Related papers: Coupling of the Finite Element Method with Physics…
Traditional fluid flow predictions require large computational resources. Despite recent progress in parallel and GPU computing, the ability to run fluid flow predictions in real-time is often infeasible. Recently developed machine learning…
In this paper, we present a multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum…
The prediction non-equilibrium transport phenomena in disordered media is a difficult problem for conventional numerical methods. An example of a challenging problem is the prediction of gas flow fields through porous media in the rarefied…
The accurate solution of nonlinear hyperbolic partial differential equations (PDEs) remains challenging due to steep gradients, discontinuities, and multiscale structures that make conventional solvers computationally demanding.…
Physics-informed neural networks (PINNs) provide a mesh-free framework for solving partial differential equations by embedding governing physics into neural-network training. Recent studies have shown that parameterized PINNs can learn…
The computational cost of fluid simulations increases rapidly with grid resolution. This has given a hard limit on the ability of simulations to accurately resolve small scale features of complex flows. Here we use a machine learning…
Form-finding of unilateral membrane structures is commonly addressed by solving equilibrium equations with Finite Element Methods (FEMs). This paper investigates Physics-Informed Neural Networks (PINNs) as an alternative, where the…
Successfully training Physics Informed Neural Networks (PINNs) for highly nonlinear PDEs on complex 3D domains remains a challenging task. In this paper, PINNs are employed to solve the 3D incompressible Navier-Stokes (NS) equations at…
The numerical simulation and optimization of technical systems described by partial differential equations is expensive, especially in multi-query scenarios in which the underlying equations have to be solved for different parameters. A…
Capillary phenomena are involved in many industrial processes, especially those dealing with composite manufacturing. However, their modelling is still challenging. Therefore, a finite element setting is proposed to better investigate this…
Physics-informed neural networks (PINNs) are a newly emerging research frontier in machine learning, which incorporate certain physical laws that govern a given data set, e.g., those described by partial differential equations (PDEs), into…
Physics-informed neural networks (PINNs) have attracted considerable attention for their ability to integrate partial differential equation priors into deep learning frameworks; however, they often exhibit limited predictive accuracy when…
Fluid mechanics is a fundamental field in engineering and science. Solving the Navier-Stokes equation (NSE) is critical for understanding the behavior of fluids. However, the NSE is a complex partial differential equation that is difficult…
This paper deals with the following important research questions. Is it possible to solve challenging advection-dominated diffusion problems in one and two dimensions using Physics Informed Neural Networks (PINN) and Variational Physics…
In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using…
Severe accident analysis using system-level codes such as MELCOR is indispensable for nuclear safety assessment, yet the computational cost of repeated simulations poses a significant bottleneck for parametric studies and uncertainty…
Deep learning techniques with neural networks have been used effectively in computational fluid dynamics (CFD) to obtain solutions to nonlinear differential equations. This paper presents a physics-informed neural network (PINN) approach to…
Physics-informed neural networks (PINNs) have recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by…
In this study, the capabilities of the Physics-Informed Neural Network (PINN) method are investigated for three major tasks: modeling, simulation, and optimization in the context of the heat conduction problem. In the modeling phase, the…
Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…