# Marek MorzynskiPoznan University of Technology · Chair of Virtual Engineering

Marek Morzynski

Professor

## About

139

Publications

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Introduction

## Publications

Publications (139)

Data-driven methods have become an essential part of the methodological portfolio of fluid dynamicists, motivating students and practitioners to gather practical knowledge from a diverse range of disciplines. These fields include computer science, statistics, optimization, signal processing, pattern recognition, nonlinear dynamics, and control. Flu...

We propose a self-supervised cluster-based hierarchical reduced-order modelling methodology to model and analyse the complex dynamics arising from a sequence of bifurcations for a two-dimensional incompressible flow of the fluidic pinball. The hierarchy is guided by a triple decomposition separating a slowly varying base flow, dominant shedding and...

We address a challenge of active flow control: the optimization of many actuation parameters guaranteeing fast convergence and avoiding suboptimal local minima. This challenge is addressed by a new optimizer, called the explorative gradient method (EGM). EGM alternatively performs one exploitive downhill simplex step and an explorative Latin hyperc...

We propose a self-supervised cluster-based hierarchical reduced-order modelling methodology to model and analyse the complex dynamics arising from a sequence of bifurcations for a two-dimensional incompressible flow of the unforced fluidic pinball. The hierarchy is guided by a triple decomposition separating a slowly varying base flow, dominant she...

We stabilize the flow past a cluster of three rotating cylinders-the fluidic pinball-with automated gradient-enriched machine learning algorithms. The control laws command the rotation speed of each cylinder in an open-and closed-loop manner. These laws are optimized with respect to the average distance from the target steady solution in three succ...

In this work, we are interested in the transient dynamics of a fluid configuration consisting of three fixed cylinders whose axes distribute over an equilateral triangle in transverse flow << fluidic pinball >>. As the Reynolds number is increased on the route to chaos, its transient dynamics tell us about the contribution of the elementary degrees...

The fluidic pinball is a geometrically simple flow configuration with three rotating cylinders on the vertex of an equilateral triangle. Yet, it remains physically rich enough to host a range of interacting frequencies and to allow testing of control laws within minutes on a laptop. The system has multiple inputs (the three cylinders can independen...

The fluidic pinball has been recently proposed as an attractive and effective flow configuration for exploring machine learning fluid flow control. In this contribution, we focus on the route to chaos in this system without actuation, as the Reynolds number is smoothly increased. It was found to be of the Newhouse-Ruelle-Takens kind, with a seconda...

We propose an automatable data-driven methodology for robust nonlinear reduced-order modelling from time-resolved snapshot data. In the kinematical coarse-graining, the snapshots are clustered into a few centroids representing the whole ensemble. The dynamics is conceptualized as a directed network, where the centroids represent nodes and the direc...

We propose an aerodynamic force model associated with a Galerkin model for the unforced fluidic pinball, the two-dimensional flow around three equal cylinders with one radius distance to each other. The starting point is a Galerkin model of a bluff-body flow. The force on this body is derived as a constant-linear-quadratic function of the mode ampl...

We stabilize the flow past a cluster of three rotating cylinders, the fluidic pinball, with automated gradient-enriched machine learning algorithms. The control laws command the rotation speed of each cylinder in an open- and closed-loop manner. These laws are optimized with respect to the average distance from the target steady solution in three s...

We address a challenge of active flow control: the optimization of many actuation parameters guaranteeing fast convergence and avoiding sub-optimal local minima. This challenge is addressed by a new optimizer, called explorative gradient method (EGM). EGM alternatively performs one exploitive downhill simplex step and an explorative Latin hypercube...

We propose an automated analysis of the flow control behaviour from an ensemble of control laws and associated time-resolved flow snapshots. The input may be the rich data base of machine learning control (MLC) optimizing a feedback law for a cost function in the plant. The proposed methodology provides (1) insights into control landscape which map...

We propose an automatable data-driven methodology for robust nonlinear reduced-order modeling from time-resolved snapshot data. In the kinematical coarse-graining, the snapshots are clustered into few centroids representable for the whole ensemble. The dynamics is conceptualized as a directed network where the centroids represent nodes and the dire...

Low-order model for successive bifurcations of the fluidic pinball - Volume 884 - Nan Deng, Bernd R. Noack, Marek Morzyński, Luc R. Pastur

The aim of our work is to advance a self‐learning, model‐free control method to tame complex nonlinear flows—building on the pioneering work of Dracopoulous [1]. The cornerstone is the formulation of the control problem as a function optimization problem. The control law is derived by solving a nonsmooth optimization problem thanks to an artificial...

We present the first general metric for attractor overlap (MAO) facilitating an unsupervised comparison of flow data sets. The starting point is two or more attractors, i.e. ensembles of states representing different operating conditions. The proposed metric generalizes the standard Hilbert-space distance between two snapshot-to-snapshot ensembles...

Reduced-order representations of an ensemble of cylinder wake transients are investigated. Locally linear embedding identifies a two-dimensional manifold with a maximum error of 1% from new snapshot data. This representation outperforms a 50-dimensional POD expansion from the same data and is not obtainable with cluster-based coarse graining of sim...

The fluidic pinball is a geometrically simple wake flow configuration with three rotating cylinders on the vertex of an equilateral triangle. Yet, it remains physically rich enough to host a range of interacting frequencies and to allow testing of control laws within minutes on a laptop. The system has multiple inputs (the three cylinders can indep...

We advance the computation of physical modal expansions for unsteady incompressible flows. Point of departure is a linearization of the Navier–Stokes equations around its fixed point in a frequency domain formulation. While the most amplified stability eigenmode is readily identified by a power method, the technical challenge is the computation of...

We propose the first least-order Galerkin model of an incompressible flow undergoing two successive supercritical bifurcations of Hopf and pitchfork type. A key enabler is a mean-field consideration exploiting the symmetry of the base flow and the asymmetry of the fluctuation. These symmetries generalize mean-field theory, e.g. no assumption of slo...

We present the first application of a Smith predictor in the model-based feedback control of a convectively unstable flow. The two-dimensional incompressible mixing layer is chosen as a plant and integrated with a finite-element Navier-Stokes solver. The flow is actuated by a modulation of the inflow mimicking a pulsed jet actuator. The state is mo...

The fluidic pinball has been recently proposed as an attractive and effective flow configuration for exploring machine learning fluid flow control. In this contribution, we focus on the route to chaos in this system without actuation, as the Reynolds number is smoothly increased. It was found to be of the Newhouse-Ruelle-Takens kind, with a seconda...

We advance the computation of physical modal expansions for unsteady incompressible flows. Point of departure is a linearization of the Navier-Stokes equations around its fixed point in a frequency domain formulation. While the most amplified stability eigenmode is readily identified by a power method, the technical challenge is the computation of...

We present the first general metric for attractor overlap (MAO) facilitating an unsupervised data comparison. The starting point is two or more attractors, i.e. ensembles of states representing different operating conditions. The proposed metric quantifies the overlap between these attractors in three steps. First, all states are clustered into dis...

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. The proposed closed-loop control framework addresses a key issue of model-based control: The actuation effect often results from slow dynamics of strongly nonlinear interactions which the flow reveals at timescales much longer t...

The paper aims to build a reduced order model (ROM) of the left and right ventricle of a human heart. The input heart model is build from 3D sets of registered, flexible surface meshes for the left and right ventricle, resulting from the MRI data. Spatial and temporal variables are separated using Proper Orthogonal Decomposition. It enables data re...

We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier–Stokes solution and converges to a periodic limit...

Characterizing and controlling nonlinear, multi-scale phenomena play important roles in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron-Frobenius operator, resulting in a probabilistic mod...

A novel data-driven modal decomposition of fluid flow is proposed, comprising key features of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). The first mode is the normalized real or imaginary part of the DMD mode that minimizes the time-averaged residual. The $N$ th mode is defined recursively in an analogous manner bas...

In this paper, we propose a novel framework to extract features such as
vortex cores and saddle points in two-dimensional unsteady flows. This feature
extraction strategy generalizes critical points of snapshot topology in a
Galilean-invariant manner, allows to prioritize features according to their
strength and longevity, enables to track the temp...

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. Here, a cluster-based control framework is proposed to determine optimal control laws with respect to a cost function for unsteady flows. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional,...

Reduced order models allow quickly predict fluid behaviour and to better understand flow phenomena. They are the key enablers of closed-loop flow control. In this paper, reduced-order model (ROM) of an incompressible flow around a wall-mounted cylinder is constructed, by means of Galerkin projection of Navier-Stokes equations onto space spanned by...

A novel data-driven modal decomposition of fluid flow is proposed comprising
key features of POD and DMD. The first mode is the normalized real or imaginary
part of the DMD mode which minimizes the time-averaged residual. The N-th mode
is defined recursively in an analogous manner based on the residual of an
expansion using the first N-1 modes. The...

The method for computation of stability modes for two- and three-dimensional flows is presented. The method is based on the Dynamic Mode Decomposition of the data resulting from Direct Numerical Simulation of the flow in the regime close to stable flow (fixed-point dynamics, small perturbations about steady flow). The proposed approach is demonstra...

In the IDIHOM Project three aeroelastic testcases have been calculated. Two of them - LANN Wing and DLR-F6 wing-body configuration - have been conducted by PUT. The last one, the HART II rotor has been prepared by NLR. Each partner has used different technology and software tools, hence each of the testcases describes the results of the simulation...

Article presents the development process of aeroelastic system basing on finite volume CFD solver for higher order methods. The main aspect is interpolation tools which allows application of Discontinuous Galerkin solution of CFD solver. There is also described the elastic analogy deformation tool for curvilinear mesh. To summarize, the two testcas...

The article presents elastic analogy approach of deformation curvilinear meshes applied in aeroelastic simulations. The details of algorithm used in developed software with the new metrics designated for high-order mesh quality assessment are presented. The article ends the example of LANN wing deformed by featured tool. Presented software allows c...

In this paper analysis of scalability of the solver UNS3, dedicated to direct numerical simula-tion (DNS) of Navier-Stokes equations, is presented. Efficiency of parallel computations has been examined with the use of a PC cluster built by the Division of Virtual Engineering. Tests have been carried out on a different number of partitions, in the r...

Cluster-based reduced-order modelling (CROM) builds on the pioneering works of Gunzburger's group in cluster analysis [1] and Eckhardt's group in transition matrix models [2] and constitutes a potential alternative to reduced-order models based on a proper-orthogonal decomposition (POD). This strategy frames a time-resolved sequence of fl...

This article presents application of modal analysis for the computation of biometric data base (3D faces) and extraction of three dimensional geometrical features. Traditional anthropometric database contains information only about some characteristic points recorded as linear or angular dimensions. The current face recognition systems are also bas...

Physical flow modes are of particular interest for Reduced Order Flow Control-Oriented Models. Computation of physical modes as the eigensolution of linearized Navier-Stokes equations is a cumbersome and difficult task, especially for large, 3D problems. Instead we propose the solution of Navier-Stokes equation in the frequency domain and investiga...

Phenomena occurring in the flows are very complex. Their interpretation, as well as an effective impact on them in the flow control is often only possible with the use of modal analysis and low-dimensional models. In this paper, the selected modal decomposition techniques, namely Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DM...

Principal Component Analysis, a statistical tool allowing to create a low dimensional subspace basing on input data, finds many applications in biomechanics. The PCA requires the same topology (mesh connectivity, number of nodes) for all objects in database. To achieve this, each new object added to database must be registered. In this article the...

Flow-induced de§ections of aircraft structures result in oscillations that might turn into such a dangerous phenomena like §utter or bueting. In this paper the design of an aeroelastic system consisting of Reduced Order Model (ROM) of the §ow with a moving boundary is presented. The model is based on Galerkin projection of governing equation onto s...

The mitigation of oscillatory vortex shedding behind a cylinder is chosen as a well-investigated benchmark problem to compare model-based feedback flow control approaches. The flow is sensed by a single velocity signal in the wake and is manipulated via a single volume force actuator. A low-dimensional proper orthogonal decomposition Galerkin model...

We propose a general framework for parameter-free identification of a class
of dynamical systems. Here, the propagator is approximated in terms of an
arbitrary function of the state, in contrast to a polynomial or Galerkin
expansion used in traditional approaches. The proposed formulation relies on
variational data assimilation using measurement da...

Expansion of computer technologies allow using numerical simulation in the early stages of aircraft design more and more often. The role of both wind tunnels and initial test flights used to verify the validity of solutions seems to be diminishing. Big systems for three-dimensional simulations of Fluid-Structure Interactions (FSI) constitute highly...

In the current study, Reduced Order Models (ROMs) targeting strategies
for experimental feedback flow control are discussed. For practical
reasons, such models should incorporate a range of flow operating
conditions with a small number of degrees of freedom. Standard POD
Galerkin models are challenged by overoptimization at one operating
condition...

Galerkin Projection is one of the most popular methods of flow model’s reduction. Mode basis used in Galerkin expansion allows reconstruction of the flow for a given set boundary and operating conditions. In the case of changing flow conditions, used mode basis has to be adjusted, for example using mode parametrization [1] or Continuous Mode Interp...

Expansion of computer
technology enables use of computer simulation for prediction of aircraft
characteristics in early stages of design. These simulation nowadays include highly sophisticated and reliable aerodynamics computations as well as solutions of coupled aeroelastic interactions. In this paper we consider numerical simulation of the full...

Low order Galerkin models were originally introduced as an effective tool for stability analysis of fixed points and, later,
of attractors, in nonlinear distributed systems. An evolving interest in their use as low complexity dynamical models, goes
well beyond that original intent. It exposes often severe weaknesses of low order Galerkin models as...

This article presents application of modal analysis for the computation of data base of biological objects set and extraction
of three dimensional geometrical features. Traditional anthropometric database contains information only about some characteristic
points recorded as linear or angular dimensions. The current face recognition systems are als...

Low-dimensional models, allowing quick prediction of fluid behaviour, are key enablers of closed-loop flow control. Reduction of the model's dimension and inconsistency of high-fidelity data set and the reduced-order formulation lead to the decrease of accuracy. The quality of Reduced-Order Models might be improved by a calibration procedure. It le...

We review a strategy for low- and least-order Galerkin models suitable for the design of closed-loop stabilization of wakes. These low-order models are based on a fixed set of dominant coherent structures and tend to be incurably fragile owing to two challenges. Firstly, they miss the important stabilizing effects of interactions with the base flow...

The book focuses on the physical and mathematical foundations of model-based turbulence control: reduced-order modelling and control design in simulations and experiments. Leading experts provide elementary self-consistent descriptions of the main methods and outline the state of the art. Covered areas include optimization techniques, stability ana...

Global stability analysis of fluid flows is presented as a method of extracting physical eigenmodes with associated linear
dynamic models. These reduced-order models (ROM) are optimal for the transients near the onset of instability. We describe
the computational aspects of the eigenmode extraction in detail. This outline includes (i) the discretiz...

A Galerkin method is presented for control-oriented reduced-order models (ROM). This method generalizes linear approaches
elaborated by M. Morzyński et al. for the nonlinear Navier-Stokes equation. These ROM are used as plants for control design
in the chapters by G. Tadmor et al., S. Siegel, and R. King in this volume. Focus is placed on empirica...

The natural and periodically forced flow around a two-dimensional bluff body with a blunt rear end are numerically investigated using an unsteady Reynolds-averaged Navier-Stokes (URANS) calculation. The applied zero-net-mass-flux forcing at the rear end corners of the body leads to a drag reduction due to a significantly higher pressure at the ster...

We propose a system reduction strategy for spectral and Galerkin models of incompressible fluid flows. This approach leads to dynamic models of lower order, based on a partition in slow, dominant and fast modes. In the reduced models, slow dynamics are incorporated as non-linear manifold consistent with mean-field theory. Fast dynamics are stochast...

The necessity to include dynamic mean field representations in low order Galerkin models, and the role and form of such representations, are explored along natural and forced transients of the cylinder wake flow. The shift mode was introduced by Noack et al. J. Fluid Mech. 497, 335 2003 as a least-order Galerkin representation of mean flow variatio...

The Navier-Stokes equations are the trusted description for many flows of practical relevance. Ample physical and engineering
expertize is necessary to accommodate this description to an industrial setting. Presently and in predictable future there
will be no CFD method to simulate the flow ranging from large coherent structures to the Kolmogorov s...

This article presents application of the PCA (Principal Component Analysis) method for analysis and computation of three dimensional biometric description of 3D objects. As the data input the geometrical data sets (threedimensional points coordinates) of faces are used.
Authors apply 3D version of PCA method for numerical estimation of similarity a...