# Dynamically configured physics-informed neural network in topology optimization applications

arXiv: https://arxiv.org/abs/2312.06993 · HTML: https://mlsanity.com/paper/2312.06993/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 61 references that are in the map.
- First posted on arXiv 12 Dec 2023.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications](https://mlsanity.com/paper/1908.10407/) (2019)
- [TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain](https://mlsanity.com/paper/2003.04685/) (2020)
- [Deep learning for determining a near-optimal topological design without any iteration](https://mlsanity.com/paper/1801.05463/) (2018)
- [A Physics-Guided Neural Network Framework for Elastic Plates: Comparison of Governing Equations-Based and Energy-Based Approaches](https://mlsanity.com/paper/2010.06050/) (2020)
- [Meshless physics-informed deep learning method for three-dimensional solid mechanics](https://mlsanity.com/paper/2012.01547/) (2020)
- [Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy](https://mlsanity.com/paper/2012.15744/) (2020)
- [Topology Optimization via Machine Learning and Deep Learning: A Review](https://mlsanity.com/paper/2210.10782/) (2022)
- [Generative Design by Reinforcement Learning: Enhancing the Diversity of Topology Optimization Designs](https://mlsanity.com/paper/2008.07119/) (2020)
- [IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures](https://mlsanity.com/paper/2103.02588/) (2021)
- [Data-Driven Multiscale Design of Cellular Composites with Multiclass Microstructures for Natural Frequency Maximization](https://mlsanity.com/paper/2106.06478/) (2021)
- [Deep energy method in topology optimization applications](https://mlsanity.com/paper/2207.03072/) (2022)

## Built on by (most cited first, 3 of 3)

- [Precise-Physics Driven Text-to-3D Generation](https://mlsanity.com/paper/2403.12438/) (2024)
- [Improved Physics-informed neural networks loss function regularization with a variance-based term](https://mlsanity.com/paper/2412.13993/) (2024)
- [Compliance Minimization via Physics-Informed Gaussian Processes](https://mlsanity.com/paper/2507.09968/) (2025)

## Abstract (arXiv)

Integration of machine learning (ML) into the topology optimization (TO) framework is attracting increasing attention, but data acquisition in data-driven models is prohibitive. Compared with popular ML methods, the physics-informed neural network (PINN) can avoid generating enormous amounts of data when solving forward problems and additionally provide better inference. To this end, a dynamically configured PINN-based topology optimization (DCPINN-TO) method is proposed. The DCPINN is composed of two subnetworks, namely the backbone neural network (NN) and the coefficient NN, where the coefficient NN has fewer trainable parameters. The designed architecture aims to dynamically configure trainable parameters; that is, an inexpensive NN is used to replace an expensive one at certain optimization cycles. Furthermore, an active sampling strategy is proposed to selectively sample collocations depending on the pseudo-densities at each optimization cycle. In this manner, the number of collocations will decrease with the optimization process but will hardly affect it. The Gaussian integral is used to calculate the strain energy of elements, which yields a byproduct of decoupling the mapping of the material at the collocations. Several examples with different resolutions validate the feasibility of the DCPINN-TO method, and multiload and multiconstraint problems are employed to illustrate its generalization. In addition, compared to finite element analysis-based TO (FEA-TO), the accuracy of the displacement prediction and optimization results indicate that the DCPINN-TO method is effective and efficient.