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Neural networks have emerged as powerful surrogates for solving partial differential equations (PDEs), offering significant computational speedups over traditional methods. However, these models suffer from a critical limitation: error…

Physics-informed neural networks (PINN) have achieved notable success in solving partial differential equations (PDE), yet solving the Navier-Stokes equations (NSE) with complex boundary conditions remains a challenging task. In this paper,…

Recently, physics-driven deep learning methods have shown particular promise for the prediction of physical fields, especially to reduce the dependency on large amounts of pre-computed training data. In this work, we target the…

Soft- and hard-constrained Physics Informed Neural Networks (PINNs) have achieved great success in solving partial differential equations (PDEs). However, these methods still face great challenges when solving the Navier-Stokes equations…

The work is a continuation of a paper by Iskhakov A.S. and Dinh N.T. "Physics-integrated machine learning: embedding a neural network in the Navier-Stokes equations". Part I // arXiv:2008.10509 (2020) [1]. The proposed in [1]…

We introduce a method for training exactly conservative physics-informed neural networks and physics-informed deep operator networks for dynamical systems. The method employs a projection-based technique that maps a candidate solution…

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,…

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by…

In this paper, physics-informed neural network (PINN) based on characteristic-based split (CBS) is proposed, which can be used to solve the time-dependent Navier-Stokes equations (N-S equations). In this method, The output parameters and…

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…

Physics-informed neural networks (PINNs) are able to solve partial differential equations (PDEs) by incorporating the residuals of the PDEs into their loss functions. Variational Physics-Informed Neural Networks (VPINNs) and hp-VPINNs use…

We introduce an evidence-driven Bayesian formulation of physics-informed neural networks that enables automatic optimization of loss weights between PDE residuals, boundary conditions, and observational data. Unlike existing Bayesian PINN…

The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and validated to find solutions to both linear and non-linear partial…

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…

The paper presents an efficient and robust data-driven deep learning (DL) computational framework developed for linear continuum elasticity problems. The methodology is based on the fundamentals of the Physics Informed Neural Networks…

The predictive accuracy of the Navier-Stokes equations is known to degrade at the limits of the continuum assumption, thereby necessitating expensive and often highly approximate solutions to the Boltzmann equation. While tractable in one…

Recent research has used deep learning to develop partial differential equation (PDE) models in science and engineering. The functional form of the PDE is determined by a neural network, and the neural network parameters are calibrated to…

Can neural networks learn to solve partial differential equations (PDEs)? We investigate this question for two (systems of) PDEs, namely, the Poisson equation and the steady Navier--Stokes equations. The contributions of this paper are…

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…

This paper proposes a physics-informed learning framework for a class of recurrent neural networks tailored to large-scale and networked systems. The approach aims to learn control-oriented models that preserve the structural and stability…