Newton-Type Minimization via the Lanczos Method

We present an estimate approach to compute the viscoplastic behavior of a polymer matrix composite (PMC) under different thermomechanical environments. This investigation incorporates computational neural network as the tool for deter-mining the creep behavior of the composite. We propose a new second-order learning algorithm for training the multilayer networks. Training in the neural network is generally specified as the minimization of an appropriate error function with respect to parameters of the network (weights and learning rates) corresponding to excitory and inhibitory connections. We propose here a technique for error minimization based on the use of the truncated Newton (TN) large-scale unconstrained minimization technique with quadratic convergence rate. This technique offers a more sophisticated use of the gradient information compared to simple steepest descent or conjugate gradient methods. In this work we briefly specify the necessary details for implementing the truncated Newton method for training the neural networks that predicts the viscoplastic behavior of the polymeric composite. We provide comparative experimental results and explicit model results to verify the effectiveness of the neural networks-based model. These results verify the 1 Corresponding author, Tel: 850-644-6560. E-mail address: navon@csit.fsu.edu. 2 superiority of the present approach compared to the explicit modeling scheme. Moreover, the present study demonstrates for the first time the feasibility of introducing the truncated Newton method, with quadratic convergence rate, to the field of neural networks.

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“…Similar conclusions and more detailed discussion of the truncated Newton method can be found at [29][30][31][32], [47], [25].…”

Section: The Truncated Newton Algorithmsupporting

confidence: 57%

Truncated-Newton training algorithm for neurocomputational viscoplastic model

Al-Haik

Garmestani

Navon

2003

Computer Methods in Applied Mechanics and Engineering

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“…Different algorithms that use many of the same key principles have appeared in the literature of various communities under different names such as Newton-CG, CG-Steihaug, Newton-Lanczos, and Truncated Newton (Nash, 1984(Nash, , 2000Nocedal and Wright, 1999), but applications to machine learning and especially neural networks, have been limited or non-existent until the work of Martens (2010). In Martens (2010) and later it was demonstrated that such an approach, if carefully designed and implemented, works very well for training deep neural networks and recurrent neural networks, given sensible random initializations.…”

Section: Introductionmentioning

confidence: 99%

Training Deep and Recurrent Networks with Hessian-Free Optimization

Martens

Sutskever

2012

Lecture Notes in Computer Science

388

464

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“…Accordingly we use two unconstrained minimization methods suited for the large-parameter case. Given the Gaussian noise in the measured data, we use the limited-memory BFGS quasi-Newton method described by Nocedal (1980) and Liu & Nocedal (1989) to find an initial estimate of the minimum, and a truncated Newton method to refine the solution (Nash 1984). Both methods work well in the largeparameter case.…”

Section: Autocorrelation Polarization Self-calibrationmentioning

confidence: 99%

Circular polarization measurement in millimeter-wavelength spectral-line VLBI observations

Kemball

Richter

2011

A&A

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This paper considers the problem of accurate measurement of circular polarization in imaging spectral-line VLBI observations in the λ = 7 mm and λ = 3 mm wavelength bands. This capability is especially valuable for the full observational study of compact, polarized SiO maser components in the near-circumstellar environment of late-type, evolved stars. Circular VLBI polarimetry provides important constraints on SiO maser astrophysics, including the theory of polarized maser emission transport, and on the strength and distribution of the stellar magnetic field and its dynamical role in this critical circumstellar region. We perform an analysis here of the data model containing the instrumental factors that limit the accuracy of circular polarization measurements in such observations, and present a corresponding data reduction algorithm for their correction. The algorithm is an enhancement of existing spectral line VLBI polarimetry methods using autocorrelation data for calibration, but with innovations in bandpass determination, autocorrelation polarization self-calibration, and general optimizations for the case of low SNR, as applicable at these wavelengths. We present an example data reduction at λ = 7 mm and derive an estimate of the predicted accuracy of the method of m c ≤ 0.5% or better at λ = 7 mm and m c ≤ 0.5−1% or better at λ = 3 mm. Both the strengths and weaknesses of the proposed algorithm are discussed, along with suggestions for future work.

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Newton-Type Minimization via the Lanczos Method

Cited by 294 publications

References 13 publications

Truncated-Newton training algorithm for neurocomputational viscoplastic model

Truncated-Newton training algorithm for neurocomputational viscoplastic model

Training Deep and Recurrent Networks with Hessian-Free Optimization

Circular polarization measurement in millimeter-wavelength spectral-line VLBI observations

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