9 papers
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…
A universal linearized subspace refinement framework for neural networks
Wenbo Cao, Weiwei Zhang
Neural networks are predominantly trained using gradient-based methods, yet in many applications their final predictions remain far from the accuracy attainable within the model's…
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…