54 citations · 163 across the 20 of their papers we have counts for
21 papers
Single-condition neural solvers encode transferable response spaces for parametric differential equations
Wenbo Cao, Weiwei Zhang
Operator learning for parametric partial differential equations (PDEs) typically builds global models over prescribed domains, requiring cross-condition data or costly physics-cons…
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…
Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects
Weiwei Zhang, Wei Suo, Jiahao Song +1
In recent years, Physics-Informed Neural Networks (PINNs) have become a representative method for solving partial differential equations (PDEs) with neural networks. PINNs provide…
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…
TSONN: Time-stepping-oriented neural network for solving partial differential equations
Wenbo Cao, Weiwei Zhang
Deep neural networks (DNNs), especially physics-informed neural networks (PINNs), have recently become a new popular method for solving forward and inverse problems governed by par…
A novel convergence enhancement method based on Online Dimension Reduction Optimization
Wenbo Cao, Yilang Liu, Xianglin Shan +2
Iterative steady-state solvers are widely used in computational fluid dynamics. Unfortunately, it is difficult to obtain steady-state solution for unstable problem caused by physic…
High Reynolds number airfoil turbulence modeling method based on machine learning technique
Xuxiang Sun, Wenbo Cao, Yilang Liu +2
In this paper, a turbulence model based on deep neural network is developed for turbulent flow around airfoil at high Reynolds numbers. According to the data got from the Spalart-A…
Analysis on numerical stability and convergence of RANS turbulence models from the perspective of coupling modes
Yilang Liu, Weiwei Zhang, Zhenhua Xia
Reynolds-averaged Navier-Stokes simulations are still the main method to study complex flows in engineering. However, traditional turbulence models cannot accurately predict flow f…
Machine Learning of Partial Differential Equations from Noise Data
Wenbo Cao, Weiwei Zhang
Machine learning of partial differential equations from data is a potential breakthrough to solve the lack of physical equations in complex dynamic systems, but because numerical d…