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Physics-Informed Neural Networks (PINNs) are mesh-free approaches for the numerical approximation of partial differential equations, where a neural network is trained by minimizing a loss function derived from the governing equations and…
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…
Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient…
We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem. Integrated within a single-step exact observer linearization framework, the proposed PINN approach aims at learning a…
Physics-Informed Neural Networks (PINNs) have recently emerged as a novel approach to simulate complex physical systems on the basis of both data observations and physical models. In this work, we investigate the use of PINNs for various…
We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems. The PINN is a scientific machine learning framework that offers a promising perspective for finding numerical…
We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…
Interest is rising in Physics-Informed Neural Networks (PINNs) as a mesh-free alternative to traditional numerical solvers for partial differential equations (PDEs). However, PINNs often struggle to learn high-frequency and multi-scale…
Physics-informed neural networks (PINNs) are trained using physical equations and can also incorporate unmodeled effects by learning from data. PINNs for control (PINCs) of dynamical systems are gaining interest due to their prediction…
A method is presented that allows to reduce a problem described by differential equations with initial and boundary conditions to the problem described only by differential equations. The advantage of using the modified problem for…
Physics-informed Neural Networks (PINNs) have recently emerged as a principled way to include prior physical knowledge in form of partial differential equations (PDEs) into neural networks. Although PINNs are generally viewed as mesh-free,…
With the remarkable empirical success of neural networks across diverse scientific disciplines, rigorous error and convergence analysis are also being developed and enriched. However, there has been little theoretical work focusing on…
Physics-informed neural networks (PINNs) have attracted a lot of attention in scientific computing as their functional representation of partial differential equation (PDE) solutions offers flexibility and accuracy features. However, their…
Machine learning techniques are employed to perform the full characterization of a quantum system. The particular artificial intelligence technique used to learn the Hamiltonian is called physics informed neural network (PINN). The idea…
Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws…
Physics Informed Neural Networks (PINNs) have been emerging as a powerful computational tool for solving differential equations. However, the applicability of these models is still in its initial stages and requires more standardization to…
We introduce NewPINNs, a physics-informing learning framework that couples neural networks with conventional numerical solvers for solving differential equations. Rather than enforcing governing equations and boundary conditions through…
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…
Physics-informed neural networks (PINNs) have gained significant attention for solving forward and inverse problems related to partial differential equations (PDEs). While advancements in loss functions and network architectures have…
We address the neutral inclusion problem with imperfect boundary conditions, focusing on designing interface functions for inclusions of arbitrary shapes. Traditional Physics-Informed Neural Networks (PINNs) struggle with this inverse…