no code implementations • 12 Apr 2024 • Zongren Zou, Tingwei Meng, Paula Chen, Jérôme Darbon, George Em Karniadakis
We provide several examples from SciML involving noisy data and \textit{epistemic uncertainty} to illustrate the potential advantages of our approach.
no code implementations • 13 Nov 2023 • Paula Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, George Em Karniadakis
This connection allows us to reinterpret incremental updates to learned models as the evolution of an associated HJ PDE and optimal control problem in time, where all of the previous information is intrinsically encoded in the solution to the HJ PDE.
1 code implementation • 22 Mar 2023 • Paula Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, George Em Karniadakis
Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences.