14 citations · 43 across the 11 of their papers we have counts for
17 papers
Graphical conditional generative modeling for digital twin modeling
Zongren Zou, Théo Bourdais, Ricardo Baptista +1
Digital twin modeling, including control and data assimilation under model uncertainty, often faces an open-ended fidelity problem: adding variables, data streams, and time scales…
Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles
Khemraj Shukla, Zongren Zou, Theo Kaeufer +2
Physics-informed neural networks (PINNs) have emerged as a promising framework for solving inverse problems governed by partial differential equations (PDEs), including the reconst…
Bilevel optimization for learning hyperparameters: Application to solving PDEs and inverse problems with Gaussian processes
Nicholas H. Nelsen, Houman Owhadi, Andrew M. Stuart +2
Methods for solving scientific computing and inference problems, such as kernel- and neural network-based approaches for partial differential equations (PDEs), inverse problems, an…
Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble
Zongren Zou, Zhicheng Wang, George Em Karniadakis
We explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs),…
From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning
Juan Diego Toscano, Vivek Oommen, Alan John Varghese +4
Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and…
HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models
Tingwei Meng, Zongren Zou, Jérôme Darbon +1
The interplay between stochastic processes and optimal control has been extensively explored in the literature. With the recent surge in the use of diffusion models, stochastic pro…