7 papers
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…
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…