This paper proposes an improved version of physics-informed neural networks (PINNs), the physics-informed kernel function neural networks (PIKFNNs), to solve various linear and some specific nonlinear ...
Differential equations are involved in modeling many engineering problems. Many efforts have been devoted to solving differential equations. Due to the flexibility of neural networks, Physics Informed ...
Evolution equations with convolution-type integral operators have a history of study, yet a gap exists in the literature regarding the link between certain convolution kernels and new models, ...
This paper proposes an efficient numerical method to obtain analytical-numerical solutions for a class of system of boundary value problems. This new algorithm is based on a reproducing kernel Hilbert ...
We study the regularity properties of solutions for various classes of Volterra functional integrodifferential equations with nonvanishing delays and weakly singular kernels. In particular, we ...
Abstract: The overall goal of the paper is to develop a deep kernel principal component analysis (KPCA) for time-dependent data that are nonlinearly distributed in high dimensions. Instead of ...
Boundary integral equation (BIE) methods have emerged as a robust computational framework for addressing problems in elasticity analysis by reformulating partial differential equations into equivalent ...
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