Related papers: A Boundary Integral-based Neural Operator for Mesh…
In this work, we have applied physics-informed neural networks (PINN) for solving mesh deformation problems. We used the collocation PINN method to capture the new positions of the vertex nodes while preserving the connectivity information.…
We proposed the boundary-integral type neural networks (BINN) for the boundary value problems in computational mechanics. The boundary integral equations are employed to transfer all the unknowns to the boundary, then the unknowns are…
Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural…
For linear partial differential equations with known fundamental solutions, this work introduces a novel operator learning framework that relies exclusively on domain boundary data, including solution values and normal derivatives, rather…
Boundary value problems (BVPs) play a central role in the mathematical analysis of constrained physical systems subjected to external forces. Consequently, BVPs frequently emerge in nearly every engineering discipline and span problem…
We introduce a novel Multimodal Neural Operator (MNO) architecture designed to learn solution operators for multi-parameter nonlinear boundary value problems (BVPs). Traditional neural operators primarily map either the PDE coefficients or…
Initial boundary value problems arise commonly in applications with engineering and natural systems governed by nonlinear partial differential equations (PDEs). Operator learning is an emerging field for solving these equations by using a…
We propose a Weak-form Physics-Informed Neural Operator (WINO), a data-free framework that combines the efficiency of neural operators with the geometric flexibility of the $\varphi$-finite element method ($\varphi$-FEM). $\varphi$-FEM is…
Fractional diffusion equations have been an effective tool for modeling anomalous diffusion in complicated systems. However, traditional numerical methods require expensive computation cost and storage resources because of the memory effect…
Implicit Neural Representations (INRs), characterized by neural network-encoded signed distance fields, provide a powerful means to represent complex geometries continuously and efficiently. While successful in computer vision and…
This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order…
Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…
A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition…
Accurate prediction of machining deformation in structural components is essential for ensuring dimensional precision and reliability. Such deformation often originates from residual stress fields, whose distribution and influence vary…
This paper proposes a physics-informed neural operator (PINO) framework for solving inverse scattering problems, enabling rapid and accurate reconstructions under diverse measurement conditions. In the proposed approach, the dielectric…
In multi-body dynamics, the motion of a complicated physical object is described as a coupled ordinary differential equation system with multiple unknown solutions. Engineers need to constantly adjust the object to meet requirements at the…
This work presents a robust and efficient sharp interface immersed boundary (IBM) framework, which is applicable for all-speed flow regimes and is capable of handling arbitrarily complex bodies (stationary or moving). The work deploys an…
In this paper, we present a novel Fredholm Integral Equation Neural Operator (FIE-NO) method, an integration of Random Fourier Features and Fredholm Integral Equations (FIE) into the deep learning framework, tailored for solving data-driven…
We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function and…
We propose a novel method for fast and accurate training of physics-informed neural networks (PINNs) to find solutions to boundary value problems (BVPs) and initial boundary value problems (IBVPs). By combining the methods of training deep…