相关论文: Physics-informed neural networks for aggregation k…

Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…

Machine learning and neural networks have advanced numerous research domains, but challenges such as large training data requirements and inconsistent model performance hinder their application in certain scientific problems. To overcome…

In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…

This dissertation investigates physics-informed neural networks (PINNs) as candidate models for encoding governing equations, and assesses their performance on experimental data from two different systems. The first system is a simple…

Physics-informed neural networks have emerged as a prominent new method for solving differential equations. While conceptually straightforward, they often suffer training difficulties that lead to relatively large discretization errors or…

Physics informed neural networks have been gaining popularity due to their unique ability to incorporate physics laws into data-driven models, ensuring that the predictions are not only consistent with empirical data but also align with…

In machine learning and statistical modeling, the mean square or absolute error is commonly used as an error metric, also called a "loss function." While effective in reducing the average error, this approach may fail to address localized…

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…

This study introduces a unified control framework that addresses the challenge of precise quadruped locomotion with unknown payloads, named as online payload identification-based physics-informed neural network predictive control…

In this research, the application of the Physics-Informed Neural Network (PINN) model is explored to solve transport equation-based Partial Differential Equations (PDEs). The primary objective is to analyze the impact of different…

Data-driven methods have become increasingly more prominent for musculoskeletal modelling due to their conceptually intuitive simple and fast implementation. However, the performance of a pre-trained data-driven model using the data from…

We prove a priori and a posteriori error estimates for physics-informed neural networks (PINNs) for linear PDEs. We analyze elliptic equations in primal and mixed form, elasticity, parabolic, hyperbolic and Stokes equations; and a PDE…

Musculoskeletal models have been widely used for detailed biomechanical analysis to characterise various functional impairments given their ability to estimate movement variables (i.e., muscle forces and joint moment) which cannot be…

Physics-informed neural networks (PINNs) are employed to solve the Dyson--Schwinger equations of quantum electrodynamics (QED) in Euclidean space, with a focus on the non-perturbative generation of the fermion's dynamical mass function in…

Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of…

Surrogate modeling is used to replace computationally expensive simulations. Neural networks have been widely applied as surrogate models that enable efficient evaluations over complex physical systems. Despite this, neural networks are…

The application of deep learning methods to speed up the resolution of challenging power flow problems has recently shown very encouraging results. However, power system dynamics are not snap-shot, steady-state operations. These dynamics…

This paper proposes a tractable framework to determine key characteristics of non-linear dynamic systems by converting physics-informed neural networks to a mixed integer linear program. Our focus is on power system applications.…

Physics-informed neural networks (PINNs) have emerged as a versatile and widely applicable concept across various science and engineering domains over the past decade. This article offers a comprehensive overview of the fundamentals of…

Accurate prediction of hydrogen sorption in fine-grained geological materials is essential for evaluating underground hydrogen storage capacity, assessing caprock integrity, and characterizing hydrogen migration in subsurface energy…