Modal Decomposition of Flow Data via Gradient-Based Transport Optimization

Black, Felix; Schulze, Philipp; Unger, Benjamin

doi:10.1007/978-3-030-90727-3_13

Cited by 4 publications

(7 citation statements)

References 32 publications

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“…Since our problem is dominated by transport, we apply the sPOD introduced in [35,36] and formalized in [5,6,8]. To capture the transport terms, sPOD allows the construction of multiple reduced ansatz spaces traveling in the spatial domain.…”

Section: Overview Of Mor Approachmentioning

confidence: 99%

“…From the full order simulation in Figure 1 we observe that the wavefront of the transmembrane voltage travels at an approximately constant speed through the spatial domain. Following this observation, we only account for constant shift velocities of the basis functions and construct a constant-speed shifted reduced ansatz space, in contrast to [5,8] where also non-constant shift velocities are allowed.…”

Section: Overview Of Mor Approachmentioning

confidence: 99%

“…We use sPOD [8,34], an adapted version of POD [18,20,22,32], to obtain the reduced basis functions from the results of the full order simulation, explicitly accounting for the shift variables p j . To obtain the ROM, we use these reduced basis functions instead while following the same Galerkin approach in comparison to the FOM.…”

Section: Overview Of Mor Approachmentioning

confidence: 99%

“…We construct the basis functions {ϕ j } r j =1 of the reduced space R as elements of the finite dimensional ansatz space V h of the FOM to obtain continuous reduced basis functions. Since they should capture the transport quantities, we evaluate them in a shifted and time-dependent position based on unknown paths p j : T 0 , T → R [8].…”

Section: Adaptive Reduced Ansatz Spacementioning

confidence: 99%

“…With these preparations, we can define our modified reduced ansatz space. Let T (p j (t )) be a suitable transformation operator, compare [8], with linear shifts p j (t ) = p j t with the path coefficients p ∈ R r for all j = 1, ... , r . We define the time-shifted reduced basis functions {φ j } r j =1 through…”

Section: Adaptive Reduced Ansatz Spacementioning

confidence: 99%

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Model Order Reduction with Dynamically Transformed Modes for Electrophysiological Simulations

Hornischer

2023

GAMMAS

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The numerical simulation of neuromuscular processes in skeletal muscles typically imposes high computational costs, resulting in the need for techniques to reduce these costs. One submodel in these types of multiphysics multiscale simulations is the electrophysiological model, describing the propagation of an action potential (AP) in a muscle fiber. Involved in the simulation of the propagation are two traveling waves, resulting in difficulties for classical model order reduction (MOR) techniques based on linear subspaces. Instead, we apply the nonlinear MOR method shifted Proper Orthogonal Decomposition (sPOD) to construct dynamically transformed reduced basis functions depending on time-dependent paths spanning the adaptive reduced ansatz space. Our numerical experiments demonstrate that the constructed reduced ansatz space can accurately capture the dynamics of two fully separated wavefronts and reduce the degrees of freedom of the whole simulation. However, it cannot represent the activation of the AP in the center of the fiber and overlapping wave parts. The constructed reduced order model outperforms the high-dimensional full order model in terms of the computational costs while the accuracy is maintained and reaches speedup factors between 2 and 73 depending on the time discretization.

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Section: Overview Of Mor Approachmentioning

confidence: 99%

Section: Overview Of Mor Approachmentioning

confidence: 99%

Section: Overview Of Mor Approachmentioning

confidence: 99%

Section: Adaptive Reduced Ansatz Spacementioning

confidence: 99%

Section: Adaptive Reduced Ansatz Spacementioning

confidence: 99%

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Model Order Reduction with Dynamically Transformed Modes for Electrophysiological Simulations

Hornischer

2023

GAMMAS

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Modal Decomposition of Flow Data via Gradient-Based Transport Optimization

Black

Schulze

Unger

2021

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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Front Transport Reduction for Complex Moving Fronts

et al. 2023

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This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction–diffusion process. Such systems are especially challenging for model order reduction since the transport cannot be captured by linear reduction methods. Moreover, topological changes, such as splitting or merging of fronts pose difficulties for many nonlinear reduction methods and the small non-vanishing support of the underlying partial differential equations dynamics makes most nonlinear hyper-reduction methods infeasible. We propose a new decomposition method together with a hyper-reduction scheme that addresses these shortcomings. The decomposition uses a level-set function to parameterize the transport and a nonlinear activation function that captures the structure of the front. This approach is similar to autoencoder artificial neural networks, but additionally provides insights into the system, which can be used for efficient reduced order models. In addition to the presented decomposition method, we outline a tailored hyper-reduction method that is based on the reduced integration domain method. The capability of the approach is illustrated by various numerical examples in one and two spatial dimensions, including an advection–reaction–diffusion system with a Kolmogorov–Petrovsky–Piskunov reaction term and real life application to a two-dimensional Bunsen flame.

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Modal Decomposition of Flow Data via Gradient-Based Transport Optimization

Cited by 4 publications

References 32 publications

Model Order Reduction with Dynamically Transformed Modes for Electrophysiological Simulations

Model Order Reduction with Dynamically Transformed Modes for Electrophysiological Simulations

Modal Decomposition of Flow Data via Gradient-Based Transport Optimization

Front Transport Reduction for Complex Moving Fronts

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