A Causality-DeepONet for Causal Responses of Linear Dynamical Systems (Communications in Computational Physics, 2024)
In this paper, we propose a DeepONet structure with causality to representcausal linear operators between Banach spaces of time-dependent signals. The theorem of universal approximations to nonlinear operators proposed in [5] is extendedto operators with causalities, and the proposed Causality-DeepONet implements thephysical causality in its framework. The proposed Causality-DeepONet considerscausality (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 weightin its design. To demonstrate its effectiveness in handling the causal response of aphysical system, the Causality-DeepONet is applied to learn the operator representingthe 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 retardeddynamic responses of the seismic response operator with good accuracy.