Invariance priors for Bayesian feed-forward neural networks

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Abstract. Integrated Data Analysis (IDA) offers a unified way of combining information relevant to fusion experiments. Thereby, IDA meets with typical issues arising in fusion data analysis. In IDA, all information is consistently formulated as probability density functions quantifying uncertainties in the analysis within the Bayesian probability theory. For a single diagnostic, IDA allows the identification of faulty measurements and improvements in the setup. For a set of diagnostics, IDA gives joint error distributions allowing the comparison and integration of different diagnostics results. Validation of physics models can be performed by model comparison techniques. Typical data analysis applications benefit from IDA capabilities of nonlinear error propagation, the inclusion of systematic effects and the comparison of different physics models. Applications range from outlier detection, background discrimination, model assessment and design of diagnostics. In order to cope with next step fusion device requirements, appropriate techniques are explored for fast analysis applications. Keywords DATA ANALYSIS FOR MAGNETIC CONFINEMENT FUSION DEVICESNext step fusion devices define several new requirements for data analysis. Since the demonstration of fusion reactor capabilities aims at steady-state operation, the data processing paradigm needs to be shifted from a shoot-and-collect to a view-and-react philosophy. Therefore, fast and reliable physics information is mandatory to use the experimental devices most efficiently and off-line analysis schemes as in pulsed devices will restrict operational capabilities. Long-time scales due to plasma-wall effects and magnetic field relaxation will require intelligent control schemes which employ physical models in multi-variate adaptive controllers.The major challenge for data analysis in magnetic fusion experiments is to link many different heterogeneous information sources [1]. The reason for the heterogeneity lies in the variety of methods in plasma diagnostics which is required to

Section: More Applications Of Bayesian Probability Theory In Fusionmentioning

confidence: 99%

Integrated Data Analysis for Fusion: A Bayesian Tutorial for Fusion Diagnosticians

Dinklage

Dreier

Fischer

et al. 2008

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“…As a result, the NN's reconstruction can fail if the channel data is too different from the training set, although this may be detected [5], while the FB's has always some artifacts which must be filtered by a post-processing algorithm.…”

Section: Discussionmentioning

confidence: 99%

“…The training and layer optimization of the network was performed using bayesian methods [5] and produced a two hidden layer network where the first hidden layer has 9 neurons and the second hidden layer also has 9 neurons. The inputs for the network are the data channels from the photodiodes and the (x, y) position of the pixel being reconstructed and the output is the value of this pixel.…”

Section: Neural Networkmentioning

confidence: 99%

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Fast tomographic methods for the tokamak ISTTOK

Carvalho¹,

Thomsen

Gori

et al. 2008

Abstract. 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 bolometric 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.

“…This has been demonstrated by a mock bolometry example with realistic uncertainties. The straightforward next step is the addition of a suitable MCMC-method (see [13]) to improve on the presently used evidence approximations and the integration into the framework of Bayesian Neural Networks [14] to achieve real-time deconvolution capabilities with ≈ 10 3 deconvolutions/s.…”

Section: Discussionmentioning

confidence: 99%

Deconvolution using thin-plate splines

Toussaint

Gori

2007

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The ubiquitous problem of estimating 2-dimensional profile information from a set of line integrated measurements is tackled with Bayesian probability theory by exploiting prior information about local smoothness. For this purpose thin-plate-splines (the 2-D minimal curvature analogue of cubic-splines in 1-D) are employed. The optimal number of support points required for inversion of 2-D tomographic problems is determined using model comparison. Properties of this approach are discussed and the question of suitable priors is addressed. Finally, we illustrated the properties of this approach with 2-D inversion results using data from line-integrated measurements from fusion experiments.