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Fourier Neural Operators (FNOs) have demonstrated exceptional accuracy in mapping functional spaces by leveraging Fourier transforms to establish a connection with underlying physical principles. However, their opaque inner workings often…
Eigenvalue problems are critical to several fields of science and engineering. We expand on the method of using unsupervised neural networks for discovering eigenfunctions and eigenvalues for differential eigenvalue problems. The obtained…
In the present study, the capabilities of a new Convolutional Neural Network (CNN) model are explored with the paramount objective of reconstructing the temperature field of wall-bounded flows based on a limited set of measurement points…
The simulation of microcirculatory blood flow in realistic vascular architectures poses significant challenges due to the multiscale nature of the problem and the topological complexity of capillary networks. In this work, we propose a…
Active researches are currently being performed to incorporate the wealth of scientific knowledge into data-driven approaches (e.g., neural networks) in order to improve the latter's effectiveness. In this study, the Theory-guided Neural…
Physics-informed neural networks (PINNs) is an emerging category of neural networks which can be trained to solve supervised learning tasks while taking into consideration given laws of physics described by general nonlinear partial…
We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…
Physics Informed Machine Learning has emerged as a popular approach for modeling and simulation in digital twins, enabling the generation of accurate models of processes and behaviors in real-world systems. However, existing methods either…
In this paper, we train turbulence models based on convolutional neural networks. These learned turbulence models improve under-resolved low resolution solutions to the incompressible Navier-Stokes equations at simulation time. Our study…
We study the subsonic flows governed by full Euler equations in the half plane bounded below by a piecewise smooth curve asymptotically approaching x1-axis. Nonconstant conditions in the far field are prescribed to ensure the real Euler…
We employ physics-informed neural networks (PINNs) to simulate the incompressible flows ranging from laminar to turbulent flows. We perform PINN simulations by considering two different formulations of the Navier-Stokes equations: the…
Traditionally, deriving aerodynamic parameters for an airfoil via Computational Fluid Dynamics requires significant time and effort. However, recent approaches employ neural networks to replace this process, it still grapples with…
Physics-informed neural networks (PINNs), owing to their mesh-free nature, offer a powerful approach for solving high-dimensional partial differential equations (PDEs) in complex geometries, including irregular domains. This capability…
The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC)…
In many computational problems in engineering and science, function or model differentiation is essential, but also integration is needed. An important class of computational problems include so-called integro-differential equations which…
Turbulence remains a problem that is yet to be fully understood, with experimental and numerical studies aiming to fully characterise the statistical properties of turbulent flows. Such studies require huge amount of resources to capture,…
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…
In recent years, deep learning-based methods have been proposed for solving inverse scattering problems (ISPs), but most of them heavily rely on data and suffer from limited generalization capabilities. In this paper, a new solving scheme…
In this paper, the physics-informed neural networks (PINN) is applied to high-dimensional system to solve the (N+1)-dimensional initial boundary value problem with 2N+1 hyperplane boundaries. This method is used to solve the most classic…
Big-data-based artificial intelligence (AI) supports profound evolution in almost all of science and technology. However, modeling and forecasting multi-physical systems remain a challenge due to unavoidable data scarcity and noise.…