1 citations · 1 across the 4 of their papers we have counts for
4 papers
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…
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…
Neural Control of Parametric Solutions for High-dimensional Evolution PDEs
Nathan Gaby, Xiaojing Ye, Haomin Zhou
We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs). By employing a general nonlinear reduced-order mode…
Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximation
Nathan Gaby, Fumin Zhang, Xiaojing Ye
We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net guarantees pos…