论文标题
线性动力学系统因果关系的因果关系深处
A Causality-DeepONet for Causal Responses of Linear Dynamical Systems
论文作者
论文摘要
在本文中，我们提出了一种具有因果关系的deponet结构，以代表时间依赖性信号的Banach空间之间的因果线性算子。在\ cite {tianpingchen1995}中提出的非线性算子的通用近似值扩展到有因果关系的运营商，并且提议的因果关系 - 深处在其框架中实现了物理因果关系。拟议的因果关系 - 深处考虑因果关系（当前系统状态不受未来的影响，而仅受当前状态和过去历史的影响），并且在其设计中使用了卷积型重量。为了证明其在处理物理系统的因果反应方面的有效性，应用因果关系，以学习代表由于地震地面加速而建筑物响应的操作员。进行了广泛的数值测试和与Deponet的某些现有变体进行的比较，而因果关系深层人群清楚地表明了其独特的能力，可以很好地学习地震响应操作员的动态反应的迟滞性动态响应。
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.
