# Localized Physics-informed Gaussian Processes with Curriculum Training for Topology Optimization

arXiv: https://arxiv.org/abs/2503.15561 · HTML: https://mlsanity.com/paper/2503.15561/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 27 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Builds on (most cited first, 10 of 10)

- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Curriculum Learning: A Survey](https://mlsanity.com/paper/2101.10382/) (2021)
- [Latent Map Gaussian Processes for Mixed Variable Metamodeling](https://mlsanity.com/paper/2102.03935/) (2021)
- [On the Convergence of Step Decay Step-Size for Stochastic Optimization](https://mlsanity.com/paper/2102.09393/) (2021)
- [GP+: A Python Library for Kernel-based learning via Gaussian Processes](https://mlsanity.com/paper/2312.07694/) (2023)
- [Student-Teacher Curriculum Learning via Reinforcement Learning: Predicting Hospital Inpatient Admission Location](https://mlsanity.com/paper/2007.01135/) (2020)
- [Parametric Encoding with Attention and Convolution Mitigate Spectral Bias of Neural Partial Differential Equation Solvers](https://mlsanity.com/paper/2403.15652/) (2024)
- [A Gaussian Process Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations](https://mlsanity.com/paper/2401.03492/) (2024)
- [A Curriculum-Training-Based Strategy for Distributing Collocation Points during Physics-Informed Neural Network Training](https://mlsanity.com/paper/2211.11396/) (2022)
- [Simultaneous and Meshfree Topology Optimization with Physics-informed Gaussian Processes](https://mlsanity.com/paper/2408.03490/) (2024)

## Built on by (most cited first, 2 of 2)

- [Compliance Minimization via Physics-Informed Gaussian Processes](https://mlsanity.com/paper/2507.09968/) (2025)
- [Multi-material Multi-physics Topology Optimization with Physics-informed Gaussian Process Priors](https://mlsanity.com/paper/2602.17783/) (2026)

## Abstract (arXiv)

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.