6 papers
Quantum-Classical Physics-Informed Kolmogorov-Arnold Networks for Solving Fuzzy Differential Equations
Xiang Rao, Yuxuan Shen
In this study, we propose a quantum-classical physics-informed Kolmogorov-Arnold network (QCPIKAN) dedicated to the solution of fuzzy differential equations. The network takes the…
Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs
Xiang Rao, Yuxuan Shen
We develop QCPIKAN, the first quantum-classical physics-informed Kolmogorov-Arnold network designed to solve partial differential equations (PDEs). Built upon Chebyshev-polynomial…
Quantum-Classical Physics-Informed Neural Networks for Solving Reservoir Seepage Equations
Xiang Rao, Yina Liu, Yuxuan Shen
Solving reservoir seepage partial differential equations (PDEs) is critical for hydrocarbon development optimization and production forecasting. Conventional numerical solvers suff…
A Novel Meshless Method Based on the Virtual Construction of Node Control Domains for Porous Flow Problems
Xiang Rao
In this paper, a novel meshless method that can handle porous flow problems with singular source terms is developed by virtually constructing the node control domains. By defining…
An Upwind Generalized Finite Difference Method (GFDM) for Meshless Analysis of Heat and Mass Transfer in Porous Media
Xiang Rao
In this paper, an upwind GFDM is developed for the coupled heat and mass transfer problems in porous media. GFDM is a meshless method that can obtain the difference schemes of spat…
An Upwind Generalized Finite Difference Method for Meshless Solution of Two-phase Porous Flow Equations
Xiang Rao, Yina Liu, Hui Zhao
This paper makes the first attempt to apply newly developed upwind GFDM for the meshless solution of two-phase porous flow equations. In the presented method, node cloud is used to…