arXiv subjects

Matthias Frey

Publications and source records attributed to Matthias Frey.

31 records · Page 2Linked to original sources

arXiv2021

Input Beam Matching and Beam Dynamics Design Optimization of the IsoDAR RFQ using Statistical and Machine Learning Techniques

We present a novel machine learning-based approach to generate fast-executing virtual radiofrequency quadrupole (RFQ) particle accelerators using surrogate modelling. These could potentially be used as on-line feedback tools during beam commissioning and operation, and to optimize the RFQ beam dynamics design prior to construction. Since surrogate models execute orders of magnitude faster than corresponding physics beam dynamics simulations using standard tools like PARMTEQM and RFQGen, the computational complexity of the multi-objective optimization problem reduces significantly. Ultimately, this presents a computationally inexpensive and time efficient method to perform sensitivity studies and an optimization of the crucial RFQ beam output parameters like transmission and emittances. Two different methods of surrogate model creation (polynomial chaos expansion and neural networks) are discussed and the achieved model accuracy is evaluated for different study cases with gradually increasing complexity, ranging from a simple FODO cell example to the full RFQ optimization. We find that variations of the beam input Twiss parameters can be reproduced well. The prediction of the beam with respect to hardware changes, e.g. of the electrode modulation, are challenging on the other hand. We discuss possible reasons.

physics.acc-ph↗

arXiv2021

Over-The-Air Computation in Correlated Channels

Over-the-Air (OTA) computation is the problem of computing functions of distributed data without transmitting the entirety of the data to a central point. By avoiding such costly transmissions, OTA computation schemes can achieve a better-than-linear (depending on the function, often logarithmic or even constant) scaling of the communication cost as the number of transmitters grows. Among the most common functions computed OTA are linear functions such as weighted sums. In this work, we propose and analyze an analog OTA computation scheme for a class of functions that contains linear functions as well as some nonlinear functions such as $p$-norms of vectors. We prove error bound guarantees that are valid for fast-fading channels and all distributions of fading and noise contained in the class of sub-Gaussian distributions. This class includes Gaussian distributions, but also many other practically relevant cases such as Class A Middleton noise and fading with dominant line-of-sight components. In addition, there can be correlations in the fading and noise so that the presented results also apply to, for example, block fading channels and channels with bursty interference. We do not rely on any stochastic characterization of the distributed arguments of the OTA computed function; in particular, there is no assumption that these arguments are drawn from identical or independent probability distributions. Our analysis is nonasymptotic and therefore provides error bounds that are valid for a finite number of channel uses. OTA computation has a huge potential for reducing communication cost in applications such as Machine Learning (ML)-based distributed anomaly detection in large wireless sensor networks. We illustrate this potential through extensive numerical simulations.

cs.IT↗

arXiv2020

Global Sensitivity Analysis on Numerical Solver Parameters of Particle-In-Cell Models in Particle Accelerator Systems

Every computer model depends on numerical input parameters that are chosen according to mostly conservative but rigorous numerical or empirical estimates. These parameters could for example be the step size for time integrators, a seed for pseudo-random number generators, a threshold or the number of grid points to discretize a computational domain. In case a numerical model is enhanced with new algorithms and modelling techniques the numerical influence on the quantities of interest, the running time as well as the accuracy is often initially unknown. Usually parameters are chosen on a trial-and-error basis neglecting the computational cost versus accuracy aspects. As a consequence the cost per simulation might be unnecessarily high which wastes computing resources. Hence, it is essential to identify the most critical numerical parameters and to analyze systematically their effect on the result in order to minimize the time-to-solution without losing significantly on accuracy. Relevant parameters are identified by global sensitivity studies where Sobol' indices are common measures. These sensitivities are obtained by surrogate models based on polynomial chaos expansion. In this paper, we first introduce the general methods for uncertainty quantification. We then demonstrate their use on numerical solver parameters to reduce the computational costs and discuss further model improvements based on the sensitivity analysis. The sensitivities are evaluated for neighbouring bunch simulations of the existing PSI Injector II and PSI Ring as well as the proposed Daedalus Injector cyclotron and simulations of the rf electron gun of the Argonne Wakefield Accelerator.

physics.comp-ph↗

arXiv2020

Sparse Grids based Adaptive Noise Reduction strategy for Particle-In-Cell schemes

We propose a sparse grids based adaptive noise reduction strategy for electrostatic particle-in-cell (PIC) simulations. Our approach is based on the key idea of relying on sparse grids instead of a regular grid in order to increase the number of particles per cell for the same total number of particles, as first introduced in Ricketson and Cerfon (Plasma Phys. and Control. Fusion, 59(2), 024002). Adopting a new filtering perspective for this idea, we construct the algorithm so that it can be easily integrated into high performance large-scale PIC code bases. Unlike the physical and Fourier domain filters typically used in PIC codes, our approach automatically adapts to mesh size, number of particles per cell, smoothness of the density profile and the initial sampling technique. Thanks to the truncated combination technique, we can reduce the larger grid-based error of the standard sparse grids approach for non-aligned and non-smooth functions. We propose a heuristic based on formal error analysis for selecting the optimal truncation parameter at each time step, and develop a natural framework to minimize the total error in sparse PIC simulations. We demonstrate its efficiency and performance by means of two test cases: the diocotron instability in two dimensions, and the three-dimensional electron dynamics in a Penning trap. Our run time performance studies indicate that our new scheme can provide significant speedup and memory reduction as compared to regular PIC for achieving comparable accuracy in the charge density deposition.

physics.comp-ph↗

arXiv2019

Distributed Approximation of Functions over Fast Fading Channels with Applications to Distributed Learning and the Max-Consensus Problem

In this work, we consider the problem of distributed approximation of functions over multiple-access channels with additive noise. In contrast to previous works, we take fast fading into account and give explicit probability bounds for the approximation error allowing us to derive bounds on the number of channel uses that are needed to approximate a function up to a given approximation accuracy. Neither the fading nor the noise process is limited to Gaussian distributions. Instead, we consider sub-gaussian random variables which include Gaussian as well as many other distributions of practical relevance. The results are motivated by and have immediate applications to a) computing predictors in models for distributed machine learning and b) the max-consensus problem in ultra-dense networks.

cs.IT↗

arXiv2019

On Architecture and Performance of Adaptive Mesh Refinement in an Electrostatics Particle-In-Cell Code

This article presents a hardware architecture independent implementation of an adaptive mesh refinement Poisson solver that is integrated into the electrostatic Particle-In-Cell beam dynamics code OPAL. The Poisson solver is solely based on second generation Trilinos packages to ensure the desired hardware portability. Based on the massively parallel framework AMReX, formerly known as BoxLib, the new adaptive mesh refinement interface provides several refinement policies in order to enable precise large-scale neighbouring bunch simulations in high intensity cyclotrons. The solver is validated with a built-in multigrid solver of AMReX and a test problem with analytical solution. The parallel scalability is presented as well as an example of a neighbouring bunch simulation that covers the scale of the later anticipated physics simulation.

physics.comp-ph↗

arXiv2019

Matching of turn pattern measurements for cyclotrons using multi-objective optimization

The usage of numerical models to study the evolution of particle beams is an essential step in the design process of particle accelerators However, uncertainties of input quantities such as beam energy and magnetic field lead to simulation results that do not fully agree with measurements, hence the final machine will behave slightly differently than the simulations In case of cyclotrons such discrepancies affect the overall turn pattern or may even alter the number of turns in the machine Inaccuracies at the PSI Ring cyclotron facility that may harm the isochronism are compensated by additional magnetic fields provided by 18 trim coils These are often absent from simulations or their implementation is very simplistic In this paper a newly developed realistic trim coil model within the particle accelerator framework OPAL is presented that was used to match the turn pattern of the PSI Ring cyclotron Due to the high-dimensional search space consisting of 48 design variables (simulation input parameters) and 182 objectives (i.e turns) simulation and measurement cannot be matched in a straightforward manner Instead, an evolutionary multi-objective optimisation with a population size of more than 8000 individuals per generation together with a local search approach were applied that reduced the maximum absolute error to 4.54 mm over all 182 turns.

physics.acc-ph↗

arXiv2019

OPAL a Versatile Tool for Charged Particle Accelerator Simulations

Many sophisticated computer models have been developed to understand the behaviour of particle accelerators. Even these complex models often do not describe the measured data. Interactions of the beam with external fields, other particles in the same beam and the beam walls all present modelling challenges. These can be challenging to model correctly even with modern supercomputers. This paper describes OPAL (Object Oriented Parallel Accelerator Library), a parallel open source tool for charged-particle optics in linear accelerators and rings, including 3D space charge. OPAL is built from the ground up as a parallel application exemplifying the fact that high performance computing is the third leg of science, complementing theory and experiment. Using the MAD language with extensions, OPAL can run on a laptop as well as on the largest high performance computing systems. The OPAL framework makes it easy to add new features in the form of new C++ classes, enabling the modelling of many physics processes and field types. OPAL comes in two flavours: OPAL-cycl: tracks particles with 3D space charge including neighbouring turns in cyclotrons and FFAs with time as the independent variable. OPAL-t: models beam lines, linacs, rf-photo injectors and complete XFELs excluding the undulator. The code is managed through the git distributed version control system. A suite of unit tests have been developed for various parts of OPAL, validating each part of the code independently. System tests validate the overall integration of different elements.

physics.acc-ph↗

arXiv2019

A Scalable Max-Consensus Protocol For Noisy Ultra-Dense Networks

We introduce \emph{ScalableMax}, a novel communication scheme for achieving max-consensus in a network of multiple agents which harnesses the interference in the wireless channel as well as its multicast capabilities. In a sufficiently dense network, the amount of communication resources required grows logarithmically with the number of nodes, while in state-of-the-art approaches, this growth is at least linear. ScalableMax can handle additive noise and works well in a high SNR regime. For medium and low SNR, we propose the \emph{ScalableMax-EC} scheme, which extends the ideas of ScalableMax by introducing a novel error correction scheme. It achieves lower error rates at the cost of using more channel resources. However, it preserves the logarithmic growth with the number of agents in the system.

cs.IT↗

arXiv2018

Resolvability on Continuous Alphabets

We characterize the resolvability region for a large class of point-to-point channels with continuous alphabets. In our direct result, we prove not only the existence of good resolvability codebooks, but adapt an approach based on the Chernoff-Hoeffding bound to the continuous case showing that the probability of drawing an unsuitable codebook is doubly exponentially small. For the converse part, we show that our previous elementary result carries over to the continuous case easily under some mild continuity assumption.

cs.IT↗

arXiv2018

The MAC Resolvability Region, Semantic Security and Its Operational Implications

Building upon previous work on the relation between secrecy and channel resolvability, we revisit a secrecy proof for the multiple-access channel (MAC) from the perspective of resolvability. In particular, we refine and extend the proof to obtain novel results on the second-order achievable rates. Then we characterize the resolvability region of the memoryless MAC by establishing a conceptually simple converse proof for resolvability that relies on the uniform continuity of Shannon's entropy with respect to the variational distance. We discuss the operational meaning of the information theoretic concept of semantic security from the viewpoint of Ahlswede's General Theory of Information Transfer and show interesting implications on the resilience against a large class of attacks even if no assumption can be made about the distributions of the transmitted messages. Finally we provide details on how the resolvability results can be used to construct a wiretap code that achieves semantic security.

cs.IT↗

arXiv2017

MAC Resolvability: First And Second Order Results

Building upon previous work on the relation between secrecy and channel resolvability, we revisit a secrecy proof for the multiple-access channel from the perspective of resolvability. We then refine the approach in order to obtain some novel results on the second-order achievable rates.

cs.IT↗

arXiv2017

User Activity Detection via Group Testing and Coded Computation

Inspired by group testing algorithms and the coded computation paradigm, we propose and analyze a novel multiple access scheme for detecting active users in large-scale networks. The scheme consists of a simple randomized detection algorithm that uses computation coding as intermediate steps for computing logical disjunction functions over the multiple access channel (MAC). First we show that given an efficient MAC code for disjunction computation the algorithm requires $O(k \log (\frac{N}{k }))$ decision steps for detecting $k$ active users out of $N+k$ users. Subsequently we present a simple suboptimal code for a class of MACs with arbitrarily varying sub-gaussian noise that uniformly requires $O (k \log (N) \max \{ \log k , \log \log N \} )$ channel uses for solving the activity detection problem. This shows that even in the presence of noise an efficient detection of active users is possible. Our approach reveals that the true crux of the matter lies in constructing efficient codes for computing disjunctions over a MAC.

cs.IT↗