2 citations · 3 across the 6 of their papers we have counts for
6 papers
Mathematical Foundations of Deep Learning
Xiaojing Ye
This draft book offers a comprehensive and rigorous treatment of the mathematical principles underlying modern deep learning. The book spans core theoretical topics, from the appro…
Maximum Principle of Optimal Probability Density Control
Nathan Gaby, Xiaojing Ye
We develop a general theoretical framework for optimal probability density control on standard measure spaces, aimed at addressing large-scale multi-agent control problems. In part…
A parameterized Wasserstein Hamiltonian flow approach for solving the Schrödinger equation
Hao Wu, Shu Liu, Xiaojing Ye +1
In this paper, we propose a new method to compute the solution of time-dependent Schrödinger equation (TDSE). Using push-forward maps and Wasserstein Hamiltonian flow, we reformula…
Parameterized Wasserstein Gradient Flow
Yijie Jin, Shu Liu, Hao Wu +2
We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduc…
Approximation of Solution Operators for High-dimensional PDEs
Nathan Gaby, Xiaojing Ye
We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By em…
Approximating High-Dimensional Minimal Surfaces with Physics-Informed Neural Networks
Steven Zhou, Xiaojing Ye
In this paper, we compute numerical approximations of the minimal surfaces, an essential type of Partial Differential Equation (PDE), in higher dimensions. Classical methods cannot…