Related papers: Deep neural network Grad-Shafranov solver constrai…

Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to…

Nonlinear differential equations are challenging to solve numerically and are important to understanding the dynamics of many physical systems. Deep neural networks have been applied to help alleviate the computational cost that is…

Graduated optimization is a global optimization technique that is used to minimize a multimodal nonconvex function by smoothing the objective function with noise and gradually refining the solution. This paper experimentally evaluates the…

We address the efficiency issue for the construction of a deep graph neural network (GNN). The approach exploits the idea of representing each input graph as a fixed point of a dynamical system (implemented through a recurrent neural…

Partial differential equations and variational problems can be solved with physics informed neural networks (PINNs). The unknown field is approximated with neural networks. Minimizing the residuals of the static Maxwell equation at…

In the last decade, deep learning has become a major component of artificial intelligence. The workhorse of deep learning is the optimization of loss functions by stochastic gradient descent (SGD). Traditionally in deep learning, neural…

Deep neural networks (DNNs) are widely used in pattern-recognition tasks for which a human comprehensible, quantitative description of the data-generating process, e.g., in the form of equations, cannot be achieved. While doing so, DNNs…

A computational graph in a deep neural network (DNN) denotes a specific data flow diagram (DFD) composed of many tensors and operators. Existing toolkits for visualizing computational graphs are not applicable when the structure is highly…

We propose a novel deep network architecture for image\\ denoising based on a Gaussian Conditional Random Field (GCRF) model. In contrast to the existing discriminative denoising methods that train a separate model for each noise level, the…

The graph neural network (GNN) has demonstrated its superior performance in various applications. The working mechanism behind it, however, remains mysterious. GNN models are designed to learn effective representations for graph-structured…

We develop an approach of Grad-Shafranov (GS) reconstruction for toroidal structures in space plasmas, based on in-situ spacecraft measurements. The underlying theory is the GS equation that describes two-dimensional magnetohydrostatic…

The success of deep neural networks (DNNs) is attributable to three factors: increased compute capacity, more complex models, and more data. These factors, however, are not always present, especially for edge applications such as autonomous…

Our contributions are motivated by fusion reactors that rely on maintaining magnetohydrodynamic (MHD) equilibrium, where the balance between plasma pressure and confining magnetic fields is required for stable operation. In axisymmetric…

The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…

Currently there is great interest in the utility of deep neural networks (DNNs) for the physical layer of radio frequency (RF) communications. In this manuscript, we describe a custom DNN specially designed to solve problems in the RF…

This paper introduces an incremental training framework for compressing popular Deep Neural Network (DNN) based unfolded multiple-input-multiple-output (MIMO) detection algorithms like DetNet. The idea of incremental training is explored to…

Despite their successful application to a variety of tasks, neural networks remain limited, like other machine learning methods, by their sensitivity to shifts in the data: their performance can be severely impacted by differences in…

Deep learning networks have shown promising results in fast magnetic resonance imaging (MRI) reconstruction. In our work, we develop deep networks to further improve the quantitative and the perceptual quality of reconstruction. To begin…

A longstanding goal in deep learning research has been to precisely characterize training and generalization. However, the often complex loss landscapes of neural networks have made a theory of learning dynamics elusive. In this work, we…

Current deep neural networks (DNNs) are overparameterized and use most of their neuronal connections during inference for each task. The human brain, however, developed specialized regions for different tasks and performs inference with a…