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Motivated by recent research on Physics-Informed Neural Networks (PINNs), we make the first attempt to introduce the PINNs for numerical simulation of the elliptic Partial Differential Equations (PDEs) on 3D manifolds. PINNs are one of the…
We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fixed or…
Physics Informed Neural Networks (PINNs) have frequently been used for the numerical approximation of Partial Differential Equations (PDEs). The goal of this paper is to construct PINNs along with a computable upper bound of the error,…
Physics-Informed Neural Networks (PINNs) represent a groundbreaking paradigm in scientific computing, seamlessly integrating the robust framework of deep learning with fundamental physical laws. This paper meticulously applies the standard…
We develop a flexible framework based on physics-informed neural networks (PINNs) for solving boundary value problems involving minimal surfaces in curved spacetimes, with a particular emphasis on singularities and moving boundaries. By…
This work aims to provide an effective deep learning framework to predict the vector-soliton solutions of the coupled nonlinear equations and their interactions. The method we propose here is a physics-informed neural network (PINN)…
Modeling stiff partial differential equations (PDEs) with sharp gradients remains a significant challenge for scientific machine learning. While Physics-Informed Neural Networks (PINNs) struggle with spectral bias and slow training times,…
Physics-informed neural networks (PINNs) are an emerging technique to solve partial differential equations (PDEs). In this work, we propose a simple but effective PINN approach for the phase-field model of ferroelectric microstructure…
This paper presents a physics-informed training framework for projection-based Reduced Order Models (ROMs). We extend the PROM-ANN architecture by complementing snapshot-based training with a FEM-based, discrete physics-informed residual…
Accurate reconstruction of localized extreme structures remains a critical bottleneck in the physics-informed modeling of electro-thermal-convective flows. Although conventional physics-informed neural networks effectively capture smooth…
We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs…
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…
Physics-Informed Neural Networks (PINNs) embed the partial differential equations (PDEs) governing the system under study directly into the training of Neural Networks, ensuring solutions that respect physical laws. While effective for…
Physics-Informed Neural Networks (PINNs) have received increased interest for forward, inverse, and surrogate modeling of problems described by partial differential equations (PDE). However, their application to multiphysics problem,…
Solving Singularly Perturbed Differential Equations (SPDEs) presents challenges due to the rapid change of their solutions at the boundary layer. In this manuscript, We propose Asymptotic Physics-Informed Neural Networks (ASPINN), a…
The prohibitive cost and low fidelity of experimental data in industry scale thermofluid systems limit the usefulness of pure data-driven machine learning methods. Physics-informed neural networks (PINN) strive to overcome this by embedding…
Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in…
Physics-Informed Neural Networks (PINNs) combine deep learning with physical constraints for solving partial differential equations (PDEs), and are widely applied in fluid mechanics, heat transfer, and solid mechanics. However, PINN…
Physics-informed neural networks (PINNs) provide a means of obtaining approximate solutions of partial differential equations and systems through the minimisation of an objective function which includes the evaluation of a residual function…
We introduce the Transformed Generative Pre-Trained Physics-Informed Neural Networks (TGPT-PINN) for accomplishing nonlinear model order reduction (MOR) of transport-dominated partial differential equations in an MOR-integrating PINNs…