1 code implementation • 15 Jul 2024 • Xinling Yu, Sean Hooten, Ziyue Liu, Yequan Zhao, Marco Fiorentino, Thomas Van Vaerenbergh, Zheng Zhang
We provide a universal approximation theorem for SepONet proving the existence of a separable approximation to any nonlinear continuous operator.
no code implementations • 31 Dec 2023 • Yequan Zhao, Xian Xiao, Xinling Yu, Ziyue Liu, Zhixiong Chen, Geza Kurczveil, Raymond G. Beausoleil, Zheng Zhang
Despite the ultra-high speed of optical neural networks, training a PINN on an optical chip is hard due to (1) the large size of photonic devices, and (2) the lack of scalable optical memory devices to store the intermediate results of back-propagation (BP).
no code implementations • 18 Aug 2023 • Yequan Zhao, Xinling Yu, Zhixiong Chen, Ziyue Liu, Sijia Liu, Zheng Zhang
Backward propagation (BP) is widely used to compute the gradients in neural network training.
1 code implementation • 25 Feb 2023 • Ziyue Liu, Yixing Li, Jing Hu, Xinling Yu, Shinyu Shiau, Xin Ai, Zhiyu Zeng, Zheng Zhang
In this paper, for the first time, we propose DeepOHeat, a physics-aware operator learning framework to predict the temperature field of a family of heat equations with multiple parametric or non-parametric design configurations.
no code implementations • 23 Feb 2023 • Xinling Yu, José E. C. Serrallés, Ilias I. Giannakopoulos, Ziyue Liu, Luca Daniel, Riccardo Lattanzi, Zheng Zhang
PIFON-EPT is the first method that can simultaneously reconstruct EP and transmit fields from incomplete noisy MR measurements, providing new opportunities for EPT research.
no code implementations • 23 Oct 2022 • Xinling Yu, José E. C. Serrallés, Ilias I. Giannakopoulos, Ziyue Liu, Luca Daniel, Riccardo Lattanzi, Zheng Zhang
Electrical properties (EP), namely permittivity and electric conductivity, dictate the interactions between electromagnetic waves and biological tissue.
no code implementations • 4 Jul 2022 • Ziyue Liu, Xinling Yu, Zheng Zhang
Physics-informed neural networks (PINNs) have been increasingly employed due to their capability of modeling complex physics systems.
1 code implementation • 28 Jul 2020 • Sifan Wang, Xinling Yu, Paris Perdikaris
In this work, we aim to investigate these questions through the lens of the Neural Tangent Kernel (NTK); a kernel that captures the behavior of fully-connected neural networks in the infinite width limit during training via gradient descent.