Multiscale DeepONet for Nonlinear Operators in Oscillatory Function Spaces for Building Seismic Wave Responses

Abstract

In this paper, we propose a multiscale DeepONet to represent nonlinear operator between Banach spaces of highly oscillatory continuous functions. The multiscale deep neural network (DNN) utilizes a multiple scaling technique to convert high frequency function to lower frequency functions before using a DNN to learn a specific range of frequency of the function. The multi-scale concept is integrated into the DeepONet which is based on a universal approximation theory of nonlinear operators. The resulting multi-scale DeepONet is shown to be effective to represent building seismic response operator which maps oscillatory seismic excitation to the oscillatory building responses.

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• Solving high-dimensional partial differential equations using deep learning
• NSFnets (Navier-Stokes Flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations
• Fourier Neural Operator for Parametric Partial Differential Equations

Cited by in corpus (5)

• Reliable extrapolation of deep neural operators informed by physics or sparse observations
• Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems
• SVD Perspectives for Augmenting DeepONet Flexibility and Interpretability
• RiemannONets: Interpretable Neural Operators for Riemann Problems
• Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows