FPGA acceleration of Bayesian model based analysis for time-independent problems

A Three-Dimensional Finite Volume Arbitrary Lagrangian-Eulerian simulation code was developed to study different plasma physics problems in 3D+t. The code is based on a complex multi-component species program with transport and radiation terms written and applied to plasma and fusion physics problems. The integration domain is represented with a structured irregular mesh, with fixed connectivity made of hexahedral cells. Coordinates and velocities are assigned to cell vertices. After each calculation cycle, mesh vertices are moved arbitrary over the fluid. The adaptive method consists of shifting mesh vertices over the fluid in order to keep a reasonable mesh structure and increase the spatial resolution where the physical solution demands. The code was a valuable tool for parametric study of different physical problems, mainly optimization of Plasma Focus Machine, detonation and propagation of thermonuclear reactions, and Kelvin-Helmholtz instabilities in the boundary layer of the terrestrial magnetopause.

This paper deals with the numerical identification of the plasma current density in a Tokamak, from experimental measurements. This problem consists in the identification of a non-linearity in a semi-linear 2D elliptic equation from Cauchy boundary measurements and from integrals of the magnetic field over several chords. A simplified problem, corresponding to the cylindrical approximation, is first solved by a SQP algorithm, where the non-linearity is decomposed in a basis of B-splines and where Tikhonov regularization is used, the regularizing parameter being determined by a cross-validation procedure. An alternative approach based on the decomposition of the non-linearity in a basis of compactly supported wavelets and the use of a new scalar product in the HH2 space has enabled to solve the identification problem in a robust way, without using Tikhonov regularization Finally several test-cases are presented for the determination of the current density in the real toroidal configuration from magnetic, interferometric and polarimetric measurements.KeywordsInverse ProblemSequential Quadratic ProgrammingTikhonov RegularizationMagnetic SurfaceFlux LineThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Dynamic load balancing with enhanced shared-memory parallelism for particle-in-cell codes

The impedance technique, also known as a particular case of the invariant embedding approach, is generalized for modeling electromagnetic wave propagation in anisotropic and gyrotropic media with spatial dispersion such as hot magnetized plasmas. That provides a new way for analytical and numerical studies of ‘full-wave’ problems in plasma physics that require exact solutions of Maxwell equations. Several examples of such a treatment are considered to demonstrate the flexibility and computational robustness of the proposed technique.

We study nonlinear inverse problems of the form F ( x ) = y , and their stable solution via iterative regularization methods, in particular by Newton-type methods, which are well-known for their fast convergence for well-posed problems. A basic step of Newton’s method consists of calculating the update Δ x k via solution of a linearized equation , which will in general be ill-posed if the nonlinear problem is. Thus, for ill-posed problems, the linearized equations have to be solved by some regularization method. In particular for large scale problems, e.g., inverse problems in partial differential equations, where F ( x ) is only defined implicitly via the solution of a PDE, iterative methods have to be used for this purpose. In order to keep the overall effort, i.e., the overall number of iterations, as small as possible, appropriate preconditioning has to be applied. We propose and analyse a general preconditioning strategy in Hilbert scales, and show that the overall number of iterations can be reduced to about the square root by preconditioning. Moreover, in many examples differential operators can be used as preconditioners, and thus preconditioning is almost for free. The theoretical results are illustrated in numerical examples. A comparison with preconditioned Landweber iteration shows that the iteration numbers can be further reduced, if fast iterative methods, e.g., the v -methods, are used for the solution of the linearized problems.

Two main aims of this paper are to develop a numerical method to solve an inverse source problem for parabolic equations and apply it to solve a nonlinear coefficient inverse problem. The inverse source problem in this paper is the problem to reconstruct a source term from external observations. Our method to solve this inverse source problem consists of two stages. We first establish an equation of the derivative of the solution to the parabolic equation with respect to the time variable. Then, in the second stage, we solve this equation by the quasi-reversibility method. The inverse source problem considered in this paper is the linearization of a nonlinear coefficient inverse problem. Hence, iteratively solving the inverse source problem provides the numerical solution to that coefficient inverse problem. Numerical results for the inverse source problem under consideration and the corresponding nonlinear coefficient inverse problem are presented.

This reference is for an abstract only. A full paper was not submitted for this conference. Abstract AVO (amplitude-varying-with-offset) is a seismic prestack inversion technique for estimating elastic parameters of the subsurface. The seismic AVO inversion problem can be formulated as a linearized or nonlinear inverse problem. It is a multidimensional and highly ill-posed inverse problem. It is affected by strong noise and measurement uncertainty. Therefore, in seismic AVO analysis, the goal is not only to find the model that best-fits the data, but also to characterize the uncertainty of the analysis. Uncertainty characterization of seismic analysis makes the geophysical interpretation more reliable. The Bayesian formalism generally constitutes a powerful approach for solving many seismic inverse problems. It allows combining available prior knowledge with the information contained in the seismic data. The solution of a Bayesian inverse problem is given by the joint posterior distribution of model parameters. Stochastic approximations of the true posterior are exemplified by the MCMC method and more recently by the particle filtering (PF) method. For most seismic inverse problems, stochastic approximation techniques are computationally unappealing. The maximum a posteriori (MAP) is the simplest Bayesian method for estimating model parameters. It provides the explanation that maximizes the posterior distribution. The maximum likelihood (ML) is a popular non-Bayesian method for estimating model parameters. It provides the explanation that maximizes the likelihood of the data. It assumes that the model parameters are deterministic and omits the pertinent prior knowledge on them. In practice, both MAP and ML point estimators have severe problems with over-fitting the data and model order estimation. In this paper, the recently-developed variational Bayesian learning is proposed as a new method for solving the linearized seismic AVO inversion problem. Variational Bayesian learning allows the true joint posterior distribution of model parameters to be approximated by a simpler approximating ensemble for which the required inferences are tractable. The main advantage in resorting to variational Bayesian learning is its robustness to the over-fitting problem, which is major in practice. This probabilistic machine learning method allows finding an optimum balance between the representation power and the model complexity of the data.

Various works from the literature aimed at accelerating Bayesian inference in inverse problems. Stochastic spectral methods have been recently proposed as surrogate approximations of the forward uncertainty propagation model over the support of the prior distribution. These representations are efficient because they allow affordable simulation of a large number of samples from the posterior distribution. Unfortunately, they do not perform well when the forward model exhibits strong nonlinear behavior with respect to its input.In this work, we first relate the fast (exponential) L2-convergence of the forward approximation to the fast (exponential) convergence (in terms of Kullback-Leibler divergence) of the approximate posterior. In particular, we prove that in case the prior distribution isuniform, the posterior is at least twice as fast as the convergence rate of the forwardmodel in those norms. The Bayesian inference strategy is developed in the framework of a stochastic spectral projectionmethod. The predicted convergence rates are then demonstrated for simple nonlinear inverse problems of varying smoothness.We then propose an efficient numerical approach for the Bayesian solution of inverse problems presenting strongly nonlinear or discontinuous systemresponses. This comes with the improvement of the forward model that isadaptivelyapproximated by an iterative generalized Polynomial Chaos-based representation. The numerical approximations and predicted convergence rates of the former approach are compared to the new iterative numericalmethod for nonlinear time-dependent test cases of varying dimension and complexity, which are relevant regarding our hydrodynamics motivations and therefore regarding hyperbolic conservation laws and the apparition of discontinuities in finite time.

The results of transport modeling codes, e.g., GENE for the plasma core or SOLPS-ITER for the plasma edge, depend critically on reliable profile and equilibrium estimates. The propagation of uncertainties (UP) of input quantities to the results of modeling codes, e.g., power and particle exhaust and plasma stability, is frequently neglected because of the costs of running the codes as well as because of the missing uncertainty quantification of input quantities. The situation becomes even more cumbersome if profile gradients and their uncertainties are of major concern for transport analyses. Two different techniques are presented to estimate profiles, profile gradients, their uncertainties, and candidate profiles for UP in modeling codes. Markov Chain Monte Carlo sampling of the posterior probability density of an integrated data analysis approach is applied to estimate electron density and temperature profiles. Nonstationary Gaussian process regression is applied to estimate ion temperature and angular velocity profiles. Both methods provide in a natural way profile gradients, profile logarithmic gradients, and their uncertainties. Modeling codes benefit also from reliable equilibrium reconstructions and quantification of the uncertainty of various equilibrium parameters. For the analysis of diagnostics data, the position and uncertainty of flux surfaces as well as of the magnetic axis are important. For plasma transport and stability codes, the estimation of uncertainties of current and q-profiles is presented. For plasma edge codes the position of the separatrix contour and its uncertainty at various poloidal positions is of primary interest especially if steep profile gradients are present. Examples of uncertainties and their sources in magnetic scalar quantities, profiles, and separatrix contours are shown.

This research apply two algorithms namely Mathematic Algorithm and table lookup Algorithm. From both algorithms, the research examine what algorithm have the fasted processing time and the smallest memory occupation. From the examination results the Mathematic Algorithm have 20.62 milliseconds processing time and the Table lookup algorithm have 14.08 milliseconds processing time. The Table lookup algorithm have the fastest processing time because the Matematic algorithm need the rounding process of the fi gure. Eventhough such processing time is not exceed from the 125 millisecond of delay time, in real condition, the total processing time are include the error correction processing time and voice compression processing time such as ADPCM or QCELP voice compression techniques.<br>

The turnaround time (TAT) for pre-transfusion testing is important for prompt clinical decision-making. TAT includes the time between the arrival of the sample and the initiation of testing, plus the processing time (PT) required to generate and report a result. The TAT in larger blood banks is mostly dependent upon the capability of the analyzer used. In smaller blood banks, where manual work is often performed, the TAT is dependent on availability and experience of staff, testing resources, and workload. Our site performed a comparative analysis of the ORTHO VISION® (Ortho Clinical Diagnostics, Raritan, NJ) and the Echo® (Immucor, Norcross, GA) blood bank analyzers, using the TAT and PT of standard blood bank tests as the outcome metrics. Tests were run in various combinations to reflect the standard workflow of a busy hospital transfusion service and under routine and immediate or STAT conditions. We also compared manual versus automated processing TATs for a variety of pre-transfusion tests and antibody titers. We found that the capacity of the VISION to load and run new samples, even while several other tests were ongoing, allowed for faster overall TAT when compared with samples run on the Echo. The PTs of the two analyzers (from load to result) were also compared, and we found them to be equivalent. These findings highlight the inherent flaw in considering only PT when assessing a laboratory's ability to efficiently and consistently make results available to best meet customer and patient needs. In addition, we observed a tighter distribution of TATs and PTs when the VISION was compared with the Echo analyzer, providing a higher level of predictability for availability of results. Finally, when compared with manual antibody titer testing, the VISION analyzer showed a faster PT.

An energy–momentum tensor for the microscopic plasma model is constructed from the action integral by allowing for dynamics of special relativity. The energy density is then identified with the 44-component of the energy–momentum tensor. The result is compared with that obtained from an ad hoc method with the Legendre transformation. The Hamiltonian obtained can be used to tackle nonlinear problems in plasma physics.

Neural networks (NNs) are successfully used to solve inverse and other problems in geophysics. The aim of this work, which is a continuation of a series of works by a group of authors, is to improve the efficiency of the NN method for solving nonlinear inverse 3D problems of geoelectrics, based on the construction of the author’s convolutional neural network. The network includes a number of additional special transformations (data compression, suppression of the influence of an unknown background environment, etc.) preceding the training of a classical MLP neural network and adapted to the inverse problem that is being solved. This allows us to formally, excluding the human factor, solve inverse problems of geoelectrics of large dimensions without specifying a first approximation based on data measured in areas whose dimensions exceed the dimensions of the network training area. The inversion speed is a few tens of seconds and does not depend on the physical dimensionality (2D or 3D) of the data. The solution to the inverse problem found using a trained neural network can, if necessary, be refined using a random search method. Numerical results of solving 3D geoelectric problems on model and field data are presented, confirming the stated development parameters.

A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields.

Symbolic vector analysis in plasma physics