Physics-informed shape optimization using coordinate projection

• Published in: Scientific reports Vol. 14; no. 1; pp. 6537 - 12
• Main Authors: Zhang, Zhizhou, Lin, Chungwei, Wang, Bingnan
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 19.03.2024; Nature Publishing Group; Nature Portfolio
• Subjects: 639/301/1034; 639/705/1042; 639/766/25; Adaptability; Artificial intelligence; Coordinate projection; Design; Finite element method; Humanities and Social Sciences; multidisciplinary; Neural networks; Optimization; Permeability; Physics; Physics-informed neural network; Science; Science (multidisciplinary); Shape optimization; Structural engineering; Weak formulation; Physics-informed neural network; Coordinate projection; Weak formulation; Shape optimization
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-024-57137-4

The rapid growth of artificial intelligence is revolutionizing classical engineering society, offering novel approaches to material and structural design and analysis. Among various scientific machine learning techniques, physics-informed neural network (PINN) has been one of the most researched subjects, for its ability to incorporate physics prior knowledge into model training. However, the intrinsic continuity requirement of PINN demands the adoption of domain decomposition when multiple materials with distinct properties exist. This greatly complicates the gradient computation of design features, restricting the application of PINN to structural shape optimization. To address this, we present a novel framework that employs neural network coordinate projection for shape optimization within PINN. This technique allows for direct mapping from a standard shape to its optimal counterpart, optimizing the design objective without the need for traditional transition functions or the definition of intermediate material properties. Our method demonstrates a high degree of adaptability, allowing the incorporation of diverse constraints and objectives directly as training penalties. The proposed approach is tested on magnetostatic problems for iron core shape optimization, a scenario typically plagued by the high permeability contrast between materials. Validation with finite-element analysis confirms the accuracy and efficiency of our approach. The results highlight the framework’s capability as a viable tool for shape optimization in complex material design tasks.