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Deliverable D5.4 in the ROMSOC project

Astronomical imaging with ground-based telescopes suffers from quickly varying optical distortions, which cause blurring and loss of contrast. These optical distortions are induced by turbulences in the earth's atmosphere. Since the contrast and sharpness of images are essential for astronomical observations, a method that compensates for these aberrations is required. This technique is called Adaptive Optics (AO). It utilizes a combination of wavefront sensors, that measure the deformations of wavefronts emitted by guide stars, and deformable mirrors to correct for them. Classical AO systems, using only one guide star, achieve high image quality only near to this guide star. Since there are not enough bright guide stars available close to scientific objects of interest, AO systems that achieve a good correction over a large field have been developed. These systems involve a tomographic estimation of the 3D atmospheric wavefront disturbance. Mathematically, the reconstruction of turbulent layers in the atmosphere is severely ill-posed, hence, limits the achievable solution accuracy. Moreover, the reconstruction has to be performed in real-time at a few hundred to thousand Hertz frame rates. This leads to a computational challenge, especially for the AO systems of future Extremely Large Telescopes (ELTs) with a primary mirror up to 40 m. The aim of this work is to develop and implement an efficient real-time reconstruction algorithm on the high-performance hardware of the industrial partner Microgate. In particular, we present a novel, conjugate gradient (CG) based method called augmented Finite Element Wavelet Hybrid Algorithm (augmented FEWHA) for atmospheric tomography. Our method is based on the classical FEWHA, which uses a dual-domain discretization strategy to obtain sparse operators. The matrix-free representation of these operators leads to a significant reduction in the computational load and memory. Moreover, the method is highly parallelizable. A crucial indicator for the run-time of iterative solvers is the number of iterations. We extend the classical FEWHA with an augmented Krylov subspace method in order to reduce the number of CG iterations. Moreover, we provide an efficient, parallel implementation of both algorithms on a multi-core CPU and a GPU. We analyze the performance of augmented FEWHA in terms of quality and run-time via numerical simulations for ELT-sized test configurations. As a quality benchmark we use the classical FEWHA, which is known to yield excellent results. In terms of run-time augmented FEWHA requires less CG iterations compared to the classical version, which results in a significant performance boost. Die astronomische Bilderfassung mit erdgebundenen Teleskopen leidet stark unter sich schnell veränderten optischen Effekten, welche Unschärfe und Kontrastverlust zur Folge haben. Diese Störungen werden durch Turbulenzen in der Erdatmosphäre hervorgerufen. Um die Bildqualität zu verbessern, werden sogenannte Adaptive Optik (AO) Systeme eingesetzt. Diese Systeme benutzen Wellenfrontsensoren, welche die Aberrationen der Lichtwellen von Leitsternen erkennen, sowie verformbare Spiegel, welche die atmosphäri-schen Störungen kompensieren. Klassische AO Syteme benutzen lediglich einen Leitstern und erreichen deshalb einen hohe Bildqualität nur für Objekte in der Nähe dieses Sterns. Da nicht genug helle Leitsterne für beliebige astronomische Objekte verfügbar sind, wurden AO Systeme entwickelt die eine gute Bildqualität über ein breites Sichtfeld liefern. Solche System erfordern die tomografische Berechnung der dreidimensionale atmospherischen Wellenfrontstörungen. Aus mathematischer Sicht ist diese Problem schlecht gestellt, d.h. die Lösungsgenauigkeit ist stark eingeschränkt. Zudem muss die Rekonstruktion in Echtzeit, bei einer Bildrate von einigen hunderten bis zu tausend Hertz, passieren. Dies führt zur erheblichen Herausforderungen im Bereich der Rechenleistung, im Speziellen für die AO Syteme der zukünfigen Riesenteleskopen (ELTs), welche einen Primärspiegel von bis zu 40 m besitzen. Das Ziel dieser Arbeit ist es, einen effiziente Echtzeitrekonstruktor zu entwickeln und in die Hardware des Industriepartners Microgate zu integrieren. Wir präsentieren den augmented Finite Element Wavelet Hybrid Algorithm (augmented FEWHA), welcher auf dem klassichen FEWHA beruht und somit auf der Methode der konjugierten Gradienten. FEWHA benutzt eine duale Domän-Diskretisierungsstrategie, um eine effiziente matrixfreie Darstellung aller zugrundeliegender Operatoren zu erhalten. Diese Darstellung reduziert den Rechenaufwand und die Speicherauslatung erheblich. Außerdem ist der Algorithmus sehr gut parallelisierbar. Ein entscheidender Faktor für die Laufzeit iterativer Löser ist die Anzahl der Iterationen. In dieser Arbeit erweitern wir FEWHA mit einer augmentierten Krylov-Unterraum-Methode und reduzieren so die Anzahl der Iterationen. Außerdem präsentieren wir eine parallele Implementierung beider Algorithmen auf einer multi-core CPU und einer GPU. Wir analysieren die Leistung des Algorithmus hinsichtlich Qualität und Laufzeit für ELT Testkonfigurationen. Letzendlich ist es uns möglich bei gleichbleibender Qualität die Anzahl der Iterationen für augmented FEWHA zu verringern und so die Laufzeit deutlich zu reduzieren. submitted by Dipl.-Ing. Bernadett Stadler, BSc. Dissertation Universität Linz 2021

Project Deliverable D4.2

Atmospheric tomography, i.e., the reconstruction of the turbulence profile in the atmosphere, is a challenging task for adaptive optics (AO) systems for the next generation of extremely large telescopes. Within the AO community, the solver of first choice is the so-called Matrix Vector Multiplication (MVM) method, which directly applies the (regularized) generalized inverse of the system operator to the data. For small telescopes this approach is feasible, however, for larger systems such as the European Extremely Large Telescope (ELT), the atmospheric tomography problem is considerably more complex, and the computational efficiency becomes an issue. Iterative methods such as the Finite Element Wavelet Hybrid Algorithm (FEWHA) are a promising alternative. FEWHA is a wavelet-based reconstructor that uses the well-known iterative preconditioned conjugate gradient (PCG) method as a solver. The number of floating point operations and the memory usage are decreased significantly by using a matrix-free representation of the forward operator. A crucial indicator for the real-time performance are the number of PCG iterations. In this paper, we propose an augmented version of FEWHA, where the number of iterations is decreased by 50% using an augmented Krylov subspace method. We demonstrate that a parallel implementation of augmented FEWHA allows the fulfilment of the real-time requirements of the ELT.

Based on the multitude of industrial applications, benchmarks for model hierarchies will be created that will form a basis for the interdisciplinary research and for the training programme. These will be equipped with publically available data and will be used for training in modelling, model testing, reduced order modelling, error estimation, efficiency optimization in algorithmic approaches, and testing of the generated MSO/MOR software. The present document includes the description about the selection of (at least) eight benchmark cases of model hierarchies. The present document has been structured in three main parts to distinguish those contributions which are focused on coupling methods, model order reduction methods, and optimization methods., Project Deliverable (D5.1), Version 3.0

Based on the multitude of industrial applications, benchmarks for model hierarchies will be created that will form a basis for the interdisciplinary research and for the training programme. These will be equipped with publically available data and will be used for training in modelling, model testing, reduced order modelling, error estimation, efficiency optimization in algorithmic approaches, and testing of the generated MSO/MOR software. The present document includes a detailed description of the computer implementation of these benchmarks involving not only the required publically available data but also the used software packages, libraries and any other relevant information, which guarantee a fully reproducibility of the reported numerical results. The present document has been structured in three main parts to distinguish those contributions which are focused on coupling methods, model order reduction methods, and optimization methods., Project Deliverable (D5.2), Version 2.0

Contributed talk at the AHPC2020 – Austrian HPC Meeting 2020 Klosterneuburg, February 19–21, 2020.

In the ROMSOC project, we develop specially-tailored algorithmic approaches to solve the practical problems of our industry partners. The mathematical fields involved in solving these problems are as diverse as the problems themselves. Thus, our project covers a very broad range within applied mathematics: from discrete optimization to inverse problems, from deep learning to optimal control. What all these fields have in common is that error estimation is an important topic in order to quantify the quality of a computed solution. Naturally, all of them their own error measures and different ways of computing and using them. This report summarizes the state of the art methods in the respective fields concerning error measures and their usefulness in solving real-world problems.

Proceedings of the 139 European Study Group with Industry (139ESGI) in Santiago de Compostela, 9-13th July, 2018

The new generation of ground-based extremely large telescopes require highly efficient algorithms to achieve an excellent image quality in a large eld of view. These systems rely on adaptive optics, where one aims to compensate in real-time the rapidly changing optical distortions in the atmosphere. Due to the growth of telescope sizes, the computational load is increasing drastically. Thus, current algorithms become inappropriate and there is a big interest in the development of more efficient solvers. In this work, we compare a novel method called Finite Element Wavelet Hybrid Algorithm to the frequently used MVM within the framework of MAORY, an instrument of the Extremely Large Telescope. We look in detail at the performance of both algorithms in terms of floating point operations, memory usage and parallelization possibilities. On that basis, we determine a possible real-time computing hardware architecture for both algorithms., Proceedings of the AO4ELT6, June 9-14, 2019 in Québec City, Canada

Based on the multitude of industrial applications, benchmarks for model hierarchies will be created that will form a basis for the interdisciplinary research and for the training programme. These will be equipped with publically available data and will be used for training in modelling, model testing, reduced order modelling, error estimation, efficiency optimization in algorithmic approaches, and testing of the generated MSO/MOR software. The present document includes a detailed description of the computer implementation of these benchmarks involving not only the required publically available data but also the used software packages, libraries and any other relevant information, which guarantee a fully reproducibility of the reported numerical results.

The main goal of the ROMSOC project is to develop new modelling, simulation and optimization (MSO) techniques and associated software to handle real-world scenarios which are relevant for industrial applications in different application areas. The required full order models (FOM) involve coupled multiphysics problems for which standard numerical methods used to compute accurate approximated solutions demand high computational costs and usually fail to provide real-time simulation tools. Hence, the use of reduced order models (ROM) is a must for the design of computational tools, which are potentially applicable in real-world industrial problems. The report briefly describes ROM approaches for specific applications developed within the projects of ESR1, ESR6, ESR8 and ESR10., Project Deliverable (D3.2)

The main goal of the ROMSOC project is to develop new modelling, simulation and optimization (MSO) techniques and associated software to handle real-world scenarios which are relevant for industrial applications in different application areas. The required full order models (FOM) involve coupled multiphysics problems for which standard numerical methods used to compute accurate approximated solutions demand high computational costs and usually fail to provide real-time simulation tools. Hence, the use of reduced order models (ROM) is a must for the design of computational tools, which are potentially applicable in real-world industrial problems. The report briefly describes ROM approaches, error estimators and algorithms for different applications developed within the projects of ESR1, ESR6, ESR8 and ESR10., Project Deliverable (D3.1)

Poster Presentation at the "Adaptive Optics for Extremely Large Telescopes" (AO4ELT6), June 9-14, 2019, Québec (Canada).

Presentation at the 9th International Congress on Industrial and Applied Mathematics - ICIAM 2019, July 15-19, 2019, Valencia (Spain).

Based on the multitude of industrial applications, benchmarks for model hierarchies will be created that will form a basis for the interdisciplinary research and for the training programme. These will be equipped with publically available data and will be used for training in modelling, model testing, reduced order modelling, error estimation, efficiency optimization in algorithmic approaches, and testing of the generated MSO/MOR software. The present document includes the description about the selection of (at least) eight benchmark cases of model hierarchies.

In the ROMSOC project, we develop specially-tailored algorithmic approaches to solve the practical problems of our industry partners. The mathematical fields involved in solving these problems are as diverse as the problems themselves. Thus, our project covers a very broad range within applied mathematics: from discrete optimization to inverse problems, from deep learning to optimal control. What all these fields have in common is that error estimation is an important topic in order to quantify the quality of a computed solution. Naturally, all of them their own error measures and different ways of computing and using them. This report summarizes the state of the art methods in the respective fields concerning error measures and their usefulness in solving real-world problems., Project deliverable D4.1

In the ROMSOC project, we develop specially-tailored algorithmic approaches to solve the practical problems of our industry partners. The mathematical fields involved in solving these problems are as diverse as the problems themselves. Thus, our project covers a very broad range within applied mathematics: from discrete optimization to inverse problems, from deep learning to optimal control. What all these fields have in common is that error estimation is an important topic in order to quantify the quality of a computed solution. Naturally, all of them their own error measures and different ways of computing and using them. This report summarizes the state of the art methods in the respective fields concerning error measures and their usefulness in solving real-world problems.