Improving the stellarator through advances in plasma theory

Improvements to the stellarator concept can be realized through advancements in theoretical and computational plasma physics. Herein, recent advances are reported in the topical areas of: 1) improved energetic ion confinement, 2) the impact of three-dimensional (3D) shaping on turbulent transport, 3) reducing coil complexity, 4) novel optimization and design methods, and 5) computational MHD tools. These advances enable the development of new stellarator configurations with improved confinement properties.</p

Do optimization methods in deep learning applications matter?

With advances in deep learning, exponential data growth and increasing model complexity, developing efficient optimization methods are attracting much research attention. Several implementations favor the use of Conjugate Gradient (CG) and Stochastic Gradient Descent (SGD) as being practical and elegant solutions to achieve quick convergence, however, these optimization processes also present many limitations in learning across deep learning applications. Recent research is exploring higher-order optimization functions as better approaches, but these present very complex computational challenges for practical use. Comparing first and higher-order optimization functions, in this paper, our experiments reveal that Levemberg-Marquardt (LM) significantly supersedes optimal convergence but suffers from very large processing time increasing the training complexity of both, classification and reinforcement learning problems. Our experiments compare off-the-shelf optimization functions(CG, SGD, LM and L-BFGS) in standard CIFAR, MNIST, CartPole and FlappyBird experiments.The paper presents arguments on which optimization functions to use and further, which functions would benefit from parallelization efforts to improve pretraining time and learning rate convergence

Flexible Multi-layer Sparse Approximations of Matrices and Applications

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the complexity of applying linear operators in high dimension by approximately factorizing the corresponding matrix into few sparse factors. The approach relies on recent advances in non-convex optimization. It is first explained and analyzed in details and then demonstrated experimentally on various problems including dictionary learning for image denoising, and the approximation of large matrices arising in inverse problems

Computational Heat Transfer and Fluid Mechanics

With the advances in high-speed computer technology, complex heat transfer and fluid flow problems can be solved computationally with high accuracy. Computational modeling techniques have found a wide range of applications in diverse fields of mechanical, aerospace, energy, environmental engineering, as well as numerous industrial systems. Computational modeling has also been used extensively for performance optimization of a variety of engineering designs. The purpose of this book is to present recent advances, as well as up-to-date progress in all areas of innovative computational heat transfer and fluid mechanics, including both fundamental and practical applications. The scope of the present book includes single and multiphase flows, laminar and turbulent flows, heat and mass transfer, energy storage, heat exchangers, respiratory flows and heat transfer, biomedical applications, porous media, and optimization. In addition, this book provides guidelines for engineers and researchers in computational modeling and simulations in fluid mechanics and heat transfer

Generalized X-ray and neutron crystallographic analysis: more accurate and complete structures for biological macromolecules

X-ray and neutron crystallographic data have been combined in a joint structure-refinement procedure that has been developed using recent advances in modern computational methodologies, including cross-validated maximum-likelihood target functions with gradient-based optimization and simulated annealing

Blind Source Separation with Optimal Transport Non-negative Matrix Factorization

Optimal transport as a loss for machine learning optimization problems has recently gained a lot of attention. Building upon recent advances in computational optimal transport, we develop an optimal transport non-negative matrix factorization (NMF) algorithm for supervised speech blind source separation (BSS). Optimal transport allows us to design and leverage a cost between short-time Fourier transform (STFT) spectrogram frequencies, which takes into account how humans perceive sound. We give empirical evidence that using our proposed optimal transport NMF leads to perceptually better results than Euclidean NMF, for both isolated voice reconstruction and BSS tasks. Finally, we demonstrate how to use optimal transport for cross domain sound processing tasks, where frequencies represented in the input spectrograms may be different from one spectrogram to another.Comment: 22 pages, 7 figures, 2 additional file