36 citations · 51 across the 10 of their papers we have counts for
10 papers
Generic Metrics on Preclude Linearly Stable Singular Tangent Cones of Area-Minimizing Boundaries
Zehua Cheng
We prove that for a residual (and hence dense) subset of Riemannian metrics on in the topology, no area-minimizing integral -current that is a bo…
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…
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…
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…
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…
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…
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…
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…
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…