Mehmet Akif Cördük, TU Kaiserslautern

Title:
GPU Based Price Engines

Abstract:

High performance computing is needed in many areas of the industry to reduce the cost, energy and increase performance of certain tasks. Thanks to the advancements in GPGPU computing, it is more accessible for everyone to develop high performance solutions for parallel tasks. In this work, we present a novel solution for online computation of hotel prices and combinations with other services. High cardinality of search space is a time consuming task for CPU based solutions and cache based solutions are not always up-to-date. We map the problem to GPU architecture considering hardware limitations and memory access considerations. The proposed solution provides high cardinality- , flexible searches with accurate and up-to-date results, thanks to highly parallel nature of the problem. We achieved a 45 requests/seconds throughput for a search interval of 30 days for 88000 hotel rooms by computing 120 million prices per second.

Jonas Kusch, Karlsruhe Institute of Technology

Title:
A one-shot approach for the Intrusive Polynomial Moment method

Abstract:

Uncertainty Quantification for fluid dynamics applications becomes a challenging task, especially when the solution shows shocks in the random space. To enable the use of adaptivity, we use intrusive methods, which provide a set of equations describing the time evolution of the polynomial chaos (PC) coefficients. The Intrusive Polynomial Moment (IPM) method possesses a large number of desirable quantities that are violated by standard intrusive methods such as stochastic-Galerkin. However, the IPM system requires solving a convex optimization problem which computes the entropy variables corresponding to a given set of PC coefficients. This optimization problem needs to be solved in every spatial cell in each time step, yielding high computational costs.

In this talk, we present a method to reduce computational costs for steady state problems. To drive the IPM system to its steady state solution, we use explicit Euler steps, while employing Newton’s method to solve the mentioned optimization problems. Since the PC coefficients are not at the physically correct steady state solution for a large number of Euler steps, we propose to not solve the IPM optimization problems exactly. Instead, we perform only one step of Newton’s method, i.e. we converge the PC coefficients as well as the corresponding entropy variables simultaneously to their steady state solution. It can be shown that this method converges to the steady state solution locally. Due to its similarities to the one-shot method in shape optimization, we call this method one-shot IPM.

We demonstrate the effectiveness of one-shot IPM by investigating an inviscid flow around a NACA0012 profile with an uncertain Mach number and far field pressure. When making use of the one-shot approach as well as adaptivity, we are able to compete with non-intrusive collocation methods.

PDF Version with References

Halil Kaya, Turkish Aerospace Industry

Title:
Generation of surrogate-based aerodynamic model using an adaptive co-Kriging method

Abstract:

This work presents a multi-fidelity aerodynamic modeling approach for the aerodynamic model generation of a UAV configuration. The aerodynamic data were generated with CFD simulations. A large number of cheap but less accurate, hence lower fidelity, Euler simulations are coupled with a smaller number of expensive but more accurate, hence higher fidelity, RANS simulations. Although the current study is limited to one-dimensional data, findings of the study suggest that the demonstrated method has the potential of being useful in obtaining high-resolution multi-dimensional aerodynamic models for modern aircraft with reasonable effort.

Ole Burghardt, SciComp

Title:
Multiphysics aspects of simulation and design with SU2

Abstract:

In this talk we will discuss multiphysics aspects of simulation and design with the open-source solver suite SU2. An emphasis is put the development of discrete adjoint solvers that is done at SciComp. To showcase its way of application for one of the most important coupled problems in engineering nowadays, we will set up a conjugate heat transfer problem and demonstrate how accurate gradients for finding optimal shapes can be obtained.

Tim Albring, SciComp

Title:
Automating Continuous Integration and Deployment using Github Actions and Docker

Abstract:

Continuous integration – the practice of frequently integrating one’s new or changed code with the existing code repository – should occur frequently enough such that no errors can arise without developers noticing them and correcting them immediately. Rather than periodically scheduled builds, also called ‘nightly builds’, nowadays it is normal practice to trigger these builds by every commit to a repository. While it is obvious so see the benefits for big, professional software projects, even smaller projects on a working group level at a university might benefit from automating integration, building, testing and, possibly also the deployment. In this talk we will go through the individual steps of creating such a CI/CD pipeline starting from using the container platform Docker to the recently introduced GitHub Actions feature.

Maxime Krier, TU Kaiserslautern

Title:
Bridging Neural Network Architectures and Numerical Differential Equations

Abstract:

Over the past few years, neural networks have become one of the most important tools for supervised machine learning. A class of architectures called ResNets have shown good results on tasks like image classification. We show that ResNet architectures can be interpreted as a numerical discretization of ordinary differential equations. A common problem that arises in training neural networks is the poor generalization to new data. We approach this problem by applying the well examined concept of stability of ODEs to ResNets. In this talk we discuss the construction of a network architecture based on a numerical scheme for solving ODEs. Then we analyze how stability properties of the numerical scheme can be used to deduce characterizations of robustness of the neural network. Based on our results we propose improvements to ResNet architectures that ensure better generalization ability of the network with respect to small perturbations in the data.

Xinyu Hui, Northwestern Polytechnical University Xi’an, China

Title:
Fast pressure distribution prediction and unsteady periodic flow field prediction method based on deep learning

Abstract:

In the aerodynamic design, optimization of the pressure distribution of airfoils is crucial for the aerodynamic components. Conventionally, the pressure distribution is solved by computational fluid dynamics, which is a time-consuming task. Surrogate modeling can leverage such expense to some extent, but it needs careful shape parameterization schemes for airfoils. As an alternative, deep learning approximates inputs-outputs mapping without solving the efficiency-expensive physical equations and avoids the limitations of particular parameterization methods. Therefore, I present a data-driven approach for predicting the pressure distribution over airfoils based on Convolutional Neural Network (CNN). Given the airfoil geometry, a supervised learning problem is presented for predicting aerodynamic performance. Furthermore, we utilize a universal and flexible parametrization method called Signed Distance Function to improve the performances of CNN. Given the unseen airfoils from the validation dataset to the trained model, the model achieves predicting the pressure coefficient in seconds, with a less than 2% mean square error.

A method based on deep learning to predict periodic unsteady flow field is proposed, and can predict the real-time complex vortex flow state at different moments accurately. Combining conditional generative adversarial network and convolutional neural network, improve the conditional constraint method from conditional generative adversarial network, a deep learning framework with conditional constraints is proposed, which is the regression generative adversarial network. The two scenarios of conditional generative adversarial network and regression generative adversarial network are tested and compared via giving different periodic moments to predict the corresponding flow field variables at this moment. The final results demonstrate that regression generative adversarial network can estimate complex flow fields, and way more faster than CFD simulation.

Prof. Dr. Hermann G. Matthies, Institut für Wissenschaftliches Rechnen, TU Braunschweig

Title:
Probability, Algebra, Analysis, and Numerics

Abstract:

Probability theory was axiomatically built on the concept of measure by A. Kolmogorov in the early 1930s, using the probability measure and the sigma-algebra as primary objects, and random variables, i.e. measurable functions, and their expectations as secondary. Not long after Kolmogorov ́s work, developments in operator algebras connected to quantum theory in the early 1940s lead to similar results in an approach where algebras of random variables and the expectation functional are the primary objects. Historically this picks up the view implicitly contained in the early probabilistic theory of the Bernoullis.

This algebraic approach allows extensions to more complicated concepts like non-commuting random variables and infinite dimensional function spaces, as it occurs e.g. in quantum field theory, random matrices, and tensor-valued random fields. It not only fully recovers the measure-theoretic approach, but can extend it considerably. For much practical and numerical work, which is often primarily concerned with random variables, expectations, and conditioning, it offers an independent theoretical underpinning. In short words, it is “probability without measure theory”.

This functional analytic setting has also strong connections to the spectral theory of linear operators, where analogies to integration are apparent if they are looked for. This then allows to compute other functions than just polynomials of the algebraic random variables. These links extend in a twofold way to the concept of weak distribution, which describes probability on infinite dimensional vector spaces. Here the random elements are represented by linear mappings, and factorisations of linear maps are intimately connected with representations and tensor products, as they appear in numerical approximations.

Taking this conceptual basis of vector spaces, algebras, linear functionals, and operators gives a fresh view on the concepts of expectation and conditioning, as it occurs in applications of Bayes’ theorem.

For numerical computations, this allows to represent random quantities not only as usual as samples, but as functions of an algebra of known random variables. These may be seen as functions on very high-dimensional domains. As already mentioned, tensor approximations appear naturally, and low-rank factorisations are one way to handle the resulting complexity. The resulting connections to an algebra may for example be used in the numerical processing of compressed representations of such high-dimensional objects.

Subhashri Manohar, University of Bozen, Bolzano, Italy.

Title:
A Comparison of Gradient Descent and Stochastic Gradient Descent Algorithms

Abstract:

In the current decade of Machine Learning, Neural networks are the most sought after method for its ability to solve complex problems with high accuracy. Now, the accurate results is mainly a result of the optimization algorithm contributing to reduce the errors. There are numerous optimization strategies used to produce slightly better and faster results. In this presentation we are going to discuss about the most commonly used algorithms: Standard Gradient Descent and Stochastic Gradient Descent. They are executed on Convolutional Neural Network using MNIST dataset. The results are evaluated on how well the algorithms generalize, accuracy, convergence time and error. Based on that we discuss their advantages and applications.

Pedro Gomes, Department of Aeronautics, Imperial College London

Title:
Aerodynamic Driven Multidisciplinary Topology Optimization of Compliant Airfoils

Abstract:

We propose a strategy for density-based topology optimization of fluid structure interaction problems that deals with some short-comings associated with non stiffness-based design problems.
The method is demonstrated on a problem where we seek to improve the passive load alleviation characteristics of a highly compliant airfoil at high speed while producing sufficient lift at a lower speed.
The fluid structure interaction is simulated with the multi-physics suite SU2, which includes RANS modelling of the fluid and hyper-elastic material behaviour of the geometrically-nonlinear structure. Gradient-based optimization is used with the coupled aerostructural sensitivities being obtained via an algorithmic differentiation-based coupled discrete adjoint solver.

Max Aehle, TU Kaiserslautern

Title:
Introduction to Model Predictive Control

Abstract:

Model Predictive Control (MPC) is a methodology for controller design. Assuming that the controlled system P (plant) is adequately approximated by another system M (model), MPC iteratively determines its control action by the following strategy: Compute a control sequence that is optimal for M over a certain prediction horizon, and send only the first part of it as actual control input to P. Iterate this.

This method has been employed in a paper by Aleksić-Roeßner, King et al (2014) to reduce vortex shedding behind a cylinder. We will review the authors’ derivation of the reduced-order model M approximating P, and present an introduction to different control methodologies culminating in MPC. Finally, a plan for (another) computational validation of their affirmative result is laid out.