Related papers: The Finite Element Neural Network Method: One Dime…
We describe a new finite element method (FEM) to construct continuous equilibrium distribution functions of stellar systems. The method is a generalization of Schwarzschild's orbit superposition method from the space of discrete functions…
Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches using (deep) neural networks have been developed to solve…
A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…
In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on…
In this paper, we provide a theoretical analysis of a type of operator learning method without data reliance based on the classical finite element approximation, which is called the finite element operator network (FEONet). We first…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
Among interpretable machine learning methods, the class of Generalised Additive Neural Networks (GANNs) is referred to as Self-Explaining Neural Networks (SENN) because of the linear dependence on explicit functions of the inputs. In binary…
Accurate prediction of structural displacements under external loading is fundamental to structural health monitoring and seismic safety assessment. Although the finite element method (FEM) remains the prevailing approach because of its…
A neural network architecture is presented that exploits the multilevel properties of high-dimensional parameter-dependent partial differential equations, enabling an efficient approximation of parameter-to-solution maps, rivaling…
In recent years, Physics-informed neural networks (PINNs) have been widely used to solve partial differential equations alongside numerical methods because PINNs can be trained without observations and deal with continuous-time problems…
Recently, physics-informed neural networks (PINNs) and their variants have gained significant popularity as a scientific computing method for solving partial differential equations (PDEs), whereas accuracy is still its main shortcoming.…
We propose a simple, but efficient and accurate machine learning (ML) model for developing high-dimensional potential energy surface. This so-called embedded atom neural network (EANN) approach is inspired by the well-known empirical…
I formulate a general finite element method (FEM) for self-gravitating stellar systems. I split the configuration space to finite elements, and express the potential and density functions over each element in terms of their nodal values and…
The inverse Stefan problem, as a typical phase-change problem with moving boundaries, finds extensive applications in science and engineering. Recent years have seen the applications of physics-informed neural networks (PINNs) to solving…
Ternary Neural Networks (TNNs) have received much attention due to being potentially orders of magnitude faster in inference, as well as more power efficient, than full-precision counterparts. However, 2 bits are required to encode the…
Ensembles of Deep Neural Networks (DNNs) have achieved qualitative predictions but they are computing and memory intensive. Therefore, the demand is growing to make them answer a heavy workload of requests with available computational…
Electrical machines employing superconductors are attractive solutions in a variety of application domains. Numerical models are powerful and necessary tools to optimize their design and predict their performance. The electromagnetic…
A nonlinear Helmholtz (NLH) equation with high frequencies and corner singularities is discretized by the linear finite element method (FEM). After deriving some wave-number-explicit stability estimates and the singularity decomposition for…
Accurately simulating soft tissue deformation is crucial for surgical training, pre-operative planning, and real-time haptic feedback systems. While physics-based models such as the finite element method (FEM) provide high-fidelity results,…
In this paper, we introduce the Phantom Domain Finite Element Method (PDFEM), a novel computational approach tailored for the efficient analysis of heterogeneous and composite materials. Inspired by fictitious domain methods, this method…