4 papers
An alternating learning-based collocation method for solving inverse elliptic problems
Zhizhong Kong, Jerry Zhijian Yang, Cheng Yuan
We propose the Alternating Learning-Based Collocation (ALBC) method for solving inverse elliptic problems. Our approach employs sinusoidal shallow networks as adaptive basis genera…
Nonlinear Assimilation via Score-based Sequential Langevin Sampling
Zhao Ding, Chenguang Duan, Yuling Jiao +3
This paper introduces score-based sequential Langevin sampling (SSLS), a novel approach to nonlinear data assimilation within a recursive Bayesian filtering framework. The proposed…
Provable Diffusion Posterior Sampling for Bayesian Inversion
Jinyuan Chang, Chenguang Duan, Yuling Jiao +3
We propose a novel diffusion-based posterior sampling method within a plug-and-play framework. Our approach constructs a probability transport from an easy-to-sample distribution t…
A weighted scalar auxiliary variable method for solving gradient flows: bridging the nonlinear energy-based and Lagrange multiplier approaches
Qiong-Ao Huang, Wei Jiang, Jerry Zhijian Yang +1
Two primary scalar auxiliary variable (SAV) approaches are widely applied for simulating gradient flow systems, i.e., the nonlinear energy-based approach and the Lagrange multiplie…