A Causality-DeepONet for Causal Responses of Linear Dynamical Systems

IF 2.6 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Communications in Computational Physics Pub Date : 2024-06-01 DOI:10.4208/cicp.oa-2023-0078
Lizuo Liu,Kamaljyoti Nath, Wei Cai
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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.
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线性动力系统因果响应的因果深网
在本文中,我们提出了一种具有因果性的 DeepONet 结构,用于表示时间相关信号的巴拿赫空间之间的因果线性算子。本文将[5]中提出的非线性算子通用近似定理扩展到了具有因果性的算子,并在其框架中实现了物理因果性。所提出的 Causality-DeepONet 考虑了因果性(系统当前的状态不受未来状态的影响,只受当前状态和过去历史的影响),并在设计中使用了卷积型权重。为了证明其在处理物理系统因果响应方面的有效性,我们将因果-深度网络用于学习表示建筑物在地震地面加速度作用下的响应的算子。我们进行了广泛的数值测试,并与 DeepONet 的一些现有变体进行了比较,结果清楚地表明,因果-DeepONet 具有独特的能力,能够准确地学习地震响应算子的迟滞动态响应。
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来源期刊
Communications in Computational Physics
Communications in Computational Physics 物理-物理:数学物理
CiteScore
4.70
自引率
5.40%
发文量
84
审稿时长
9 months
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.
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