no code implementations • 9 Feb 2024 • Benjamin J. Zhang, Siting Liu, Wuchen Li, Markos A. Katsoulakis, Stanley J. Osher
Via a Cole-Hopf transformation and taking advantage of the fact that the cross-entropy can be related to a linear functional of the density, we show that the HJB equation is an uncontrolled FP equation.
1 code implementation • 9 Aug 2023 • 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 trained to learn operators and solve differential equations using prompted data, during the inference stage without weight updates.
2 code implementations • 17 Apr 2023 • Liu Yang, Siting Liu, Tingwei Meng, Stanley J. Osher
This paper introduces a new neural-network-based approach, namely In-Context Operator Networks (ICON), to simultaneously learn operators from the prompted data and apply it to new questions during the inference stage, without any weight update.
no code implementations • 5 Apr 2022 • Cheng Liu, Zhen Gao, Siting Liu, Xuefei Ning, Huawei Li, Xiaowei Li
With the rapid advancements of deep learning in the past decade, it can be foreseen that deep learning will be continuously deployed in more and more safety-critical applications such as autonomous driving and robotics.