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math.NA2026
The Adaptive Solution of High-Frequency Helmholtz Equations via Multi-Grade Deep Learning
Peiyao Zhao, Rui Wang, Tingting Wu +1
The Helmholtz equation is fundamental for modeling wave propagation in acoustics, electromagnetics, and geophysics; however, high-frequency regimes remain notoriously difficult due…
math.NA2026
Adaptive Multi-Grade Deep Learning for Highly Oscillatory Fredholm Integral Equations of the Second Kind
Jie Jiang, Yuesheng Xu
This paper studies the use of Multi-Grade Deep Learning (MGDL) for solving highly oscillatory Fredholm integral equations of the second kind. We provide rigorous error analyses of…
math.NA2024
Deep Neural Network Solutions for Oscillatory Fredholm Integral Equations
Jie Jiang, Yuesheng Xu
We studied the use of deep neural networks (DNNs) in the numerical solution of the oscillatory Fredholm integral equation of the second kind. It is known that the solution of the e…