Petar Mlinarić
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View article: Greedy emulators for nuclear two-body scattering
Greedy emulators for nuclear two-body scattering Open
Applications of reduced basis method emulators are increasing in low-energy nuclear physics because they enable fast and accurate sampling of high-fidelity calculations, enabling robust uncertainty quantification. In this paper, we develop…
View article: The tangent cone to the real determinantal variety: various expressions and a proof
The tangent cone to the real determinantal variety: various expressions and a proof Open
The set of real matrices of upper-bounded rank is a real algebraic variety called the real generic determinantal variety. An explicit description of the tangent cone to that variety is given in Theorem 3.2 of Schneider and Uschmajew [SIAM …
View article: Interpolatory Necessary Optimality Conditions for Reduced-order Modeling of Parametric Linear Time-invariant Systems
Interpolatory Necessary Optimality Conditions for Reduced-order Modeling of Parametric Linear Time-invariant Systems Open
Interpolatory necessary optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of non-parametric linear time-invariant (LTI) systems are known and well-investigated. In this work, using the general framework of $\mathcal{…
View article: IRKA is a Riemannian Gradient Descent Method
IRKA is a Riemannian Gradient Descent Method Open
The iterative rational Krylov algorithm (IRKA) is a commonly used fixed-point iteration developed to minimize the $\mathcal{H}_2$ model order reduction error. In this work, IRKA is recast as a Riemannian gradient descent method with a fixe…
View article: Interpolatory $\mathcal{H}_2$-optimality Conditions for Structured Linear Time-invariant Systems
Interpolatory $\mathcal{H}_2$-optimality Conditions for Structured Linear Time-invariant Systems Open
Interpolatory necessary optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of unstructured linear time-invariant (LTI) systems are well-known. Based on previous work on $\mathcal{L}_2$-optimal reduced-order modeling o…
View article: \(\boldsymbol{\mathcal{L}_2}\)-Optimal Reduced-Order Modeling Using Parameter-Separable Forms
\(\boldsymbol{\mathcal{L}_2}\)-Optimal Reduced-Order Modeling Using Parameter-Separable Forms Open
We provide a unifying framework for L-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive the gradients o…
View article: Interpolatory necessary L2-optimality conditions numerical experiments
Interpolatory necessary L2-optimality conditions numerical experiments Open
Codes for numerical experiments supplementing: P. Mlinarić, S. Gugercin, A Unifying Framework for Interpolatory L2-Optimal Reduced-Order Modeling, SIAM Journal on Numerical Analysis, 2023, doi: 10.1137/22M1516920
View article: L2-optimal parametric reduced-order modeling numerical experiments
L2-optimal parametric reduced-order modeling numerical experiments Open
Codes for numerical experiments supplementing: P. Mlinarić, S. Gugercin, L2-Optimal Reduced-Order Modeling Using Parameter-Separable Forms, SIAM Journal on Scientific Computing, 2023, doi: 10.1137/22M1500678
View article: Optimization-based Parametric Model Order Reduction via ${{\mathcal{H}_2} \otimes {\mathcal{L}_2}}$ First-order Necessary Conditions
Optimization-based Parametric Model Order Reduction via ${{\mathcal{H}_2} \otimes {\mathcal{L}_2}}$ First-order Necessary Conditions Open
In this paper, we generalize existing frameworks for H2 ⊗ L2-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary optimality conditions for a class of stru…
View article: pyMOR - Reduced Order Modeling with Python
pyMOR - Reduced Order Modeling with Python Open
pyMOR is a free and open source software library for writing model order reduction applications with the Python programming language.Implemented algorithms include both Reduced Basis and system-theoretic reduction methods, as well as non-i…
View article: Optimization-based parametric model order reduction via $\mathcal{H}_2\otimes\mathcal{L}_2$ first-order necessary conditions
Optimization-based parametric model order reduction via $\mathcal{H}_2\otimes\mathcal{L}_2$ first-order necessary conditions Open
In this paper, we generalize existing frameworks for $\mathcal{H}_2\otimes\mathcal{L}_2$-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary ptimality con…
View article: A zero to four parameter instationary thermal-block-type benchmark model for parametric model order reduction
A zero to four parameter instationary thermal-block-type benchmark model for parametric model order reduction Open
We specify a new benchmark for parametric model order reduction that is scalable both in degrees of freedom as well as parameter dimension.
View article: System‐theoretic model order reduction with pyMOR
System‐theoretic model order reduction with pyMOR Open
This paper shows recent developments in pyMOR, in particular the addition of system‐theoretic methods. All methods are implemented using pyMOR's abstract interfaces, which allows the application to partial differential equation (PDE) model…
View article: Structure-preserving model order reduction for network systems
Structure-preserving model order reduction for network systems Open
This thesis considers structure-preserving system-theoretic model order reduction for certain structured input-output systems, particularly network systems. In the first part, our focus lies on the clustering-based approach to reduce netwo…
View article: Model reduction of linear multi-agent systems by clustering with $$\varvec{\mathcal {H}_2}$$ H 2 and $$\varvec{\mathcal {H}_\infty }$$ H ∞ error bounds
Model reduction of linear multi-agent systems by clustering with $$\varvec{\mathcal {H}_2}$$ H 2 and $$\varvec{\mathcal {H}_\infty }$$ H ∞ error bounds Open
In the recent paper (Monshizadeh et al. in IEEE Trans Control Netw Syst1(2):145–154, 2014. https://doi.org/10.1109/TCNS.2014.2311883), model reductionof leader–follower multi-agent networks by clustering was studied. For such multi-agent n…
View article: Synchronization and Aggregation of Nonlinear Power Systems with Consideration of Bus Network Structures
Synchronization and Aggregation of Nonlinear Power Systems with Consideration of Bus Network Structures Open
We study nonlinear power systems consisting of generators, generator buses, and non-generator buses. First, looking at a generator and its bus' variables jointly, we introduce a synchronization concept for a pair of such joint generators a…
View article: Model Reduction of Linear Multi-Agent Systems by Clustering and Associated $\mathcal{H}_2$- and $\mathcal{H}_\infty$-Error Bounds
Model Reduction of Linear Multi-Agent Systems by Clustering and Associated $\mathcal{H}_2$- and $\mathcal{H}_\infty$-Error Bounds Open
In this paper, we study a model reduction technique for leader-follower networked multi-agent systems defined on weighted, undirected graphs with arbitrary linear multivariable agent dynamics. In the network graph of this network, nodes re…
View article: Stability preserving model reduction for linearly coupled linear time‐invariant systems
Stability preserving model reduction for linearly coupled linear time‐invariant systems Open
We develop a stability preserving model reduction method for linearly coupled linear time‐invariant (LTI) systems. The method extends the work of Monshizadeh et al. for multi‐agent systems with identical LTI agents. They propose using Boun…