10 papers
Physics-guided correction for operator learning under model misspecification
Lei Ma, Nicolas Boullé, Yu-Sen Yang +2
Physics-informed operator learning provides an efficient framework for approximating solution operators of partial differential equations by combining observational data with gover…
Latent representation learning based model correction and uncertainty quantification for PDEs
Wenwen Zhou, Xiaodong Feng, Ling Guo +1
Model correction is essential for reliable PDE learning when the governing physics is misspecified due to simplified assumptions or limited observations. In the machine learning li…
FNWoS: Fractional Neural Walk-on-Spheres Methods for High-Dimensional PDEs Driven by -stable Lévy Process on Irregular Domains
Ling Guo, Mingxin Qin, Changtao Sheng +2
In this paper, we develop a highly parallel and derivative-free fractional neural walk-on-spheres method (FNWoS) for solving high-dimensional fractional Poisson equations on irregu…
Operator learning on domain boundary through combining fundamental solution-based artificial data and boundary integral techniques
Haochen Wu, Heng Wu, Benzhuo Lu
For linear partial differential equations with known fundamental solutions, this work introduces a novel operator learning framework that relies exclusively on domain boundary data…
Deep set based operator learning with uncertainty quantification
Lei Ma, Ling Guo, Hao Wu +1
Learning operators from data is central to scientific machine learning. While DeepONets are widely used for their ability to handle complex domains, they require fixed sensor numbe…
A Convergent Primal-Dual Algorithm for Computing Rate-Distortion-Perception Functions
Chunhui Chen, Linyi Chen, Xueyan Niu +1
Recent advances in Rate-Distortion-Perception (RDP) theory highlight the importance of balancing compression level, reconstruction quality, and perceptual fidelity. While previous…
LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process
Xiaodong Feng, Ling Guo, Xiaoliang Wan +3
We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The…
Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems
Xintong Wang, Xiaofei Guan, Ling Guo +1
Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems is a fundamental yet challenging problem in many fields of science and engineering. Existing methods…
Marcinkiewicz--Zygmund inequalities for scattered data on polygons
Hao-Ning Wu
Given a set of scattered points on a regular or irregular 2D polygon, we aim to employ them as quadrature points to construct a quadrature rule that establishes Marcinkiewicz--Zygm…
On Convergence of Discrete Schemes for Computing the Rate-Distortion Function of Continuous Source
Lingyi Chen, Shitong Wu, Wenyi Zhang +2
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typica…