4 papers
Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equations
Benjamin J. Zhang, Siting Liu, Stanley J. Osher +1
In-context operator networks (ICON) are a class of operator learning methods based on the novel architectures of foundation models. Trained on a diverse set of datasets of initial…
iTRI-QA: a Toolset for Customized Question-Answer Dataset Generation Using Language Models for Enhanced Scientific Research
Qiming Liu, Zhongzheng Niu, Siting Liu +1
The exponential growth of AI in science necessitates efficient and scalable solutions for retrieving and preserving research information. Here, we present a tool for the developmen…
Wasserstein proximal operators describe score-based generative models and resolve memorization
Benjamin J. Zhang, Siting Liu, Wuchen Li +2
We focus on the fundamental mathematical structure of score-based generative models (SGMs). We first formulate SGMs in terms of the Wasserstein proximal operator (WPO) and demonstr…
Fine-Tune Language Models as Multi-Modal Differential Equation Solvers
Liu Yang, Siting Liu, Stanley J. Osher
In the growing domain of scientific machine learning, in-context operator learning has shown notable potential in building foundation models, as in this framework the model is trai…