Related papers: Two-stage initial-value iterative physics-informed…

Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of…

Accurately and efficiently solving nonlinear differential equations is crucial for modeling dynamic behavior across science and engineering. Physics-Informed Neural Networks (PINNs) have emerged as a powerful solution that embeds physical…

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…

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

In this paper, we propose a novel inverse parameter estimation approach called Bayesian optimized physics-informed neural network (BOPINN). In this study, a PINN solves the partial differential equation (PDE), whereas Bayesian optimization…

Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving…

We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. The concept of PINNs is expanded to learn not only the solution of one particular differential equation but the…

Inverse problems arise almost everywhere in science and engineering where we need to infer on a quantity from indirect observation. The cases of medical, biomedical, and industrial imaging systems are the typical examples. A very high…

Physics-informed neural networks (PINNs) integrate fundamental physical principles with advanced data-driven techniques, driving significant advancements in scientific computing. However, PINNs face persistent challenges with stiffness in…

The recent surge of interest in physics-informed neural network (PINN) methods has led to a wave of studies that attest to their potential for solving partial differential equations (PDEs) and predicting the dynamics of physical systems.…

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.…

Physics-informed neural networks (PINNs) are neural networks that embed the laws of dynamical systems modeled by differential equations into their loss function as constraints. In this work, we present a PINN framework applied to oncology.…

Realistic sound is essential in virtual environments, such as computer games and mixed reality. Efficient and accurate numerical methods for pre-calculating acoustics have been developed over the last decade; however, pre-calculating…

We propose a framework for solving nonlinear partial differential equations (PDEs) by combining perturbation theory with one-shot transfer learning in Physics-Informed Neural Networks (PINNs). Nonlinear PDEs with polynomial terms are…

With growing investigations into solving partial differential equations by physics-informed neural networks (PINNs), more accurate and efficient PINNs are required to meet the practical demands of scientific computing. One bottleneck of…

Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially…

Deep learning-based surrogate modeling is becoming a promising approach for learning and simulating dynamical systems. Deep-learning methods, however, find very challenging learning stiff dynamics. In this paper, we develop DAE-PINN, the…

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…

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…

Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast…