S. Gori

Molecular dynamics study of grain boundary diffusion of hydrogen in tungsten

Understanding the influence of the microstructure of tungsten on hydrogen transport is crucial for the use of tungsten as first-wall material in fusion reactors. Here, we report the results of molecular dynamics and transition state studies on the influence of grain boundaries in tungsten on the transport of hydrogen. An exhaustive mapping of possible minimum activation energy migration trajectories for hydrogen as the trace impurity reveals a strongly modified activation energy distribution in the neighborhood of grain boundaries together with an altered connectivity matrix. The results indicate that grain boundaries in polycrystalline tungsten may provide an important transport channel, especially for neutron-damaged tungsten.

Invariance priors for Bayesian feed-forward neural networks

Neural networks (NN) are famous for their advantageous flexibility for problems when there is insufficient knowledge to set up a proper model. On the other hand, this flexibility can cause overfitting and can hamper the generalization of neural networks. Many approaches to regularizing NN have been suggested but most of them are based on ad hoc arguments. Employing the principle of transformation invariance, we derive a general prior in accordance with the Bayesian probability theory for feed-forward networks. An optimal network is determined by Bayesian model comparison, verifying the applicability of this approach. Additionally the prior presented affords cell pruning.

Fast tomographic methods for the tokamak ISTTOK

The achievement of long duration, alternating current discharges on the tokamak IST‐TOK requires a real‐time plasma position control system. The plasma position determination based on magnetic probes system has been found to be inadequate during the current inversion due to the reduced plasma current. A tomography diagnostic has been therefore installed to supply the required feedback to the control system. Several tomographic methods are available for soft X‐ray or bolo‐metric tomography, among which the Cormack and Neural networks methods stand out due to their inherent speed of up to 1000 reconstructions per second, with currently available technology. This paper discusses the application of these algorithms on fusion devices while comparing performance and reliability of the results. It has been found that although the Cormack based inversion proved to be faster, the neural networks reconstruction has fewer artifacts and is more accurate.

Bayesian neural-networks-based evaluation of binary speckle data

We present a new method using Bayesian probability theory and neural networks for the evaluation of speckle interference patterns for an automated analysis of deformation and erosion measurements. The method is applied to the fringe pattern reconstruction of speckle measurements with a Twyman-Green interferometer. Given a binary speckle image, the method returns the fringe pattern without noise, thus removing the need for smoothing and allowing a straightforward unwrapping procedure and determination of the surface shape. Because no parameters have to be adjusted, the method is especially suited for continuous and automated monitoring of surface changes.

Modeling hydrogen transport in large disordered systems

The diffusion of hydrogen in disordered structures (i.e. polycrystalline materials) can be modeled in terms of a network of transitions between neighbored local energetic minima. These networks have been generated for the tungsten–hydrogen system based on results of classical molecular dynamics simulations. The sparsity of the resulting energy-landscape-based networks enables within the transition-state theory approximation an efficient computation of the transport properties of hydrogen in large systems. The results confirm that grain boundaries in polycrystalline tungsten can provide a fast and extended transport channel. Finally, the relation of transition network approach with kinetic Monte Carlo is exploited to simulate break-through curves in a simple two-dimensional lattice model system.

Fitting of Functions with Uncertainities in Dependent and Independent Variables

The problem of fitting (non‐linear) functions to measured data when both, the dependent and independent variables are subject to error is very common in physics. Here we analyze the problem from a Bayesian point of view which leads to a conceptually transparent solution. However, the underlying data dependent marginalizations raise some subtle issues which are not present in the standard Bayesian estimation problem. The necessary high‐dimensional integrations in the data space have been addressed with a nested parallel‐tempering Hamilton Monte Carlo (PT‐HMC) algorithm. A nonlinear worked example is given.

Optimizing Nuclear Reaction Analysis (NRA) using Bayesian Experimental Design

Nuclear Reaction Analysis with 3He holds the promise to measure Deuterium depth profiles up to large depths. However, the extraction of the depth profile from the measured data is an ill‐posed inversion problem. Here we demonstrate how Bayesian Experimental Design can be used to optimize the number of measurements as well as the measurement energies to maximize the information gain. Comparison of the inversion properties of the optimized design with standard settings reveals huge possible gains. Application of the posterior sampling method allows to optimize the experimental settings interactively during the measurement process.

A Prior for Neural Networks utilizing Enclosing Spheres for Normalization

Neural Networks are famous for their advantageous flexibility for problems when there is insufficient knowledge to set up a proper model. On the other hand this flexibility can cause over‐fitting and can hamper the generalization properties of neural networks. Many approaches to regularize NN have been suggested but most of them based on ad‐hoc arguments. Employing the principle of transformation invariance we derive a general prior in accordance with the Bayesian probability theory for a class of feedforward networks. Optimal networks are determined by Bayesian model comparison verifying the applicability of this approach.

DIGITAL PARTICLE IMAGE VELOCIMETRY USING SPLINES IN TENSION

Digital particle imaging velocimetry has become a widely used diagnostic technique for the extraction of quantitative information about flow fields. Multiple‐view geometries are used to identify and track individual particles (tracers) at discrete times. Often particle velocities and accelerations are subsequently derived by ill‐conditioned methods based on finite‐differences of the noisy measurements of the particle positions. Here a different Bayesian approach based on a model of the particles in 3‐D velocity space using splines in tension is presented, thus automatically including the physical constraints of finite acceleration. The properties of the new algorithm will be compared with the conventional approach and it is argued that the (exponential) spline model should be formulated in the space where the quantity to be modelled is continous, instead of being placed in the data space.

Comparison of fast tomographic methods for application on the Soft X-Ray Tomography System on Wendelstein 7-X stellarator

The Wendelstein 7-X stellarator, presently under construction in Greifswald, is foreseen to operate on a steady state regime. Under such a scenario, a constant diagnosis of the plasma characteristics is strongly envisaged. A X-Ray Tomography diagnostic is a particularly useful tool since a poloidal cross-section of the plasmas X-Ray emissivity can be reconstructed and the plasmas position as well as MHD activity can be inferred.Fast tomographic algorithms such as the Cormack inversion or neural networks (NN) can be applied to obtain recon-structions at a human time scale (10∼100 reconstructions per second). This paper discusses the potential application of these algorithms on the Wendelstein 7-X stellarator by comparing performance and reliability of the results. The NN reconstruction has proven to be faster and more reliable than the Cormacks.