{"type":"ScholarlyArticle","title":"Structure-Preserving Physics-Informed Neural Networks with Energy or Lyapunov Structure","authors":[{"name":"Haoyu Chu","slug":"haoyu-chu","given":"Haoyu","family":"Chu","affiliation":"Institute of Information Science , Beijing Jiaotong University; Graduate School of Information Science and Technology , Osaka University; Beijing Key Laboratory of Advanced Information Science and Network Technology"},{"name":"Yuto Miyatake","slug":"yuto-miyatake","given":"Yuto","family":"Miyatake","affiliation":"Cybermedia Center , Osaka University"},{"name":"Wenjun Cui","slug":"wenjun-cui","given":"Wenjun","family":"Cui","affiliation":"School of Computer and Information Technology , Beijing Jiaotong University {19112001 , 19112048 ,"},{"name":"Shikui Wei","slug":"shikui-wei","given":"Shikui","family":"Wei","affiliation":"Institute of Information Science , Beijing Jiaotong University; Beijing Key Laboratory of Advanced Information Science and Network Technology"},{"name":"Daisuke Furihata","slug":"daisuke-furihata","given":"Daisuke","family":"Furihata","affiliation":"Cybermedia Center , Osaka University"}],"abstract":"Recently, there has been growing interest in using physics-informed neural networks (PINNs) to solve differential equations. However, the preservation of structure, such as energy and stability, in a suitable manner has yet to be established. This limitation could be a potential reason why the learning process for PINNs is not always efficient and the numerical results may suggest nonphysical behavior. Besides, there is little research on their applications on downstream tasks. To address these issues, we propose structure-preserving PINNs to improve their performance and broaden their applications for downstream tasks. Firstly, by leveraging prior knowledge about the physical system, a structure‐preserving loss function is designed to assist the PINN in learning the underlying structure. Secondly, a framework that utilizes structure-preserving PINN for robust image recognition is proposed. Here, preserving the Lyapunov structure of the underlying system ensures the stability of the system. Experimental results demonstrate that the proposed method improves the numerical accuracy of PINNs for partial differential equations (PDEs). Furthermore, the robustness of the model against adversarial perturbations in image data is enhanced.","doi":"10.24963/ijcai.2024/428","url":"https://ijcai.org/proceedings/2024/428","pdf":"https://ijcai.org/proceedings/2024/0428.pdf","markdown":"https://ijcai.org/proceedings/2024/428.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/428","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Machine Learning","track":"Main Track","number":428,"pages":{"first":3872,"last":3880},"keywords":["Computer Vision: CV: Machine learning for vision","Computer Vision: CV: Adversarial learning, adversarial attack and defense methods","Machine Learning: ML: Supervised Learning","Machine Learning: ML: Deep learning architectures"],"videos":[],"references":[{"position":1,"raw":"[Allen and Cahn, 1972] Samuel Miller Allen and John W Cahn. 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