Localized Physics-informed Gaussian Processes with Curriculum Training for Topology Optimization
This work addresses topology optimization for engineering design, offering a meshfree method with localized learning, but it appears incremental as it builds on existing physics-informed machine learning approaches.
The paper tackles topology optimization by introducing a physics-informed Gaussian process framework with a customized deep neural network and curriculum training, achieving well-defined material interfaces and built-in continuation for global optimality, validated against COMSOL on Stokes flow problems.
We introduce a simultaneous and meshfree topology optimization (TO) framework based on physics-informed Gaussian processes (GPs). Our framework endows all design and state variables via GP priors which have a shared, multi-output mean function that is parametrized via a customized deep neural network (DNN). The parameters of this mean function 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, unlike fully connected feed-forward DNNs, 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 three problems involving dissipated power minimization in Stokes flow.