MOR Seminar

SimTech Seminar on Model Reduction and Data Techniques for Surrogate Modelling

Type:

Seminar

Time/Place:

Thursday, 14:00, Live/Video or Hybrid Seminar, Webex-Links are provided via the mor-seminar mailing list.

Organizers:
Audience:

SimTech-PhD students, General interested audience in MOR, Surrogate Modelling, Control and Real-time Simulation from academia as well as industry.

Goals:

Since 2009, this seminar represents a general platform for talks and exchange in the field of surrogate modelling, in particular Model Order Reduction (MOR) as well as novel data-based techniques in simulation science. Both methodological as well as application oriented presentations highlight the various aspects and the relevance of surrogate modelling in mathematics, technical mechanics, material science, control theory and other fields. We aim both at university members, as well as external persons from science and industry. The seminar is organized by four research groups and represents an activity of the SimTech Cluster of Excellence.

The presentations are announced some days in advance via the mor-seminar mailing list of the University of Stuttgart.In case of interest to join this mailing list, please contact the organizers or register at

https://listserv.uni-stuttgart.de/mailman/listinfo/mor-seminar

Presentations WS 2022/2023


Program Flyer

the public Argyris Lecture gives leading personalities in the field of simulation science the opportunity to present their research to a broad audience. We are proud that for the year 2022 Prof. Serkan Gugercin received the Argyris Vising Professorship. Prof. Serkan Gugercin stands out for his excellent achievements and research results in the field of Model Order Reduction (MOR) and surrogate modelling. We would like to use the occasion of his Argyris Lecture on 07. December 2022 to introduce a broad audience to the latest trends and methods in the diverse world of model order reduction. We therefore warmly invite you to the “MOR-Day” on 07. December 2022. The program starts at 13:30 h in V7.31 with four talks from different MOR groups from the University of Stuttgart:

  • Patrick Buchfink, 13:30 – 14:00: "Model order reduction on manifolds"
  • Jonas Kneifl, 14:00 – 14:30, "Real-time Human Response Prediction in Integrated Safety Situations Using Model Reduction and Machine Learning"
  • Jonas Nicodemus, 14:30 – 15:00: Towards multi-objective optimization for reduced port-Hamiltonian systems
  • Felix Fritzen, 15:00 – 15:30, Reduced order modelling of linear and nonlinear thermo-mechanical materials

After a short break with a room change, we will meet at 16:00 h in V7.01 for the exciting Argyris Lecture by Serkan Gugercin.

  • Prof. Serkan Gugercin, 16:00 – 17:30, V7.01: "Modeling dynamical systems from data: A systems-theoretic perspective"

A reception in the foyer of the PWR5a building will round off the day with enjoyable conversation, drinks and food. With a drink in hand, the poster exhibition of further MOR groups can also be explored there.

Title: Learning dynamics of nonlinear systems via structure-preserving operator inference.

Title: Physics-aware machine learning in the small-data regime: from random walkers to random media

Presentations SS 2022


Program Flyer

Title: Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds

 

Title: Brain Networks, Gas Networks and Model Reduction

Abstract:

Dynamic network behavior is a research object in various sciences and not least in applied
mathematics: Network dynamics are studied in biological systems, such as the brain, in technical systems such as gas networks, or abstractly in neural networks.
Realistic models of such large networks not only comprise a high dimensionality either due to a large number of nodes, or mathematical conditions such as hyperbolicity, but also due to
complexities like (non-smooth) nonlinearities. Now, simulating network control or observations requires repeatedly solving a large-scale nonlinear dynamic system for many input or parameter configurations. Especially in time-constrained settings like short-term forecasts, the question if these simulations can be accelerated, arises. Data-driven system-theoretic model reduction is a remedy for this problem: A dynamic network model can be formulated as a (nonlinear) input-output system and based on the system-theoretic properties, which are approximated from simuations, a reduced order model can be computed. This approach is not unlike unsupervised learning, but instead of learning a surrogate model, rather
its system-theoretic properties, and thereby its redundant and irrelevant components in terms of measurable input-output behavior, are obtained. A generic projection-based model order reduction framework for this approach is presented, together with a discussion of particular challenges and opportunities of neuronal brain networks and gas transport networks, as well as numerical examples alongside ideas for comparing reduced order models heuristically.

Title: Compatible Port-Hamiltonian Discretization and Model Reduction of a Nonlinear Flow Problem

Abstract:

Structure-preserving approximation is still an active research area. By preserving or mimicking relevant geometric structures such as, e.g., conservation laws or symplecticities, unphysical solution behavior and numerical instabilities can be avoided in many cases. The model problem considered in this contribution describes nonlinear flows on networks. It covers a hierarchy of models used to describe gas network systems, including particularly the barotropic Euler equations.

Our discretization and model reduction approach is analyzed using energy-based modeling concepts, such as the port-Hamiltonian formalism and the so-called partial Legendre-transformation. The latter offers an elegant approach for the systematic analysis of certain variable transformations, which widens the range of formulations, for which structure-preserving Galerkin-type approximations can be derived under a few compatibility conditions, using variational arguments only.

A particular focus of the talk also lies on the realization of the snapshot-based model order- and complexity-reduction. While beneficial for the robustness and performance of the reduced models, the compatibility conditions pose a challenge in the training phase. Appropriate adaptions of the conventional model reduction methods will be presented.

Title: Microstructure property prediction through neural networks using POD, geometric and convolutional features

Presentations WS 2021/2022


Program Flyer

Webex link: https://unistuttgart.webex.com/unistuttgart/j.php?MTID=m965727048b34537876820118921cda05

Title: Data-driven complexity reduction of dynamical systems from frequency and time-domain measurements

Authors: Ion Victor Gosea, MPI Magdeburg, Germany (joint work with Serkan Gugercin and Christopher Beattie, Virginia Tech, Blacksburg, Virginia, USA)

Abstract:

In many engineering applications, the underlying dynamics of the process to be studied may be inaccessible to direct modeling, or it may be only partially known. However, with the ever-increasing prevalence of available data from various experiments, it is of interest to incorporate measurements into the modeling and complexity reduction process. Data corresponding to the underlying dynamical system (usually complex or of large scale) are available in various formats. For example, in the form of the frequency response (transfer function evaluations) or of input-output values measured in the time domain. In such cases, one could construct a simplified empirical
model of lower dimension that fits the measured data, and hence accurately approximates the original dynamical system. This reduced-order system may then be used as a surrogate to predict behavior, derive control strategies, whenever the desired performance is sensitive to the model order.

The main motivation of the proposed method comes from the fact that we can use system response data (in compressed format) that has been either measured or computed, without the need of accessing any prescribed realization of the original model. Data are represented by sampled values of the transfer function corresponding to the original model (in the frequency domain), or of evaluations of the impulse response (in the time domain). It is to be noted that we do not require at any time explicit access to the state variable of the system,
sampled at different time instances. The quantities that we need in the proposed data-driven approach are system invariants, i.e., they are not altered by coordinate transformations, and their dimensions do not scale with the number of variables (model order) needed to represent the original dynamics.

We discuss parallels that our approach bears with balanced truncation (a common model reduction method), the possibility of deriving error bounds to quantify the distance to the truth model (if known), as well as connections to the Loewner framework, a popular data-driven method. We illustrate our approach numerically for various models and data sets.

Webex link https://unistuttgart.webex.com/unistuttgart/j.php?MTID=mea13a9d845111c136e37d46dc88f1566

Title: Modelpredictive Wind Turbine Control – Modelling, Implementation, Field-Testing and Perspectives

Abstract: Due to its high energy density, wind turbines represent one of the main sources of tomorrow's energy
supply among the renewable energy sources. Because of the fluctuating wind conditions, the control
strategy is of central relevance. While the maximum yield is one of the central control objectives due
to the current legal situation, further control objectives such as economic efficiency, structural
integrity and grid services will be added due to future requirements. One possibility to optimally design
these control objectives is the model predictive control. In the lecture, the work of several research
projects between the Institute of Automatic Control at RWTH Aachen University and the plant
developer W2E will be presented, from the first simulative tests to the field test. The main focus of the
presentation will be on the aeroelastic modelling, the systematic implementation and the
experimental setup up to the field test. Especially for the field test on industrial hardware, quickly
computable surrogate models/process models are necessary. These models are obtained with dataand
physics-based approaches and a model order reduction of complex simulation models. Finally,
future perspectives will be shown, such as how structural health monitoring can be integrated into the
model predictive control.

Webex-link: https://unistuttgart.webex.com/unistuttgart/j.php?MTID=m62cbb7d6e1b4f64b59d4c64589935bd0

Teaser-Video: https://www.mib.uni-stuttgart.de/dae/video/mor_seminar_teaser.m4v

Title: "A Recurrent Neural Network-based Surrogate Model for History-Dependent Multi-scale Simulations"

Abstract: Homogenization-based multi-scale analyses are widely used to account for the effect of material heterogeneity at a structural material point. Among the existing different homogenization methods, computational homogenization solves the meso-scale heterogeneous problems using a full field discretization of the micro-structure. When embedded in a multi-scale analyses, computational homogenization results in the so-called FE2 method, which is an accurate methodology but which yields prohibitive computational time. A more efficient approach is to conduct pre-off-line finite element simulations on the meso-scale problem in order to build a surrogate model by means of constructing mapping functions. Once this so-called training step is completed, the surrogate model can be used as the constitutive law of a single-scale simulation, leading to highly efficient simulations. Artificial neural networks (NNWs) offer the possibility to build such a mapping. However, one difficulty arises for history-dependent material behaviours, such as elasto-plasticity, since state variables are needed to account for the loading history. This difficulty can be solved by considering a Recurrent Neural Network (RNN), which uses sequential information. In [1] a RNN was designed using a Gated Recurrent Unit (GRU). In order to achieve accuracy under multi-dimensional non-proportional loading conditions, the sequential training data were obtained from finite element simulations on an elastoplastic composite RVE subjected to random loading paths. The RNN predictions were found to be in agreement with the finite elements simulations. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 862015 for the project “Multi-scale Optimisation for Additive Manufacturing of fatigue resistant shock-absorbing MetaMaterials (MOAMMM)” of the H2020-EU.1.2.1. - FET Open Programme.

[1] Wu L, Nguyen V-D, Kilingar NG, Noels L. A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths. Computer Methods in Applied Mechanics and Engineering 360, 2020, p. 113234

Webex-link: https://unistuttgart.webex.com/unistuttgart/j.php?MTID=mf10552ebc5ca1f9f0a07c7d039816d99

Title: Structure-preserving dynamical reduced basis methods for Hamiltonian systems

Abstract: In this talk, we will consider reduced basis methods (RBM) for the model order reduction of parametric Hamiltonian dynamical systems describing nondissipative phenomena. The development of RBM for Hamiltonian systems is challenged by two main factors: (i) failing to preserve the geometric structure encoding the physical properties of the dynamics, such as invariants of motion or symmetries, might lead to instabilities and unphysical behaviors of the resulting approximate solutions; (ii) the local low-rank nature of transport-dominated and nondissipative phenomena demands large reduced spaces to achieve sufficiently accurate approximations. We will discuss how to address these aspects via a structure-preserving nonlinear reduced basis approach based on dynamical low-rank approximation. The gist of the proposed method is to evolve low-dimensional surrogate models on a phase space that adapts in time while being endowed with the geometric structure of the full model. If time permits, we will also discuss a rank-adaptive extension of the proposed method where the dimension of the reduced space can change during the time evolution.

Webex-link: https://unistuttgart.webex.com/unistuttgart/j.php?MTID=mbbc62b745ee3af74a4b7f6565676526c

Title: On modeling and discretization from a port-Hamiltonian perspective

Abstract: The port-Hamiltonian formalism, founded 30 years ago, is powerful for control-oriented modeling, numerical approximation and order reduction of interconnected, multi-physical systems. Port-Hamiltonian models are at the core of energy-based control designs like Control by Interconnection or IDA-PBC. In the last decade, preserving the port-Hamiltonian structure in spatial and temporal discretization and reduction has been an active field of research with results in many directions. The goal of this talk is to give an introduction to geometric discretization, which emphasizes the underlying physics. In the first part, systems of conservation laws, their discrete modeling on dual topological objects and their geometric approximation are addressed. The second part is devoted to symplectic time integration and its use for discretization of control systems and control.

Presentations SS 2021


Program Flyer

Webex: https://unistuttgart.webex.com/unistuttgart/j.php?MTID=mbf09de308226a023acc0c7c19ede65d7

"Model reduction for transport phenomena via state-dependent projections"

The standard task of projection-based model-order reduction (MOR) consists of finding a suitable low-dimensional subspace such that the solution of the problem at hand approximately evolves within this subspace. Hereby, the best subspace of a given dimension and the corresponding worst-case approximation error are quantified by the Kolmogorov n-widths. If the n-widths have a slow decay, which is typical for transport phenomena, then a good approximation with a low-dimensional subspace cannot be expected. To overcome this issue, we present a novel model reduction framework that allows the low-dimensional subspace to evolve along with the solution of the problem. Our MOR framework is inspired by the moving finite element method, yielding a nonlinear projection approach. The resulting reduced model is designed to minimize the residual, which is also the basis for an a posteriori error bound. In this talk, we discuss numerical aspects of our method, focusing on an efficient offline-online decomposition. The findings are illustrated with a wildfire application.

Webex: https://unistuttgart.webex.com/unistuttgart/j.php?MTID=m93e4574d05fb25e51f5a6ae906a8eb65

"Circumventing the limitations of projection-based model order reduction with random sketching"

This talk presents novel randomized projection-based model order reduction (MOR) methods for solving large-scale parameter-dependent linear systems. We use randomized linear algebra to address few central challenges of projection-based MOR such as: i) a high offline computational cost and the need to adapt the algorithms to modern computational architectures; ii) the requirement of approximability of the solution manifold in a low-dimensional space, that may not hold for complex problems; iii)  the need of effective certification of the reduced order model, and the stability issues related to the high condition number of the operator. Our methods rely on random sketching that consists in random embedding a set of high-dimensional vectors, defining the problem of interest, into a low-dimensional space by almost preserving the pairwise inner products in the set, and then building the reduced order model in this low-dimensional space with a negligible computational cost. Random sketching algorithms are universal and can be adapted to practically any computational architecture by considering appropriate embedding matrices.  We present new efficient, randomized versions of Petrov-Galerkin and minimal residual projection methods for finding an approximate solution in a low-dimensional space.  Then it is shown how to efficiently
generate a basis for this space with the associated greedy algorithm or randomized Proper Orthogonal Decomposition. Furthermore, we incorporate the ideas from compressed sensing and random sketching to develop a  dictionary-based
approximation method for problems with solution manifolds that can not be well approximated by a single low-dimensional space. This method proceeds with approximation of the solution by a projection onto a subspace spanned by several
vectors selected online from a set of candidate basis vectors, called dictionary. In its turn, such projection is obtained by an approximate solution of a large parametric sparse least-squares problem. In this context, random sketching plays the key role for the efficient (approximate) solution of this problem. Finally, we present strategies to construct a parameter-dependent preconditioner for the solution of ill-conditioned parametric systems and an effective error estimation/certification without the need to estimate expensive stability constants. The preconditioners are constructed by an interpolation of the inverse operator based on online minimization of an error indicator. We present several error indicators depending on the objective such as improving the quality of Petrov-Galerkin projection or residual-based error estimation. The associated heavy computations in both offline and online stages are circumvented by extending the methodology from random embeddings of vectors to random embeddings of operators.

Webex: https://unistuttgart.webex.com/unistuttgart/j.php?MTID=md2a77215c62970e2625cf1aed7320621

"Model Order Reduction Strategies in Structural Mechanics: A Selection of Eigenvalue-Analysis-Based and Data-Driven Approaches"

In order to make reliable decisions, engineers must rigorously investigate large numerical complex finite element models considering nonlinear material behavior. However, such large-scale dynamic investigations are time-consuming and require storing vast amounts of data. I will present an ongoing development of model order reduction techniques applicable to linear and nonlinear structural mechanics. The proposed strategies entail applications and extensions of the proper orthogonal decomposition, the proper generalized decomposition, substructure techniques, and methods that include artificial neural networks.

Presentations WS 2019/2020

Program Flyer

Tensor approximation meets model order reduction

Certified Reduced-Order Modeling for Multiobjective, Nonsmooth and Stochastic Optimizatio

Reduced Order Modeling via Computer Vision in Solid Mechanics

A priori reduced order modelling in fluid-structure interaction.

 

This presentation focuses on Reduced Order Modelling (ROM) techniques
adapted for Fluid-Structure Interaction (FSI) problems. The prediction
of the coupled dynamic behaviour of elastic structures in contact with
fluids (liquid or gas) is still a challenging industrial and research
topic area. Examples of application can be the design of space launchers
with liquid propellants [1] or the harvesting of electrical energy via
flutter-induced vibrations [2]. The challenges arising from such
problems are: (a) to model and predict accurately the fluid-structure
system state for a given range of time/frequency and model parameters,
(b) allowing sensitivity analyses of the quantities of interest at the
system level under varying conditions which typically requires a large
number of numerical simulations, and (c) to incorporate real-time
feedback to allow optimal control of the system state (e.g. control of
trajectory or minimize the exposure to fatigue). Reduced order
techniques play a crucial role in addressing these challenges.
The first part of the presentation will be dedicated to the development
of a priori ROM for linearized FSI problems (i.e. hydroelasticity [3] and aeroelasticity). At hand of a number of examples the computation of
the coupled eigen frequencies of FSI systems by projection on solid dry
eigenmodes will be demonstrated and discussed. The second part concerns
a priori ROM approaches based on the Proper Generalized Decomposition
[4] for nonlinear problems (e.g. geometrically nonlinear elasticity with
follower forces or the steady Navier-Stokes equations). The assumption
of variable separability is promising for multi-parametric analysis and
the methodology will be presented with several uncoupled examples.
Finally, the formulation of velocity-based monolithic fluid-structure
problems will be discussed.

[1] Morand, H.-J. & Ohayon, R. (1995). Fluid Structure Interaction, Wiley.

[2] Ravi, S., & Zilian, A. (2017). Time and frequency domain analysis of
piezoelectric energy harvesters by monolithic finite element modeling.
International Journal for Numerical Methods in Engineering,112(12),
1828–1847.

[3] Hoareau, C., Deü, J.-F. & Ohayon, R. (2019). Prestressed Vibrations
of Partially Filled Tanks
Containing a Free-Surface Fluid: Finite Element and Reduced Order
Models. Proceedings of the VIII
International Conference on Coupled Problems in Science and Engineering,
COUPLED 2019, Barcelona, Spain, June

[4] Chinesta, F., Ladeveze, P., & Cueto, E. (2011). A short review on
model order reduction based on proper generalized decomposition.
Archives of Computational Methods in Engineering, 18(4), 395.

Presentations SS 2019

Program Flyer

"Thermal model order reduction considering heat radiation"

"A priori fluctuation modes for microstructures assembled by means of Wang tiles"

" A semi-incremental scheme for fatigue damage computations"

Presentations WS 2018/2019

Programm Flyer

"Modeling and Control of Tendon-driven Elastic Continuum Mechanisms"

Abstract: In modern robots, joint-mechanisms that are built to interact with the environment 
usually features intrinsic passive compliance. Based on this design paradigm, elastic continuum 
mechanism are also applied frequently. Actively controlling the pose of the mechanism is
indispensable in robots. However, the soft structure reacts to any kind of external loading or 
disturbance. An accurate model that captures all intended deformations is usually computational 
expensive and not applicable in real time control. Therefore, this talk will deal with reduced 
models for such kind of system that allows for their capability analysis and for model-based control.

"Artificial Neural Network Surrogate Models in Structural Mechanics"

Artificial neural network surrogate models can be applied to several fields in structural engineering, e.g. to replace time consuming finite element simulations for structural optimization, reliability assessment, sensitivity analysis, system and parameter identification, structural health monitoring, real-time simulations for computer aided steering of structural processes, and structural control. This lecture contains an overview on applications of artificial neural networks in structural mechanics. Feedforward and recurrent network architectures and corresponding training algorithms are discussed. Examples for neural network based surrogate modelling of computationally expensive structural models are presented. Also the possibility of neural network based material models within the finite element method is shown. In addition, strategies are discussed to consider uncertainties of structural and material parameters within artificial neural network approaches.

Data Driven Parametric Modeling in Discrete Least Squares Norm

Presentations SS 2018

"Space-Time Model Order Reduction for nonlinear path-dependent long-term and cyclic processes"

"Efficient Large Strain Homogenization: Reduced Bases and High-dimensional Interpolation"

"Nonlinear model order reduction for explicit dynamics"

"The Reduced Basis Method for Parameter Functions and Application in Quantum Mechanics"

Presentations WS 2017/2018

"Using Feedthrough to avoid unphysical frequencies in reduced systems"

Abstract: Almost all linear model order reduction schemes for mechanical systems achieve static correctness or local precision by adding static mode shapes to the reduction basis. Since this basis is used to project mass and stiffness matrix, these static mode shape develop a entirely unphysical frequency in the reduced system which may cause serious problems if these frequencies are excited. Instead of achieving static correction by using static correction modes, a simple addition to the spectral sum is proposed. This approach has several advantages: The number of degrees of freedom is further reduced, unphysical dynamics are  eliminated, the reduction is still statically correct and the numerical  efficiency increases considerably. The potential and advantages of the approach will be discussed and demonstrated for numerical test examples.

"Greedy algorithms for optimal measurements selection in state estimation using reduced models"

Abstract: In this talk, we will talk about recent techniques developed to estimate the state of a physical system using sensor measurements and reduced models. After giving a short overview on the methodology and the approximation results, we will explain how we can use the methodology in order to select the sensors to place in the physical system in an optimal way. If time permits, we will also discuss the challenges posed when the the sensor measurements are no longer exact but polluted by noise. This is a work in collaboration with P. Binev, A. Cohen and J. Nichols.

"Automatic derivation of material laws for simulating structural components"

Abstract: In our talk we will present a novel approach to automatically derive material laws by model order reduction methods (MOR) for the component simulation of fiber reinforced plastic (FRP) materials, which is based on the output of
an injection or compression moulding simulation.

"Structure Preserving Model Reduction for Linear Elasticity"

Presentations SS 2017

"Structure-Preserving Model-Reduction"

Abstract: Reduced basis methods are popular for approximately solving large and complex systems of differential equations. However, many challenges remain to secure the flexibility, robustness, and efficiency needed for general large-scale applications, in particular for nonlinear and/or time-dependent problems. In this talk, we present a greedy approach for the construction of a reduced system that preserves the geometric structure of Hamiltonian systems. Preserving the Hamiltonian structure ensures the stability of the reduced system over long-time integration. The performance of the approach is demonstrated for both ODEs and PDEs. We then discuss how the method can be extended to preserve the symmetries and intrinsic structures of dissipative problems through the notion of port-Hamiltonian systems.

 "Controlling of the model reduction error in FE2 analysis of transient heat flow"

 "Variational Inertia Scaling for Explicit Dynamics"

"Kernel Methods for Nonlinear Control and Random Dynamical Systems"

Presentations WS 2016/2017

Milestone-Presentation:
"Error Controlled Nonlinear Model Reduction Techniques for Crash Simulations"

"A Newton-Euler approach to modelling and control of flexible manipulators"

"Homogenization of viscoplastic composites based on the complementary TFA"

14:15, PWR 5a, 0.015
Prof. Sonia Marfia (University of Cassino and Southern Lazio)

"A nonuniform TFA homogenization technique based on piecewise interpolation functions of the inelastic field"

"Kernel Methods for Accelerating Implicit Integrators"

Presentations SS 2016

"Reduced Basis Approximation of the time-discrete Algebraic Riccati Equation"

"Robust optimization of permanent magnet synchronous machines using model order reduction for the efficient computation of local and global sensitivities"

"Efficient finite element simulation for cyclic loads with a viscoelastic-viscoplastic-damage material model"

"Nonlinear modes and their suitability for model order reduction"

"Application of model order reduction techniques to the lubricated contact of elastic bodies"

Contact

This image shows Bernard Haasdonk

Bernard Haasdonk

Prof. Dr.

Head of Group Numerical Mathematics
Dean of Studies (B.Sc./M.Sc. Mathematik)

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