449 citations · 736 across the 21 of their papers we have counts for
22 papers
Sparse stochastic digital twins can outperform exact ones
Zongren Zou, Théo Bourdais, Ricardo Baptista +1
Digital twins are often built under the assumption that greater model fidelity leads to better downstream performance. We show that this is not always the case: retaining weakly de…
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…
Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiology
Mario De Florio, Zongren Zou, Daniele E. Schiavazzi +1
When predicting physical phenomena through simulation, quantification of the total uncertainty due to multiple sources is as crucial as making sure the underlying numerical model i…
NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements
Khemraj Shukla, Zongren Zou, Chi Hin Chan +3
Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due…
A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks
Khemraj Shukla, Juan Diego Toscano, Zhicheng Wang +2
Kolmogorov-Arnold Networks (KANs) were recently introduced as an alternative representation model to MLP. Herein, we employ KANs to construct physics-informed machine learning mode…
Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problem
Youngkyu Lee, Shanqing Liu, Zongren Zou +5
Three-dimensional target identification using scattering techniques requires high accuracy solutions and very fast computations for real-time predictions in some critical applicati…
Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning
Zongren Zou, Tingwei Meng, Paula Chen +2
Uncertainty quantification (UQ) in scientific machine learning (SciML) combines the powerful predictive power of SciML with methods for quantifying the reliability of the learned m…
Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators
Zongren Zou, Xuhui Meng, George Em Karniadakis
Uncertainty quantification (UQ) in scientific machine learning (SciML) becomes increasingly critical as neural networks (NNs) are being widely adopted in addressing complex problem…
Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning
Paula Chen, Tingwei Meng, Zongren Zou +2
We address two major challenges in scientific machine learning (SciML): interpretability and computational efficiency. We increase the interpretability of certain learning processe…
Correcting model misspecification in physics-informed neural networks (PINNs)
Zongren Zou, Xuhui Meng, George Em Karniadakis
Data-driven discovery of governing equations in computational science has emerged as a new paradigm for obtaining accurate physical models and as a possible alternative to theoreti…
Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regression
Zhen Zhang, Zongren Zou, Ellen Kuhl +1
Misfolded tau proteins play a critical role in the progression and pathology of Alzheimer's disease. Recent studies suggest that the spatio-temporal pattern of misfolded tau follow…
A Generative Modeling Framework for Inferring Families of Biomechanical Constitutive Laws in Data-Sparse Regimes
Minglang Yin, Zongren Zou, Enrui Zhang +3
Quantifying biomechanical properties of the human vasculature could deepen our understanding of cardiovascular diseases. Standard nonlinear regression in constitutive modeling requ…
Leveraging Multi-time Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problems
Paula Chen, Tingwei Meng, Zongren Zou +2
Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By…
L-HYDRA: Multi-Head Physics-Informed Neural Networks
Zongren Zou, George Em Karniadakis
We introduce multi-head neural networks (MH-NNs) to physics-informed machine learning, which is a type of neural networks (NNs) with all nonlinear hidden layers as the body and mul…
NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators
Zongren Zou, Xuhui Meng, Apostolos F Psaros +1
Uncertainty quantification (UQ) in machine learning is currently drawing increasing research interest, driven by the rapid deployment of deep neural networks across different field…
Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems
Kevin Linka, Amelie Schafer, Xuhui Meng +3
Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze non…
Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons
Apostolos F Psaros, Xuhui Meng, Zongren Zou +2
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challen…
Experimental self-testing of entangled states
Wen-Hao Zhang, Geng Chen, Xing-Xiang Peng +12
Quantum entanglement is the key resource for quantum information processing. Device-independent certification of entangled states is a long standing open question, which arouses th…