In this paper, we propose a DeepONet structure with causality to represent the causal linear operators between Banach spaces of time-dependent signals. The theorem of universal approximations to nonlinear operators proposed in \cite{tianpingchen1995} 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.
翻译:在本文中,我们提出一个具有因果关系的深线结构,以代表巴纳赫时间依赖信号空间之间的因果关系线操作员。在\cite{tianpingchen1995}中提议的对非线性操作员的通用近似理论扩展至有因果关系的操作员,拟议中的Causality-DeepONet在其框架中规定了实际因果关系。拟议中的Causality-DeepONet考虑因果关系(系统目前的状况不受未来的影响,但仅受其当前状况和过去历史的影响),并在设计中使用共振式的重量。为了证明它在处理物理系统因果反应方面的有效性,Causality-DeepONet被用于学习代表因地震地面加速而产生的建筑物反应的操作员。与DeepONet的某些现有变体进行了广泛的数字测试和比较,Causality-DeepONet明确显示其独特的能力,可以正确了解地震反应操作员的迟缓动态反应。