Related papers: Helicity-conservative Physics-informed Neural Netw…

We present our progress on the application of physics informed deep learning to reservoir simulation problems. The model is a neural network that is jointly trained to respect governing physical laws and match boundary conditions. The…

This work presents a physics-informed neural network (PINN) based framework to model the strain-rate and temperature dependence of the deformation fields in elastic-viscoplastic solids. To avoid unbalanced back-propagated gradients during…

Physics Informed Neural Networks offer a mesh free framework for solving PDEs but are highly sensitive to loss weight selection. We propose two dimensional analysis based weighting schemes, one based on quantifiable terms, and another also…

Physics-informed neural networks (PINNs) incorporate physical laws into their training to efficiently solve partial differential equations (PDEs) with minimal data. However, PINNs fail to guarantee adherence to conservation laws, which are…

This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results…

Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…

Accurate simulation of fluid flow in porous media is challenging due to complex pore-space geometries and the computational cost of solving the Navier-Stokes equations. This difficulty is particularly important when repeated simulations are…

We present Mechanistic PDE Networks -- a model for discovery of governing partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal data as space-time dependent linear partial differential equations in…

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional…

When a fluid flows over a solid surface, it creates a thin boundary layer where the flow velocity is influenced by the surface through viscosity, and can transition from laminar to turbulent at sufficiently high speeds. Understanding and…

Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly…

We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…

We present an efficient hybrid Neural Network-Finite Element Method (NN-FEM) for solving the viscous-plastic (VP) sea-ice model. The VP model is widely used in climate simulations to represent large-scale sea-ice dynamics. However, the…

We consider the Navier-Stokes system in a bounded domain with a smooth boundary. Given a sufficiently regular time-dependent global solution, we construct a finite-dimensional feedback control that is supported by a given open set and…

We present an efficient deep learning technique for the model reduction of the Navier-Stokes equations for unsteady flow problems. The proposed technique relies on the Convolutional Neural Network (CNN) and the stochastic gradient descent…

In this article, we propose and analyze a fully coupled, nonlinear, and energy-stable virtual element method (VEM) for solving the coupled Poisson-Nernst-Planck (PNP) and Navier--Stokes (NS) equations modeling microfluidic and…

The steady incompressible Navier--Stokes equations pose significant computational challenges due to their nonlinear convective terms and pressure--velocity coupling. Physics-informed neural networks (PINNs) provide a mesh-free framework for…

In this work, we embed hard constraints in a physics informed neural network (PINN) which predicts solutions to the 2D incompressible Navier Stokes equations. We extend the hard constraint method introduced by Chen et al. (arXiv:2012.06148)…

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…

High-fidelity reconstruction of fluids from sparse multiview RGB videos remains a formidable challenge due to the complexity of the underlying physics as well as complex occlusion and lighting in captures. Existing solutions either assume…