Max Sagebaum, SciComp

Title: Overview and introduction to MeDiPack

Abstract:

The correct Algorithmic Differentiation (AD) of message passing is by itself straight forward. Nevertheless, the handling of the different concepts in MPI like asynchronous request or collective communication and the combination with AD concepts like an index management scheme make the task quite involved. With MeDiPack (Message Differentiation Package) a novel approach is taken that uses code generation to reduce the duplication of implementations. This makes bugfixes or changes straight forward, since only one location needs to be changed and not every method where the MPI or AD concept is used.

The presentation presents the main challenges for the handling of adjoint message passing and introduces the approach taken for MeDiPack.

Title:
Selected shape optimization problems from industry and how to solve them with modern HPC techniques

In this talk we like to give a small insight into shape optimization problems from industry that we were involved in the last couple of months. We will discuss two of them – one coming from aerodynamics and one from hydrodynamics – in detail and especially why they show a need for modern techniques and the use of HPC.

Most of the all the algorithms and programs that we apply throughout an optimization loop are developed either by our team members or in cooperation with universities from all over the world, the most important ones being the open-source CFD code SU2 and the algorithmic differentiation tool CoDiPack.

Within the scope of this talk, we will however stress their application and the technical side of the topics rather than their in depth development.

Raju Ram, ITWM

Title:
Parallel Deflated Conjugate Gradient Method to Model Groundwater Flow in a Layered Grid

Abstract:

Groundwater, present beneath the earth’s surface in soil pore spaces, is the primary source of fresh water that we use in day to day life. Hydrologists at Dutch research institute Deltares are developing large groundwater models to support water managers in their decision-making process. These models use a Deltares accelerated version of MODFLOW called iMODFLOW. Together with the United State Geological Survey (USGS), Deltares has developed the Parallel Krylov Solver (PKS) package, which has recently been incorporated into iMODFLOW. It was observed that for the larger number of subdomains, the Preconditioned Conjugate Gradient (PCG) solver in PKS deteriorates the number of iterations.
We have implemented the deflation preconditioner with constant and linear deflation vectors in the PCG solver. These vectors approximate the eigenvectors that are slowing down convergence. The groundwater simulation time can be reduced by a factor of 4 using deflation in iMODFLOW. This speedup is achieved due to a decrease in the PCG iterations. The iteration drop is highest using linear deflation vectors.
In this talk, we present the mathematics behind deflation, implementation on a parallel computer and discuss the results.

The goal of the workshop is to give an overview of recent research activities at SciComp. In addition, two collaborators from University of Mannheim as well as Karlsruhe Institute of Technology will give invited presentations.

Program

11:00 – 11:30 AG SciComp: Review 2017 and Outlook 2018
(Prof. N. Gauger, U. Hahn)

11:30 – 12:15 Uncertainty Quantification for Inverse Problems
(Prof. Claudia Schillings, University of Mannheim)

12:15 – 13:00 An approximate Newton Smoothing Method for Shape Optimization
(J. Kusch, Karlsruhe Institute of Technology)

13:00 – 14:00 Lunch Break

14:30 – 17:00 AG SciComp: Scientific Short Presentations (10+5 minutes each)
(Dr. E. Özkaya, M. Sagebaum, T. Albring, B. Zhou, Dr. S. Günther, L. Kusch, Dr. J. Schüle, T. Dick, O. Burghardt)

18:00 Workshop Dinner

Prof. Dr. Claudia Schillings, Institut für Mathematik, Universität Mannheim

Title:
Uncertainty Quantification for Inverse Problems

Abstract:

Uncertainty Quantification (UQ) is an interesting, fast growing research area aimed at developing methods to address the impact of parameter, data and model uncertainty in complex systems. In this talk we will focus on the identification of parameters through observations of the response of the system – the inverse problem. The uncertainty in the solution of the inverse problem will be described via the Bayesian approach. In cases, where the model evaluations are prohibitively expensive, ad hoc methods such as the Ensemble Kalman Filter (EnKF) for inverse problems are widely and successfully used by practitioners in order to approximate the solution of the Bayesian problem.
The low computational costs, the straightforward implementation and their non-intrusive nature make them appealing in various areas of application, but, on the downside, they are underpinned by very limited theoretical understanding. In this talk, we will discuss an analysis of the EnKF based on the continuous time scaling limits, whichallows to derive estimates on the long-time behaviour of the EnKF and, hence, provides insights into the convergence properties of the algorithm. In particular, we are interested in the properties of the EnKF for a fixed ensemble size. Results from various numerical experiments supporting the theoretical findings will be presented.

Jonas Kusch, Karlsruhe Institute of Technology

Title:
An approximate Newton Smoothing Method for Shape Optimization

Abstract:

In this talk, we derive a smoothing method for shape optimization in Stokes and Navier-Stokes flows. The smoothing routine automatically picks a spatially dependent smoothing parameter in such a way that the optimization process is accelerated, turning the smoothing routine into an approximate Newton method.
This task is achieved by analytically deriving the symbol of the Hessian for the Stokes equations. We numerically investigate the Hessian symbol for convective flows and demonstrate the applicability of the symbol for the Navier-Stokes equations.
The constructed preconditioner approximates the derived symbol using windowed Fourier transform and thereby accelerates the optimization process while yielding a smooth search direction. Due to the fact that the smoothing is performed locally, the method will identify areas in which a non-smooth design is physically meaningful and will automatically turn off smoothing in these regions.

Johannes Blühdorn, TU Kaiserslautern

Title:
Efficient Solution of the Unit Cell Problem

Abstract:

For materials with complex microstructure, analytical descriptions of the effective (macroscopic) behaviour are usually not available. In the context of mathematical homogenization, the effective behaviour is approximated based on a simulation of a material unit cell on the microscopic scale. There, one has to solve an elliptic PDE. The best approximation is usually obtained with periodic boundary conditions. While the unit cell problem can traditionally be solved by finite element methods, Moulinec and Suquet proposed a more efficient algorithm that needs no meshing and can work directly on data obtained from CT images. It relies upon the reformulation of the original problem in terms of the periodic Lippmann-Schwinger equation. The solution to this integral equation is approximated in the space of trigonometric polynomials by means of a fixed point iteration. In each iteration, a PDE with constant coefficients must be solved, which is done efficiently in Fourier space. In this talk, we derive the method for linear elasticity at small deformations. We outline how it extends to nonlinear material laws and large deformations and discuss its advantages, limitations and more recent adaptions.

Dr. Stefan Görtz, Institut für Aerodynamik und Strömungstechnik, DLR Braunschweig

Title:
Surrogate and Reduced-Order Models for Use in Aerodynamic Applications, MDO and Robust Design

Abstract:

Reduced Order Models (ROMs) have found widespread application in fluid dynamics and aerodynamics. In their direct application to Computational Fluid Dynamics (CFD) ROMs seek to reduce the computational complexity of a problem by reducing the number of degrees of freedom rather than simplifying the physical model. Here, parametric nonlinear ROMs based on high-fidelity CFD are used to provide approximate flow solutions, but at lower evaluation time and storage than the original CFD model. ROMs for both steady and unsteady aerodynamic applications are presented. We consider ROMs combining proper orthogonal decomposition (POD) and Isomap, which is a manifold learning method, with surrogate-based interpolation methods as well as physics-based ROMs, where an approximate solution is found in the POD-subspace by minimizing the corresponding steady or unsteady flow-solver residual. The issue of how to best “train” the ROM with high-fidelity CFD data is also addressed. The goal is to train ROMs that yield a large domain of validity across all parameters and flow conditions at the expense of a relatively small number of CFD solutions. The different ROM methods are demonstrated on a wide-body transport aircraft configuration at transonic flow conditions.
In the second part of this talk we present a robust design optimization framework for aircraft design and show results for robust aerodynamic design. As a first step, we focus on quantifying uncertainties in the drag coefficient using non-intrusive methods. To reduce the computational effort required to compute the output uncertainties we make use of a Sobol sequence-based quasi Monte Carlo method (QMC) and a gradient-enhanced Kriging (GEK) surrogate model. A small number of samples is computed with the full-order CFD code TAU and its adjoint version to construct the GEK model. The statistics are computed by interrogating the surrogate model with a QMC method using a sufficiently large number of samples. In terms of the input uncertainties, we are interested both in operational and geometrical uncertainties. Our strategy to model the inherently large number of geometrical uncertainties is by using a truncated Karhunen-Loève expansion (tKLE), which introduces some elements of model uncertainty. Then, a Subplex algorithm is used to optimize different robustness measures. The test case used here to demonstrate the framework is a transonic RAE2822 airfoil.
Finally, current work aiming to extend our framework for uncertainty quantification and management (UQ&M) based on high-fidelity CFD to the loads process, especially at extremes of the flight envelope.

Max Stein, TU Kaiserslautern

Title:
GPU accelerated AD for a financial application

Abstract:

Pricing call options using Monte Carlo simulation is massively parallel and hence very well suited for GPU acceleration, where one might wonder if this is also the case for its adjoint reverse calculation when seeking for retrieving adjoints. After reviewing some basics from finance including modeling option prices and estimating the volatility using the Dupire formula, a GPU accelerated implementation calculating the derivatives with respect to all input variables will be presented. Concerning the implementation, there are some race conditions arising in a naive implementation which have to be resolved and there are additionally some efforts necessary for dealing with the limited GPU memory by storing very efficiently only the absolutely necessary information from forward for the reverse run. Furthermore there will be ways presented for improving performance like calculating in mixed precision, using shared memory and using texture memory. Finally the runtime and accuracy of CPU vs GPU version will be compared which will show the benefit and importance of using GPU acceleration for this application.

Johannes Blühdorn, TU Kaiserslautern

Title:
Automatic Differentiation of Fixed Points

Abstract:

In the context of automatic differentiation, special care must be taken when differentiating code that incorporates a fixed point iteration. The memory consumption due to taping for the reverse mode of AD grows with the number of iterations, and even if the forward iteration converges, it is unclear whether the corresponding reverse iteration converges as well. Following a paper by Bruce Christianson, we present conditions for a fixed point to be differentiable with respect to the independent variables, and formulate a fixed point problem for the adjoint values. The reverse iteration is then replaced by iterating the fixed point problem for the adjoint. As it turns out, recording only the last forward iteration on tape provides all that is needed for the reverse sweep, and the gradient can be obtained with the same accuracy as the original fixed point. For any of both fixed point problems, it might not always be possible or efficient to decide in advance whether or not the contraction requirement of Banach’s Fixed Point Theorem is satisfied. In the special case of a linear function, this corresponds to an iteration matrix with some eigenvalues outside the unit circle. The iteration is then in general unstable, but by means of the recursive projection method, it can be stabilized. Following a paper by Renac, we present this in the linear case, and discuss its applicability in the context of the above AD scheme.

Falco Schneider, ITWM

Title:
Speed Limit and Ramp Meter Control for Traffic Flow Networks

Abstract:

Within the scope of autonomous driving, optimal traffic control yields a possible application by metering the traffic to increase the efficiency of the traffic flow. The ambition is to control a given traffic network via speed limits and on-ramp metering, such that the total travel time can be minimized or the throughput of the network can be maximized. At the beginning of the presentation, we give a general overview of macroscopic traffic models and possibilities of traffic control. Following a paper by Goatin, Göttlich and Kolb [1], we then present a specific traffic network model based on the classical LWR traffic model, which is given by a hyperbolic PDE. Furthermore, we construct suitable coupling conditions between the roads for different types of intersections to ensure the unique solvability of the system. For the optimization, the system is first solved without any control to get an initial guess and then optimized via a “first discretize then optimize” approach. Finally, we will present some numerical results for the shown optimal traffic control model. This presentation will be given within the frame of a reading course.

[1] P. Goatin, S. Göttlich, O. Kolb – Speed limit and ramp meter control for traffic flow networks – Engineering Optimization, Vol. 48(7), pp. 1121-1144, 2016.

Daniel Baumgärtner, Chair of Structural Analysis, Technical University of Munich

Title:
Node-based shape optimization including CAD-reconstruction within an open-source multiphysics framework

Abstract:

The current state of the art in shape optimization is dominated by approaches utilizing computer-aided design (CAD) or morphing boxes. On the contrary, node-based approaches have not reached the same industrial acceptance, although e.g. the Vertex Morphing Method showed with many practical problems promising characteristics like high optimization potential, minimum modeling effort or fast design space exploration. One major reason for this limited popularity is the missing link to CAD being the primary design tool in many industrial branches.
Within this seminar, an approach is presented to close this gap. The focus is put on the seamless integration of the Vertex Morphing Method in given CAD workflows as well as the resulting design advantages. The applicability of the combined optimization and reconstruction process is demonstrated with selected examples from different industrial branches. In all examples, an application for shape optimization within the open-source multiphysics framework “KratosMultiphysics” is utilized. Its close link the popular open-source CFD code “SU2” will be discussed throughout the seminar.