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In the recent years, Physics Informed Neural Networks (PINNs) have received strong interest as a method to solve PDE driven systems, in particular for data assimilation purpose. This method is still in its infancy, with many shortcomings…

Particle methods play an important role in computational fluid dynamics, but they are among the most difficult to implement and solve. The most common method is smoothed particle hydrodynamics, which is suitable for problem settings that…

Physics-informed neural networks (PINNs) have been applied to simulate multiphase flows, yet they are limited in modeling phase changes and sharp interfaces due to optimization conflicts in the strongly coupled Allen-Cahn, Cahn-Hilliard,…

A large number of magnetohydrodynamic (MHD) equilibrium calculations are often required for uncertainty quantification, optimization, and real-time diagnostic information, making MHD equilibrium codes vital to the field of plasma physics.…

Reconstructing fields from sparsely observed data is an ill-posed problem that arises in many engineering and science applications. Here, we investigate the use of physics-informed neural networks (PINNs) to reconstruct complete…

A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…

Dense granular flows exhibit nonlocal effects due to stress transmission in microplastic events, especially in quasi-static or slowly sheared regions. Hence, traditional local rheological models fail to capture spatial cooperativity effects…

Investigating blood flow in the cardiovascular system is crucial for assessing cardiovascular health. Computational approaches offer some non-invasive alternatives to measure blood flow dynamics. Numerical simulations based on traditional…

Physics-informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering…

We develop a flexible framework based on physics-informed neural networks (PINNs) for solving boundary value problems involving minimal surfaces in curved spacetimes, with a particular emphasis on singularities and moving boundaries. By…

In this paper, we compute numerical approximations of the minimal surfaces, an essential type of Partial Differential Equation (PDE), in higher dimensions. Classical methods cannot handle it in this case because of the Curse of…

Physics-informed neural networks (PINNs) offer a promising framework by embedding partial differential equations (PDEs) into the loss function together with measurement data, making them well-suited for inverse problems. However, standard…

In recent engineering applications using deep learning, physics-informed neural network (PINN) is a new development as it can exploit the underlying physics of engineering systems. The novelty of PINN lies in the use of partial differential…

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving partial differential equations (PDEs) by embedding the governing physics into the loss function associated with a deep neural network. In this work, a…

This study employs physics-informed neural networks (PINNs) to reconstruct multiple flow fields in a transient natural convection system solely based on instantaneous temperature data at an arbitrary moment. Transient convection problems…

Flow estimation problems are ubiquitous in scientific imaging. Often, the underlying flows are subject to physical constraints that can be exploited in the flow estimation; for example, incompressible (divergence-free) flows are expected…

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by…

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…

Physics-informed neural networks (PINNs) are neural networks (NNs) that directly encode model equations, like Partial Differential Equations (PDEs), in the network itself. While most of the PINN algorithms in the literature minimize the…

Physics-informed neural networks (PINNs) have emerged as a powerful meshless tool for topology optimization, capable of simultaneously determining optimal topologies and physical solutions. However, conventional PINNs rely on density-based…