54 citations · 107 across the 15 of their papers we have counts for
16 papers
Online reduced-order modeling from primal solver trajectories for PDE-constrained optimization
Zhe Lu, Wenbo Cao, Weiwei Zhang
Repeated high-fidelity state and gradient evaluations make large-scale PDE-constrained optimization computationally expensive. Reduced-order modeling provides a natural way to redu…
Physics-informed neural networks for shock capturing in inviscid flows around an airfoil
Jiahao Song, Wenbo Cao, Weiwei Zhang
Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs sti…
Verified residual-specific explicit derivative kernels for physics-informed learning and discretized PDE adjoints
Wenbo Cao, Zhe Lu, Weiwei Zhang
Derivative computation is central to scientific computing, from space-time derivatives in physics-informed neural networks (PINNs) to residual Jacobian actions and discrete-adjoint…
Optimization-Based Discovery of A Non-Attracting Flow State in An Oscillating-Cylinder Wake
Daiwei Dong, Wenbo Cao, Wei Suo +2
In the flow past a stationary circular cylinder, the classical Karman vortex street arises from a Hopf bifurcation of the steady flow at the critical Reynolds number. Although this…
Solving compressible Navier-Stokes equations using the feature-enhanced neural network
Jiahao Song, Wenbo Cao, Weiwei Zhang
Physics-informed neural networks (PINNs) have shown remarkable prospects in solving partial differential equations (PDEs) involving fluid mechanics. However, the method has so far…
Linearized subspace refinement framework to expose hidden accuracy in trained neural networks
Wenbo Cao, Weiwei Zhang
Neural networks trained by gradient-based methods often exhibit optimization-induced accuracy plateaus in scientific machine learning tasks. We present Linearized Subspace Refineme…
A matrix preconditioning framework for physics-informed neural networks based on adjoint method
Jiahao Song, Wenbo Cao, Weiwei Zhang
Physics-informed neural networks (PINNs) have recently emerged as a popular approach for solving forward and inverse problems involving partial differential equations (PDEs). Compa…
Overcoming the Loss Conditioning Bottleneck in Optimization-Based PDE Solvers: A Novel Well-Conditioned Loss Function
Wenbo Cao, Weiwei Zhang
Optimization-based PDE solvers that minimize scalar loss functions have gained increasing attention in recent years. These methods either define the loss directly over discrete var…
FENN: Feature-enhanced neural network for solving partial differential equations involving fluid mechanics
Jiahao Song, Wenbo Cao, Weiwei Zhang
Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs sti…
Solving all laminar flows around airfoils all-at-once using a parametric neural network solver
Wenbo Cao, Shixiang Tang, Qianhong Ma +2
Recent years have witnessed increasing research interests of physics-informed neural networks (PINNs) in solving forward, inverse, and parametric problems governed by partial diffe…
Discovery of knowledge of wall-bounded turbulence via symbolic regression
ZhongXin Yang, XiangLin Shan, WeiWei Zhang
With the development of high performance computer and experimental technology, the study of turbulence has accumulated a large number of high fidelity data. However, few general tu…
An analysis and solution of ill-conditioning in physics-informed neural networks
Wenbo Cao, Weiwei Zhang
Physics-informed neural networks (PINNs) have recently emerged as a novel and popular approach for solving forward and inverse problems involving partial differential equations (PD…
New Interpretation for error propagation of data-driven Reynolds stress closures via global stability analysis
Xianglin Shan, Wenbo Cao, Weiwei Zhang
In light of the challenges surrounding convergence and error propagation encountered in Reynolds-averaged Navier-Stokes (RANS) equations with data-driven Reynolds stress closures,…
A solver for subsonic flow around airfoils based on physics-informed neural networks and mesh transformation
Wenbo Cao, Jiahao Song, Weiwei Zhang
Physics-informed neural networks (PINNs) have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). Howev…
A complete state-space solution model for inviscid flow around airfoils based on physics-informed neural networks
Wenbo Cao, Jiahao Song, Weiwei Zhang
Engineering problems often involve solving partial differential equations (PDEs) over a range of similar problem setups with various state parameters. In traditional numerical meth…
VW-PINNs: A volume weighting method for PDE residuals in physics-informed neural networks
Jiahao Song, Wenbo Cao, Fei Liao +1
Physics-informed neural networks (PINNs) have shown remarkable prospects in the solving the forward and inverse problems involving partial differential equations (PDEs). The method…