Physics-regularized neural network of the ideal-MHD solution operator in Wendelstein 7-X configurations

The stellarator is a promising concept to produce energy from nuclear fusion by magnetically confining a high-pressure plasma. In a stellarator, the confining field is three-dimensional, and the computational cost of solving the 3D MHD equations currently limits stellarator research and design. Although data-driven approaches have been proposed to provide fast 3D MHD equilibria, the accuracy with which equilibrium properties are reconstructed is unknown. In this work, we describe an artificial neural network (NN) that quickly approximates the ideal-MHD solution operator in Wendelstein 7-X (W7-X) configurations. This model fulfils equilibrium symmetries by construction. The MHD force residual regularizes the solution of the NN to satisfy the ideal-MHD equations. The model predicts the equilibrium solution with high accuracy, and it faithfully reconstructs global equilibrium quantities and proxy functions used in stellarator optimization. The regularization term enforces that the NN reduces the ideal-MHD force residual, and solutions that are better than ground truth equilibria can be obtained at inference time. We also optimize W7-X magnetic configurations, where desiderable configurations can be found in terms of fast particle confinement. This work demonstrates with which accuracy NN models can approximate the 3D ideal-MHD solution operator and reconstruct equilibrium properties of interest, and it suggests how they might be used to optimize stellarator magnetic configurations.Comment: 46 pages, 23 figures, to be submitted to Nuclear Fusio

Accelerated Bayesian inference of plasma profiles with self-consistent MHD equilibria at W7-X via neural networks

High-$\langle \beta \rangle$ operations require a fast and robust inference of plasma parameters with a self-consistent MHD equilibrium. Precalculated MHD equilibria are usually employed at W7-X due to the high computational cost. To address this, we couple a physics-regularized NN model that approximates the ideal-MHD equilibrium with the Bayesian modeling framework Minerva. We show the fast and robust inference of plasma profiles (electron temperature and density) with a self-consistent MHD equilibrium approximated by the NN model. We investigate the robustness of the inference across diverse synthetic W7-X plasma scenarios. The inferred plasma parameters and their uncertainties are compatible with the parameters inferred using the VMEC, and the inference time is reduced by more than two orders of magnitude. This work suggests that MHD self-consistent inferences of plasma parameters can be performed between shots.Comment: 18 pages, 6 figure

Maternal outcomes and risk factors for COVID-19 severity among pregnant women.

Pregnant women may be at higher risk of severe complications associated with the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which may lead to obstetrical complications. We performed a case control study comparing pregnant women with severe coronavirus disease 19 (cases) to pregnant women with a milder form (controls) enrolled in the COVI-Preg international registry cohort between March 24 and July 26, 2020. Risk factors for severity, obstetrical and immediate neonatal outcomes were assessed. A total of 926 pregnant women with a positive test for SARS-CoV-2 were included, among which 92 (9.9%) presented with severe COVID-19 disease. Risk factors for severe maternal outcomes were pulmonary comorbidities [aOR 4.3, 95% CI 1.9-9.5], hypertensive disorders [aOR 2.7, 95% CI 1.0-7.0] and diabetes [aOR2.2, 95% CI 1.1-4.5]. Pregnant women with severe maternal outcomes were at higher risk of caesarean section [70.7% (n = 53/75)], preterm delivery [62.7% (n = 32/51)] and newborns requiring admission to the neonatal intensive care unit [41.3% (n = 31/75)]. In this study, several risk factors for developing severe complications of SARS-CoV-2 infection among pregnant women were identified including pulmonary comorbidities, hypertensive disorders and diabetes. Obstetrical and neonatal outcomes appear to be influenced by the severity of maternal disease

En Route Towards Heat Load Control for Wendelstein 7-X with Machine Learning Approaches

With this thesis, studies which form the bedrock for the long term goal of first wall heat load control and optimization for the advanced stellarator Wendelstein 7-X are developed, described and put into context. It is laid out how reconstruction of features of the edge magnetic field from plasma facing component heat loads is an important first step and can successfully be achieved by artificial neural networks. A detailed study of plasma facing component heat load distribution, potential overloads and overload mitigation possibilities is made in first order approximation of the impact of the main plasma dynamic effects.Im Rahmen dieser Arbeit werden Studien zusammengefasst, die das Fundament für das Fernziel der Regelung und Optimierung der Wärmelast auf der ersten Wand des Stellarators Wendelstein 7-X bilden. Es wird dargelegt, in wiefern die Rekonstruktion von Merkmalen des Randmagnetfelds aus Bildern der Wärmelast der ersten Wand ein wichtiger erster Schritt ist und unter Zuhilfenahme künstlicher neuronaler Netze erreicht werden kann. Detaillierte Untersuchung der Wärmelastverteilung der ersten Wand, möglicher Überlastungen und Möglichkeiten zur Vermeidung von Überlastung werden in Abhängigkeit der wichtigsten plasma-dynamischen Effekte durchgeführt

Reconstruction of magnetic configurations in W7-X using artificial neural networks

It is demonstrated that artificial neural networks can be used to accurately and efficiently predict details of the magnetic topology at the plasma edge of the Wendelstein 7-X stellarator, based on simulated as well as measured heat load patterns onto plasma-facing components observed with infrared cameras. The connection between heat load patterns and the magnetic topology is a challenging regression problem, but one that suits artificial neural networks well. The use of a neural network makes it feasible to analyze and control the plasma exhaust in real-time, an important goal for Wendelstein 7-X, and for magnetic confinement fusion research in general

Proof of concept of a fast surrogate model of the VMEC code via neural networks in Wendelstein 7-X scenarios

In magnetic confinement fusion research, the achievement of high plasma pressure is key to reaching the goal of net energy production. The magnetohydrodynamic (MHD) model is used to self-consistently calculate the effects the plasma pressure induces on the magnetic field used to confine the plasma. Such MHD calculations—usually done computationally—serve as input for the assessment of a number of important physics questions. The variational moments equilibrium code (VMEC) is the most widely used to evaluate 3D ideal-MHD equilibria, as prominently present in stellarators. However, considering the computational cost, it is rarely used in large-scale or online applications (e.g. Bayesian scientific modeling, real-time plasma control). Access to fast MHD equilibria is a challenging problem in fusion research, one which machine learning could effectively address. In this paper, we present artificial neural network (NN) models able to quickly compute the equilibrium magnetic field of Wendelstein 7-X. Magnetic configurations that extensively cover the device operational space, and plasma profiles with volume-averaged normalized plasma pressure ⟨β⟩ (β = $\frac{2{\mu }_{0}p}{{B}^{2}}$) up to 5% and non-zero net toroidal current are included in the data set. By using convolutional layers, the spectral representation of the magnetic flux surfaces can be efficiently computed with a single network. To discover better models, a Bayesian hyper-parameter search is carried out, and 3D convolutional NNs are found to outperform feed-forward fully-connected NNs. The achieved normalized root-mean-squared error, the ratio between the regression error and the spread of the data, ranges from 1% to 20% across the different scenarios. The model inference time for a single equilibrium is on the order of milliseconds. Finally, this work shows the feasibility of a fast NN drop-in surrogate model for VMEC, and it opens up new operational scenarios where target applications could make use of magnetic equilibria at unprecedented scales