An analysis of numerical issues in neural training by pseudoinversion

Cancelliere, R.; Deluca, R.; Gai, M.; Gallinari, Patrick; Rubini, Luca

doi:10.1007/s40314-015-0246-z

Cited by 4 publications

(6 citation statements)

References 19 publications

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“…Introducing N sample training data examples (i.e., input-output pairs), the weights and biases can be computed in a supervised learning framework using either well established iterative back propagation methods [49] or pseudoinverse approaches [34]. As mentioned previously, the ANN architecture is trained by utilizing an ELM approach proposed in [33] for extremely fast training of an SLFN.…”

Section: A Extreme Learning Machinementioning

confidence: 99%

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Extreme learning machine for reduced order modeling of turbulent geophysical flows

San

Maulik

2018

Phys. Rev. E

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We investigate the application of artificial neural networks to stabilize proper orthogonal decomposition-based reduced order models for quasistationary geophysical turbulent flows. An extreme learning machine concept is introduced for computing an eddy-viscosity closure dynamically to incorporate the effects of the truncated modes. We consider a four-gyre wind-driven ocean circulation problem as our prototype setting to assess the performance of the proposed data-driven approach. Our framework provides a significant reduction in computational time and effectively retains the dynamics of the full-order model during the forward simulation period beyond the training data set. Furthermore, we show that the method is robust for larger choices of time steps and can be used as an efficient and reliable tool for long time integration of general circulation models.

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Section: A Extreme Learning Machinementioning

confidence: 99%

“…where λ controls the trade off between the least-squares error and the penalty term for regularization (e.g., see [34]). In the present study we set = 10 −12 .…”

Section: A Extreme Learning Machinementioning

confidence: 99%

Extreme learning machine for reduced order modeling of turbulent geophysical flows

San

Maulik

2018

Phys. Rev. E

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“…Regularisation methods have to be used [51,52] to turn the original problem into a well-posed one, i.e. roughly speaking into a problem insensitive to small changes in initial conditions.…”

Section: Neural Model and Pseudo-inversion Based Trainingmentioning

confidence: 99%

Real-time detection of driver distraction: random projections for pseudo-inversion-based neural training

et al. 2019

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There is an accumulating evidence that distracted driving is a leading cause of vehicle crashes and accidents. In order to support safe driving, numerous methods of detecting distraction have been proposed, which are empirically focused on certain driving contexts and gaze behavior. This paper aims at illustrating a method for the non-intrusive and real-time detection of visual distraction based on vehicle dynamics data and environmental data, without using eye-tracker information. Experiments are carried out in the context of the automotive domain of the European project Holides, which addresses development and qualification of Adaptive Cooperative Human-Machine Systems, and is co-funded by ARTEMIS Joint Undertaking and Italian University, Educational and Research Department. The collected data are analised by a single layer feedforward neural network trained through pseudo-inversion methods, characterized by direct determination of output weights given randomly set input weights and biases. One main feature of our work is the convenient setting of input weights by the so called random projections: the presence of a great number of null elements in the involved matrices makes especially parsimonious the use at run time of the trained network. Moreover, we use a genetic approach to better explore the input weights network space. The obtained results show both better performance with respect to classical methods and effective and parsimonious use of memory resources.

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“…We choose τ = 10 −12 for the present study which indicates the trade-off between the least-squares error and the penalty term for regularization [84]. The unknown weights can be calculated by using Equation (31).…”

Section: Artificial Neural Network Based Non-intrusive Reduced-order mentioning

confidence: 99%

A Hybrid Approach for Model Order Reduction of Barotropic Quasi-Geostrophic Turbulence

Rahman

San

Rasheed

2018

Fluids

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We put forth a robust reduced-order modeling approach for near real-time prediction of mesoscale flows. In our hybrid-modeling framework, we combine physics-based projection methods with neural network closures to account for truncated modes. We introduce a weighting parameter between the Galerkin projection and extreme learning machine models and explore its effectiveness, accuracy and generalizability. To illustrate the success of the proposed modeling paradigm, we predict both the mean flow pattern and the time series response of a single-layer quasi-geostrophic ocean model, which is a simplified prototype for wind-driven general circulation models. We demonstrate that our approach yields significant improvements over both the standard Galerkin projection and fully non-intrusive neural network methods with a negligible computational overhead.

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An analysis of numerical issues in neural training by pseudoinversion

Cited by 4 publications

References 19 publications

Extreme learning machine for reduced order modeling of turbulent geophysical flows

Extreme learning machine for reduced order modeling of turbulent geophysical flows

Real-time detection of driver distraction: random projections for pseudo-inversion-based neural training

A Hybrid Approach for Model Order Reduction of Barotropic Quasi-Geostrophic Turbulence

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