A radial basis function neural network approach for solving a diffusion partial differential equation efficiently

Tao Liu and Bolin Ding

Applied Mathematics and Computation, 2026, vol. 509, issue C

Abstract: This paper presents an approach that utilizes TensorFlow to construct a computational graph for solving a time-dependent partial differential equation using kernel-based approximations. Although TensorFlow is predominantly known for its deep learning applications, it also offers tools for numerical computations involving tensors. The proposed method leverages TensorFlow's capabilities to achieve efficient approximations. Compared to traditional methods, this approach highlights its potential for computationally solving partial differential equations on regular domains.

Keywords: Machine learning; Neural network; Kernel-based approximation; TensorFlow; Diffusion PDE; Adam optimizer (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:509:y:2026:i:c:s0096300325003777

DOI: 10.1016/j.amc.2025.129651

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