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Physics-informed neural networks (PINNs) provide a framework to build surrogate models for dynamical systems governed by differential equations. During the learning process, PINNs incorporate a physics-based regularization term within the…

Stirred tanks are vital in chemical and biotechnological processes, particularly as bioreactors. Although computational fluid dynamics (CFD) is widely used to model the flow in stirred tanks, its high computational cost$-$especially in…

The transformative impact of machine learning, particularly Deep Learning (DL), on scientific and engineering domains is evident. In the context of computational fluid dynamics (CFD), Physics-Informed Neural Networks (PINNs) represent a…

In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology,…

Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations (PDEs). We employ PINNs for solving the Reynolds-averaged Navier$\unicode{x2013}$Stokes…

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…

This study introduces a computational approach leveraging Physics-Informed Neural Networks (PINNs) for the efficient computation of arterial blood flows, particularly focusing on solving the incompressible Navier-Stokes equations by using…

Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training…

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving inverse problems, especially in cases where no complete information about the system is known and scatter measurements are available. This is especially…

We leverage Physics-Informed Neural Networks (PINNs) to learn solution functions of parametric Navier-Stokes Equations (NSE). Our proposed approach results in a feasible optimization problem setup that bypasses PINNs' limitations in…

Physics-Informed Neural Networks (PINNs) have recently shown great promise as a way of incorporating physics-based domain knowledge, including fundamental governing equations, into neural network models for many complex engineering systems.…

Traditional computational fluid dynamics and physics-informed neural networks (PINNs) often suffer from high computational cost, mesh sensitivity, and reduced accuracy for strongly nonlinear and time-dependent flows. To address these…

We describe a Physics-Informed Neural Network (PINN) that simulates the flow induced by the astronomical tide in a synthetic port channel, with dimensions based on the Santos - S\~ao Vicente - Bertioga Estuarine System. PINN models aim to…

Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs) by directly embedding them into the loss function. Despite their notable success, existing PINNs often exhibit training…

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…

Computational fluid dynamics (CFD) solvers employing two-equation eddy viscosity models are the industry standard for simulating turbulent flows using the Reynolds-averaged Navier-Stokes (RANS) formulation. While these methods are…

The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like…

Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…

In chemical engineering, process data are expensive to acquire, and complex phenomena are difficult to fully model. We explore the use of physics-informed neural networks (PINNs) for modeling dynamic processes with incomplete mechanistic…

Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating…