# Multi-material Multi-physics Topology Optimization with Physics-informed Gaussian Process Priors

arXiv: https://arxiv.org/abs/2602.17783 · HTML: https://mlsanity.com/paper/2602.17783/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 75 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Builds on (most cited first, 16 of 16)

- [Curriculum Learning: A Survey](https://mlsanity.com/paper/2101.10382/) (2021)
- [TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain](https://mlsanity.com/paper/2003.04685/) (2020)
- [Neural reparameterization improves structural optimization](https://mlsanity.com/paper/1909.04240/) (2019)
- [Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networks](https://mlsanity.com/paper/2105.00862/) (2021)
- [Neural topology optimization: the good, the bad, and the ugly](https://mlsanity.com/paper/2407.13954/) (2024)
- [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)
- [Deep energy method in topology optimization applications](https://mlsanity.com/paper/2207.03072/) (2022)
- [Large scale three-dimensional topology optimisation of heat sinks cooled by natural convection](https://mlsanity.com/paper/1508.04596/) (2015)
- [An AI-Assisted Design Method for Topology Optimization Without Pre-Optimized Training Data](https://mlsanity.com/paper/2012.06384/) (2020)
- [Computational synthesis of locomotive soft robots by topology optimization](https://mlsanity.com/paper/2310.10985/) (2023)
- [Localized Physics-informed Gaussian Processes with Curriculum Training for Topology Optimization](https://mlsanity.com/paper/2503.15561/) (2025)
- [Co-design of magnetic soft robots with large deformation and contacts via material point method and topology optimization](https://mlsanity.com/paper/2503.22767/) (2025)
- [Compliance Minimization via Physics-Informed Gaussian Processes](https://mlsanity.com/paper/2507.09968/) (2025)
- [Neural Co-Optimization of Structural Topology, Manufacturable Layers, and Path Orientations for Fiber-Reinforced Composites](https://mlsanity.com/paper/2505.03779/) (2025)
- [Large-Scale Topology Optimisation of Time-dependent Thermal Conduction Using Space-Time Finite Elements and a Parallel Space-Time Multigrid Preconditioner](https://mlsanity.com/paper/2508.09589/) (2025)

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

- [On the Importance of Geometric Nonlinearity and Temperature-Dependent Properties in Multi-Material Thermo-Mechanical Topology Optimization](https://mlsanity.com/paper/2608.10344/) (2026)
- [How the Classical Baseline Shapes Machine-Learning Speed Claims in Topology Optimization](https://mlsanity.com/paper/2610.16051/) (2026)

## Abstract (arXiv)

Machine learning (ML) has been increasingly used for topology optimization (TO). However, most existing ML-based approaches focus on simplified benchmark problems due to their high computational cost, spectral bias, and difficulty in handling complex physics. These limitations become more pronounced in multi-material, multi-physics problems whose objective or constraint functions are not self-adjoint. To address these challenges, we propose a framework based on physics-informed Gaussian processes (PIGPs). In our approach, the primary, adjoint, and design variables are represented by independent GP priors whose mean functions are parametrized via neural networks whose architectures are particularly beneficial for surrogate modeling of PDE solutions. We estimate all parameters of our model simultaneously by minimizing a loss that is based on the objective function, multi-physics potential energy functionals, and design-constraints. We demonstrate the capability of the proposed framework on benchmark TO problems such as compliance minimization, heat conduction optimization, and compliant mechanism design under single- and multi-material settings. Additionally, we leverage thermo-mechanical TO with single- and multi-material options as a representative multi-physics problem. We also introduce differentiation and integration schemes that dramatically accelerate the training process. Our results demonstrate that the proposed PIGP framework can effectively solve coupled multi-physics and design problems simultaneously -- generating super-resolution topologies with sharp interfaces and physically interpretable material distributions. We validate these results using open-source codes and the commercial software package COMSOL.