Related papers: Physics-informed graph neural Galerkin networks: A…
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…
Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even…
This work proposes a Variational Physics-Informed Neural Network (VPINN) framework that integrates the Petrov-Galerkin formulation with deep neural networks (DNNs) for solving one-dimensional singularly perturbed boundary value problems…
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…
The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their…
We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal control problems subject to partial differential equations…
PINN models have demonstrated capabilities in addressing fluid PDE problems, and their potential in solid mechanics is beginning to emerge. This study identifies two key challenges when using PINN to solve general solid mechanics problems.…
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) 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…
Non-linear convection-reaction-diffusion (CRD) partial differential equations (PDEs) are crucial for modeling complex phenomena in fields such as biology, ecology, population dynamics, physics, and engineering. Numerical approximation of…
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…
In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design…
Physics-Informed Neural Networks (PINNs) have recently emerged as a promising alternative for solving partial differential equations, offering a mesh-free framework that incorporates physical laws directly into the learning process. In this…
Regular physics-informed neural networks (PINNs) predict the solution of partial differential equations using sparse labeled data but only over a single domain. On the other hand, fully supervised learning models are first trained usually…
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…
Physics Informed Neural Networks (PINNs) have recently gained popularity for solving partial differential equations, given the fact they escape the curse of dimensionality. In this paper, we present Physics Informed Neural Networks as an…
Numerically solving high-dimensional partial differential equations (PDEs) is a major challenge. Conventional methods, such as finite difference methods, are unable to solve high-dimensional PDEs due to the curse-of-dimensionality. A…
Recent studies have demonstrated the success of deep learning in solving forward and inverse problems in engineering and scientific computing domains, such as physics-informed neural networks (PINNs). Source inversion problems under sparse…
This paper introduces a framework based on physics-informed neural networks (PINNs) for addressing key challenges in nonlinear lattices, including solution approximation, bifurcation diagram construction, and linear stability analysis. We…
In solving partial differential equations (PDEs), machine learning utilizing physical laws has received considerable attention owing to advantages such as mesh-free solutions, unsupervised learning, and feasibility for solving…