{"title":"A Causality-DeepONet for Causal Responses of Linear Dynamical Systems","authors":"Lizuo Liu,Kamaljyoti Nath, Wei Cai","doi":"10.4208/cicp.oa-2023-0078","DOIUrl":null,"url":null,"abstract":"In this paper, we propose a DeepONet structure with causality to represent\ncausal linear operators between Banach spaces of time-dependent signals. The theorem of universal approximations to nonlinear operators proposed in [5] is extended\nto operators with causalities, and the proposed Causality-DeepONet implements the\nphysical causality in its framework. The proposed Causality-DeepONet considers\ncausality (the state of the system at the current time is not affected by that of the future, but only by its current state and past history) and uses a convolution-type weight\nin its design. To demonstrate its effectiveness in handling the causal response of a\nphysical system, the Causality-DeepONet is applied to learn the operator representing\nthe response of a building due to earthquake ground accelerations. Extensive numerical tests and comparisons with some existing variants of DeepONet are carried out,\nand the Causality-DeepONet clearly shows its unique capability to learn the retarded\ndynamic responses of the seismic response operator with good accuracy.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Computational Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.4208/cicp.oa-2023-0078","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we propose a DeepONet structure with causality to represent
causal linear operators between Banach spaces of time-dependent signals. The theorem of universal approximations to nonlinear operators proposed in [5] is extended
to operators with causalities, and the proposed Causality-DeepONet implements the
physical causality in its framework. The proposed Causality-DeepONet considers
causality (the state of the system at the current time is not affected by that of the future, but only by its current state and past history) and uses a convolution-type weight
in its design. To demonstrate its effectiveness in handling the causal response of a
physical system, the Causality-DeepONet is applied to learn the operator representing
the response of a building due to earthquake ground accelerations. Extensive numerical tests and comparisons with some existing variants of DeepONet are carried out,
and the Causality-DeepONet clearly shows its unique capability to learn the retarded
dynamic responses of the seismic response operator with good accuracy.
期刊介绍:
Communications in Computational Physics (CiCP) publishes original research and survey papers of high scientific value in computational modeling of physical problems. Results in multi-physics and multi-scale innovative computational methods and modeling in all physical sciences will be featured.