Model order reduction based on Runge–Kutta neural networks

The electric properties of an interface between an electrode and a neuron are highly dependent on interface geometry and other parameters. Finite element models can be used to study these properties to a certain extent. Unfortunately, such models are computationally very expensive. By reducing these models, the computational time can be decreased. In this work, we use Krylovsubspace based model order reduction to reduce a simplified, linearized finite element model of an electrode-neuron interface. This facilitates the coupling to the Hodgkin-Huxley model at system level and reduces the computational time considerably. The accuracy of the original finite element model is preserved to a large extent.

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“…We plan to develop and employ suitable methods of model order reduction. A promising approach is MOR via artificial neural networks [18].…”

Section: Discussionmentioning

confidence: 99%

Reduced Order Model of a Neuron-Electrode Interface Coupled to a Hodgkin-Huxley Model

Fitzer¹,

Hohlfeld²,

Bechtold³

2022

World Congress on Electrical Engineering and Computer Systems and Science

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“…In this case the inputs to the Neural Network are the current state of the system y r,i and µ i , and the new reduced state y r,i+1 is calculated as y r,i+1 = y r,i + δtg ee (y r,i , µ i ) (11) this looks similar to an Explicit Euler integrator, so we denote the network's function as g ee (y r,i , µ i ). And we call such a network Explicit Euler Neural Network (EENN) [9,23]. From Equation 11, we know that an EENN is essentially a variant of residual network [24] which learns the increment between two system states instead of learning to map the new state directly from the old state.…”

Section: Rom Identification Using Annsmentioning

confidence: 99%

“…surrogate ROMs [9]. Other network architectures such as Long-short-term-memory (LSTM) Neural Network [10] and Recurrent Neural Network (RNN) [11,12] have also been tested for the purpose of reduced modelling.…”

Section: Introductionmentioning

confidence: 99%

Active-learning-based non-intrusive Model Order Reduction

Zhuang¹,

Hartmann²,

Bungartz³

et al. 2022

Preprint

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The Model Order Reduction (MOR) technique can provide compact numerical models for fast simulation. Different from the intrusive MOR methods, the non-intrusive MOR does not require access to the Full Order Models (FOMs), especially system matrices. Since the non-intrusive MOR methods strongly rely on the snapshots of the FOMs, constructing good snapshot sets becomes crucial. In this work, we propose a new active learning approach with two novelties. A novel idea with our approach is the use of single-time step snapshots from the system states taken from an estimation of the reduced-state space. These states are selected using a greedy strategy supported by an error estimator based Gaussian Process Regression (GPR). Additionally, we introduce a use case-independent validation strategy based on Probably Approximately Correct (PAC) learning. In this work, we use Artificial Neural Networks (ANNs) to identify the Reduced Order Model (ROM), however the method could be similarly applied to other ROM identification methods. The performance of the whole workflow is tested by a 2-D thermal conduction and a 3-D vacuum furnace model. With little required user interaction and a training strategy independent to a specific use case, the proposed method offers a huge potential for industrial usage to create so-called executable Digital Twins (DTs).

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“…Currently, most data-driven MOR methods are based on machine learning (ML). For example, Feed-forward Neural Network (Regazzoni et al, 2019), operator inference (OpInf) (Peherstorfer and Willcox, 2016), Long-short-term-memory (LSTM) neural network (Mohan and Gaitonde, 2018), recurrent neural network (RNN) (Kani and Elsheikh, 2017;Wang et al, 2020;Wu and Noels, 2022), deep learning (Fresca and Manzoni, 2022), sparse identification of nonlinear dynamics (SINDy) (Champion et al, 2019), and Runge-Kutta neural network (Zhuang et al, 2021) have been tested for reduced modeling.…”

Section: Introductionmentioning

confidence: 99%

Active-learning-based nonintrusive model order reduction

Zhuang

Hartmann²,

Bungartz³

et al. 2023

DCE

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Model order reduction (MOR) can provide low-dimensional numerical models for fast simulation. Unlike intrusive methods, nonintrusive methods are attractive because they can be applied even without access to full order models (FOMs). Since nonintrusive MOR methods strongly rely on snapshots of the FOMs, constructing good snapshot sets becomes crucial. In this work, we propose a novel active-learning-based approach for use in conjunction with nonintrusive MOR methods. It is based on two crucial novelties. First, our approach uses joint space sampling to prepare a data pool of the training data. The training data are selected from the data pool using a greedy strategy supported by an error estimator based on Gaussian process regression. Second, we introduce a case-independent validation strategy based on probably approximately correct learning. While the methods proposed here can be applied to different MOR methods, we test them here with artificial neural networks and operator inference.

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Model order reduction based on Runge–Kutta neural networks

Cited by 12 publications

References 32 publications

Reduced Order Model of a Neuron-Electrode Interface Coupled to a Hodgkin-Huxley Model

Reduced Order Model of a Neuron-Electrode Interface Coupled to a Hodgkin-Huxley Model

Active-learning-based non-intrusive Model Order Reduction

Active-learning-based nonintrusive model order reduction

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