes global optimality. Other unique features of our approach include (1) its customized DNN which has a localized learning capacity that enables capturing intricate topologies and reducing residuals in high gradient fields, (2) its loss function that leverages localized weights to promote solution accuracy around interfaces, and (3) its use of curriculum training to avoid local optimality. To demonstrate the power of our framework, we validate it against commercial TO package COMSOL on problems involving dissipated power minimization in Stokes flow.