{"type":"ScholarlyArticle","title":"Causality-enhanced Discreted Physics-informed Neural Networks for Predicting Evolutionary Equations","authors":[{"name":"Ye Li","slug":"ye-li","given":"Ye","family":"Li","affiliation":"College of Computer Science and Technology , Nanjing University of Aeronautics and Astronautics; MIIT Key Laboratory of Pattern Analysis and Machine Intelligence , Nanjing , China"},{"name":"Siqi Chen","slug":"siqi-chen","given":"Siqi","family":"Chen","affiliation":"College of Electronic and Information Engineering , Nanjing University of Aeronautics and Astronautics"},{"name":"Bin Shan","slug":"bin-shan","given":"Bin","family":"Shan","affiliation":""},{"name":"Sheng-Jun Huang","slug":"sheng-jun-huang","given":"Sheng-Jun","family":"Huang","affiliation":"College of Computer Science and Technology , Nanjing University of Aeronautics and Astronautics; MIIT Key Laboratory of Pattern Analysis and Machine Intelligence , Nanjing , China"}],"abstract":"Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. \r\nHowever, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical systems whose solutions exhibit multi-scale or turbulent behavior over time.\r\nThe reason is that PINNs may violate the temporal causality property since all the temporal features in the PINNs loss are trained simultaneously. \r\nThis paper proposes to use implicit time differencing schemes to enforce temporal causality, and use transfer learning to sequentially update the PINNs in space as surrogates for PDE solutions in different time frames.\r\nThe evolving PINNs are better able to capture the varying complexities of the evolutionary equations, while only requiring minor updates between adjacent time frames.\r\nOur method is theoretically proven to be convergent if the time step is small and each PINN in different time frames is well-trained.\r\nIn addition, we provide state-of-the-art (SOTA) numerical results for a variety of benchmarks for which existing PINNs formulations may fail or be inefficient.\r\nWe demonstrate that the proposed method improves the accuracy of PINNs approximation for evolutionary PDEs and improves efficiency by a factor of 4–40x.\r\nThe code is available at https://github.com/SiqiChen9/TL-DPINNs.","doi":"10.24963/ijcai.2024/497","url":"https://ijcai.org/proceedings/2024/497","pdf":"https://ijcai.org/proceedings/2024/0497.pdf","markdown":"https://ijcai.org/proceedings/2024/497.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/497","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":497,"pages":{"first":4497,"last":4505},"keywords":["Machine Learning: ML: Applications","Machine Learning: ML: Regression","Machine Learning: ML: Deep learning architectures","Machine Learning: ML: Causality"],"videos":[],"references":[{"position":1,"raw":"[Bradbury et al., 2018] James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake Vander- Plas, Skye Wanderman-Milne, and Qiao Zhang. 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