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cs.LG2023★ 2 cited
Harnessing the Power of Neural Operators with Automatically Encoded Conservation Laws
Ning Liu, Yiming Fan, Xianyi Zeng +3
Neural operators (NOs) have emerged as effective tools for modeling complex physical systems in scientific machine learning. In NOs, a central characteristic is to learn the govern…
math.NA2023
An Explicit Fourth-Order Hybrid-Variable Method for Euler Equations with A Residual-Consistent Viscosity
Xianyi Zeng
In this paper we present a formally fourth-order accurate hybrid-variable method for the Euler equations in the context of method of lines. The hybrid-variable (HV) method seeks nu…
math.DS2023
Equivariant Hopf Bifurcation in a Class of Partial Functional Differential Equations on a Circular Domain
Yaqi Chen, Xianyi Zeng, Ben Niu
Circular domains frequently appear in the fields of ecology, biology and chemistry. In this paper, we investigate the equivariant Hopf bifurcation of partial functional differentia…