Related papers: Statistical-Physics-Informed Neural Networks (Stat…

We consider the computation of statistical moments to operator equations with stochastic data. We remark that application of PINNs -- referred to as TPINNs -- allows to solve the induced tensor operator equations under minimal changes of…

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…

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving Partial Differential Equations (PDEs) by incorporating physical constraints into deep learning models. However, standard PINNs often require a large…

Physics-informed neural networks (PINNs) have demonstrated promise as a framework for solving forward and inverse problems involving partial differential equations. Despite recent progress in the field, it remains challenging to quantify…

As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great…

Machine learning recently has been used to identify the governing equations for dynamics in physical systems. The promising results from applications on systems such as fluid dynamics and chemical kinetics inspire further investigation of…

This paper explores the potential of Physics-Informed Neural Networks (PINNs) to serve as Reduced Order Models (ROMs) for simulating the flow field within stirred tank reactors (STRs). We solve the two-dimensional stationary Navier-Stokes…

In recent years, Physics-informed neural networks (PINNs) have been widely used to solve partial differential equations alongside numerical methods because PINNs can be trained without observations and deal with continuous-time problems…

Physics-Informed Neural Network (PINN) is a deep learning framework that integrates the governing equations underlying data into a loss function. In this study, we consider the problem of estimating state variables and parameters in…

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…

We introduce a class of Sparse, Physics-based, and partially Interpretable Neural Networks (SPINN) for solving ordinary and partial differential equations (PDEs). By reinterpreting a traditional meshless representation of solutions of PDEs…

In this paper, we review the new method Physics-Informed Neural Networks (PINNs) that has become the main pillar in scientific machine learning, we present recent practical extensions, and provide a specific example in data-driven discovery…

Ocean current, fluid mechanics, and many other spatio-temporal physical dynamical systems are essential components of the universe. One key characteristic of such systems is that certain physics laws -- represented as ordinary/partial…

When investigating epidemic dynamics through differential models, the parameters needed to understand the phenomenon and to simulate forecast scenarios require a delicate calibration phase, often made even more challenging by the scarcity…

Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to…

Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer most times from paucity of data, while they may…

The effectiveness of the Physics Informed Neural Networks (PINNs) for learning the dynamics of constrained Hamiltonian systems is demonstrated using the Dirac theory of constraints for regular systems with holonomic constraints and systems…

Seismogenic plate boundaries are presumed to behave in a similar manner to a densely packed granular medium, where fault and blocks systems rapidly rearrange the distribution of forces within themselves, as particles do in slowly sheared…

For Prognostics and Health Management (PHM) of Lithium-ion (Li-ion) batteries, many models have been established to characterize their degradation process. The existing empirical or physical models can reveal important information regarding…

Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the…