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 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.展开更多
基金supported by the US National Science Foundation grant DMS-2207449supported by OSD/AFOSR MURI grant FA9550-20-1-0358。
文摘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.
