Second-Order Information in Data Assimilation*

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: 73%

Truncated-Newton training algorithm for neurocomputational viscoplastic model

Al-Haik

Garmestani

Navon

2003

Computer Methods in Applied Mechanics and Engineering

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“…w is an user-defined vector, and the notationλ i+1 in the last term of (10) indicates that the state derivative applies to the M * i (x i ) operator only while treating the adjoint variables λ i+1 as constants ( [10], [7]). …”

Section: Soa Model Equationsmentioning

confidence: 99%

“…To overcome this practical difficulty and to increase the effectiveness of adjoint targeting strategies, a second order adjoint (SOA) model may be considered to capture the quadratic terms in the error growth approximation. An overview of the SOA model implementation and applications to variational data assimilation is provided in [7].…”

Section: Introductionmentioning

confidence: 99%

A Second Order Adjoint Method to Targeted Observations

Godinez

Daescu

2009

Lecture Notes in Computer Science

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Abstract. The role of the second order adjoint in targeting strategies is studied and analyzed. Most targeting strategies use the first order adjoint to identify regions where additional information is of potential benefit to a data assimilation system. The first order adjoint posses a restriction on the targeting time for which the linear approximation accurately tracks the evolution of perturbation. Using second order adjoint information it is possible to maintain some accuracy for longer time intervals, which can lead to an increase on the target time. We propose the use of the dominant eigenvectors of the Hessian matrix as an indicator of the directions of maximal error growth for a given targeting functional. These vectors are a natural choice to be included in the targeting strategies given their mathematical properties.

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“…Truncated-Newton (TN) minimization methods [23,24] can be highly effective for solving the optimization problem since they take full advantage of the first-and second-order derivative information. The Hessian-free implementation (HFTN) requires only Hessian/vector products that may be obtained from a second-order adjoint model as explained in Reference [25].…”

Section: Introductionmentioning

confidence: 99%

Efficiency of a POD‐based reduced second‐order adjoint model in 4D‐Var data assimilation

Daescu

Navon

2006

Numerical Methods in Fluids

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SUMMARYOrder reduction strategies aim to alleviate the computational burden of the four-dimensional variational data assimilation by performing the optimization in a low-order control space. The proper orthogonal decomposition (POD) approach to model reduction is used to identify a reduced-order control space for a two-dimensional global shallow water model. A reduced second-order adjoint (SOA) model is developed and used to facilitate the implementation of a Hessian-free truncated-Newton (HFTN) minimization algorithm in the POD-based space. The efficiency of the SOA/HFTN implementation is analysed by comparison with the quasi-Newton BFGS and a nonlinear conjugate gradient algorithm. Several data assimilation experiments that differ only in the optimization algorithm employed are performed in the reduced control space. Numerical results indicate that first-order derivative methods are effective during the initial stages of the assimilation; in the later stages, the use of second-order derivative information is of benefit and HFTN provided significant CPU time savings when compared to the BFGS and CG algorithms. A comparison with data assimilation experiments in the full model space shows that with an appropriate selection of the basis functions the optimization in the POD space is able to provide accurate results at a reduced computational cost. The HFTN algorithm benefited most from the order reduction since computational savings were achieved both in the outer and inner iterations of the method. Further experiments are required to validate the approach for comprehensive global circulation models.

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Second-Order Information in Data Assimilation*

Cited by 155 publications

References 62 publications

Truncated-Newton training algorithm for neurocomputational viscoplastic model

Truncated-Newton training algorithm for neurocomputational viscoplastic model

A Second Order Adjoint Method to Targeted Observations

Efficiency of a POD‐based reduced second‐order adjoint model in 4D‐Var data assimilation

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