Related papers: Neural network tokamak equilibria with incompressi…

Solving partial differential equations is difficult. Recently proposed neural resolution-invariant models, despite their effectiveness and efficiency, usually require equispaced spatial points of data. However, sampling in spatial domain is…

Training deep neural networks for solving machine learning problems is one great challenge in the field, mainly due to its associated optimisation problem being highly non-convex. Recent developments have suggested that many training…

Graph Neural Networks (GNNs) are deep learning models that take graph data as inputs, and they are applied to various tasks such as traffic prediction and molecular property prediction. However, owing to the complexity of the GNNs, it has…

We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning…

Physics-Informed Neural Network (PINN) has proven itself a powerful tool to obtain the numerical solutions of nonlinear partial differential equations (PDEs) leveraging the expressivity of deep neural networks and the computing power of…

Achievement of solutions in Navier-Stokes equation is one of challenging quests, especially for its closure problem. For achievement of particular solutions, there are variety of numerical simulations including Direct Numerical Simulation…

Learning representations of well-trained neural network models holds the promise to provide an understanding of the inner workings of those models. However, previous work has either faced limitations when processing larger networks or was…

Recent results will be presented on steady states of magnetically confined plasmas obtained by conventional and Hamiltonian methods. The presentation consists of three parts. The first one concerns the derivation of a generalized…

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…

This overview presents a tutorial introduction to the theory of magnetic plasma confinement in toroidal confinement systems with particular emphasis on axisymmetric equilibrium geometries, and tokamaks. The discussion covers three important…

Neutral-beam-driven, sub-cyclotron compressional (CAE) and global (GAE) \Alfven eigenmodes are routinely excited in spherical tokamaks such as NSTX(-U) and MAST, have been observed on the conventional aspect ratio tokamak DIII-D, and may be…

We formulate the training of generative adversarial networks (GANs) as a Nash equilibrium seeking problem. To stabilize the training process and find a Nash equilibrium, we propose an asymmetric regularization mechanism based on the classic…

We compute the ground-state properties of fully polarized, trapped, one-dimensional fermionic systems interacting through a gaussian potential. We use an antisymmetric artificial neural network, or neural quantum state, as an ansatz for the…

Sets represent a fundamental abstraction across many types of data. To handle the unordered nature of set-structured data, models such as DeepSets and PointNet rely on fixed, non-learnable pooling operations (e.g., sum or max) -- a design…

The surge in interest in Artificial Intelligence (AI) over the past decade has been driven almost exclusively by advances in Artificial Neural Networks (ANNs). While ANNs set state-of-the-art performance for many previously intractable…

In recent years, graph neural networks (GNNs) have emerged as a successful tool in a variety of graph-related applications. However, the performance of GNNs can be deteriorated when noisy connections occur in the original graph structures;…

The Neural Tangent Kernel (NTK) viewpoint is widely employed to analyze the training dynamics of overparameterized Physics-Informed Neural Networks (PINNs). However, unlike the case of linear Partial Differential Equations (PDEs), we show…

Turbulence modeling is a classical approach to address the multiscale nature of fluid turbulence. Instead of resolving all scales of motion, which is currently mathematically and numerically intractable, reduced models that capture the…

It is shown that the magnetohydrodynamic equilibrium states of an axisymmetric toroidal plasma with finite resistivity and flows parallel to the magnetic field are governed by a second-order partial differential equation for the poloidal…

Although Answer Set Programming (ASP) allows constraining neural-symbolic (NeSy) systems, its employment is hindered by the prohibitive costs of computing stable models and the CPU-bound nature of state-of-the-art solvers. To this end, we…