MOR Seminar

SimTech Seminar on Model Reduction and Data Techniques for Surrogate Modelling

Type:

Seminar

Time/Place:

Thursday, 14:00, Online-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 three institutes 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.

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 picture showsBernard Haasdonk
Prof. Dr.

Bernard Haasdonk

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

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