Publications (17)
Revisiting Factorizing Aggregated Posterior in Learning Disentangled Representations
Ze Cheng, Juncheng Li, Chenxu Wang +4
In the problem of learning disentangled representations, one of the promising methods is to factorize aggregated posterior by penalizing the total correlation of sampled latent var…
Shooting Method with Sign-Changing Nonlinearity
Ze Cheng, Congming Li
In this paper, we study the existence of solution to a nonlinear system: \begin{align} \left\{\begin{array}{cl} -Îu_{i} = f_{i}(u) & \text{in } \mathbb{R}^n, u_{i} > 0 & \text{in…
NUNO: A General Framework for Learning Parametric PDEs with Non-Uniform Data
Songming Liu, Zhongkai Hao, Chengyang Ying +3
The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly n…
Accelerating PDE-Constrained Optimization by the Derivative of Neural Operators
Ze Cheng, Zhuoyu Li, Xiaoqiang Wang +4
PDE-Constrained Optimization (PDECO) problems can be accelerated significantly by employing gradient-based methods with surrogate models like neural operators compared to tradition…
GNOT: A General Neural Operator Transformer for Operator Learning
Zhongkai Hao, Zhengyi Wang, Hang Su +6
Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in prac…
A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEs
Songming Liu, Zhongkai Hao, Chengyang Ying +3
We present a unified hard-constraint framework for solving geometrically complex PDEs with neural networks, where the most commonly used Dirichlet, Neumann, and Robin boundary cond…
An Extended Discrete Hardy-Littlewood-Sobolev Inequality
Ze Cheng, Congming Li
Hardy-Littlewood-Sobolev (HLS) Inequality fails in the "critical" case: μ=n. However, for discrete HLS, we can derive a finite form of HLS inequality with logarithm correction for…
Reference Neural Operators: Learning the Smooth Dependence of Solutions of PDEs on Geometric Deformations
Ze Cheng, Zhongkai Hao, Xiaoqiang Wang +6
For partial differential equations on domains of arbitrary shapes, existing works of neural operators attempt to learn a mapping from geometries to solutions. It often requires a l…
BridgeDrive: Diffusion Bridge Policy for Closed-Loop Trajectory Planning in Autonomous Driving
Shu Liu, Wenlin Chen, Weihao Li +7
Diffusion-based planners have shown strong potential for autonomous driving by capturing multi-modal driving behaviors. A key challenge is how to effectively guide these models for…
Operator Learning with Domain Decomposition for Geometry Generalization in PDE Solving
Jianing Huang, Kaixuan Zhang, Youjia Wu +1
Neural operators have become increasingly popular in solving \textit{partial differential equations} (PDEs) due to their superior capability to capture intricate mappings between f…
Heavily Enhanced Dynamic Stark Shift in a System of Bose Einstein Condensation of Photons
Weikang Fan, Miao Yin, Ze Cheng
The dynamic Stark shift of a high-lying atom in a system of Bose Einstein condensation (BEC) of photons is discussed within the framework of nonrelativistic quantum electrodynamics…
Electron transport in a ferromagnetic/normal/ferromagnetic tunnel junction based on the surface of a topological insulator
Jian-Hui Yuan, Yan Zhang, Jian-Jun Zhang +1
We theoretically study the electron transport properties in a ferromagnetic/normal/ferromagnetic tunnel junction, which is deposited on the top of a topological surface. The conduc…
A Liouville theorem for subcritical Lane-Emden system
Ze Cheng, Genggeng Huang, Congming Li
In this paper, we present a necessary and sufficient condition to the Lane-Emden conjecture. This condition is an energy type of integral estimate on solutions to subcritical Lane-…
On the Hardy-Littlewood-Sobolev type systems
Ze Cheng, Genggeng Huang, Congming Li
In this paper, we study some qualitative properties of Hardy-Littlewood-Sobolev type systems. The HLS type systems are categorized into three cases: critical, supercritical and sub…
Qualitative analysis of three-wave interaction with periodic boundary condition
Ze Cheng, Harvey Segur
First, for 3WRI with positive wave energy, we present a regularity theorem for all spatial dimension. Second, for 3WRI with negative wave energy, we present a class of solution in…
Bi-level Physics-Informed Neural Networks for PDE Constrained Optimization using Broyden's Hypergradients
Zhongkai Hao, Chengyang Ying, Hang Su +3
Deep learning based approaches like Physics-informed neural networks (PINNs) and DeepONets have shown promise on solving PDE constrained optimization (PDECO) problems. However, exi…
Bose-Einstein condensation of photons in the matter-dominated universe
Ze Cheng
In 1914, Planck introduced the concept of a white body. In nature, no true white bodies are known. We assume that the universe after last-scattering is an ideal white body that con…