64 citations · 87 across the 10 of their papers we have counts for
11 papers
Well-posedness of neural turbulence closures and tangent dissipation
Zhen Zhang, George Em Karniadakis
A neural turbulence closure defines a new boundary-value problem, , with a coupled Jacobian , where is the original mean-flow operator and $…
Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems
Zhen Zhang, Alessandro Alla, George Em Karniadakis
Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-infor…
Neural Evolutionary Kernel Method: A Knowledge-Guided Framework for Solving Evolutionary PDEs
Shuo Ling, Wenjun Ying, Zhen Zhang
Numerical solution of partial differential equations (PDEs) plays a vital role in various fields of science and engineering. In recent years, deep neural networks (DNNs) have emerg…
Effect of Turbulence-Closure Consistency on Airfoil Identification
Zhen Zhang, George Em Karniadakis
We consider an inverse flow problem in which the airfoil shape is identified from its wake signature, namely the velocity field in the wake of a target airfoil. This is an ill-pose…
Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling
Vivek Oommen, Aniruddha Bora, Zhen Zhang +1
We integrate neural operators with diffusion models to address the spectral limitations of neural operators in surrogate modeling of turbulent flows. While neural operators offer c…
SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classification
Alan John Varghese, Zhen Zhang, George Em Karniadakis
Existing neural network models to learn Hamiltonian systems, such as SympNets, although accurate in low-dimensions, struggle to learn the correct dynamics for high-dimensional many…
CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics
Yining Luo, Yingfa Chen, Zhen Zhang
In recent years, applying deep learning to solve physics problems has attracted much attention. Data-driven deep learning methods produce fast numerical operators that can learn ap…
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…
Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networks
Mitchell Daneker, Zhen Zhang, George Em Karniadakis +1
The dynamics of systems biological processes are usually modeled by a system of ordinary differential equations (ODEs) with many unknown parameters that need to be inferred from no…
GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems
Zhen Zhang, Yeonjong Shin, George Em Karniadakis
We propose the GENERIC formalism informed neural networks (GFINNs) that obey the symmetric degeneracy conditions of the GENERIC formalism. GFINNs comprise two modules, each of whic…
Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks
Pengzhan Jin, Zhen Zhang, Ioannis G. Kevrekidis +1
We propose the Poisson neural networks (PNNs) to learn Poisson systems and trajectories of autonomous systems from data. Based on the Darboux-Lie theorem, the phase flow of a Poiss…