Multi-material Multi-physics Topology Optimization with Physics-informed Gaussian Process Priors
arXiv:2602.17783v1 Announce Type: new Abstract: 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 demo
arXiv:2602.17783v1 Announce Type: new Abstract: 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.
Executive Summary
The article presents a novel framework for multi-material, multi-physics topology optimization (TO) using physics-informed Gaussian processes (PIGPs). The proposed approach addresses the limitations of existing machine learning-based TO methods by incorporating physics-informed priors and leveraging neural networks for surrogate modeling. The framework is demonstrated on various benchmark problems, including compliance minimization, heat conduction optimization, and thermo-mechanical TO. The results show that the PIGP framework can effectively solve coupled multi-physics and design problems, generating topologies with sharp interfaces and physically interpretable material distributions. The article also introduces acceleration schemes for the training process, which significantly improve the efficiency of the method. The proposed framework has the potential to revolutionize the field of TO, enabling the design of complex systems with multiple materials and physics.
Key Points
- ▸ The article proposes a novel framework for multi-material, multi-physics TO using PIGPs.
- ▸ The framework addresses the limitations of existing ML-based TO methods by incorporating physics-informed priors.
- ▸ The approach leverages neural networks for surrogate modeling and introduces acceleration schemes for the training process.
Merits
Improves upon existing ML-based TO methods
The proposed framework addresses the limitations of existing ML-based TO methods, such as high computational cost, spectral bias, and difficulty in handling complex physics.
Enables the design of complex systems with multiple materials and physics
The framework can effectively solve coupled multi-physics and design problems, generating topologies with sharp interfaces and physically interpretable material distributions.
Demerits
Computational cost remains a challenge
While the proposed framework introduces acceleration schemes, the computational cost of the method remains a challenge, particularly for large-scale problems.
Lack of generalizability to other fields
The framework is specifically designed for TO problems and may not be directly applicable to other fields, such as materials science or engineering design.
Expert Commentary
The article presents a novel and promising approach to TO, leveraging the power of machine learning and physics-informed priors to address the challenges of complex systems with multiple materials and physics. While the framework shows significant promise, it is essential to continue exploring its limitations and potential applications. The introduction of acceleration schemes for the training process is a significant step forward, but further work is needed to improve the efficiency and scalability of the method. The proposed framework has the potential to revolutionize the field of TO, enabling the design of complex systems with multiple materials and physics, which can have significant implications for policy-making and practical applications.
Recommendations
- ✓ Further research is needed to explore the limitations and potential applications of the proposed framework.
- ✓ The framework should be tested on a wider range of problems and applications to demonstrate its generalizability and robustness.
