Introduction Using a theoretical relationship (i.e., physical laws), for given values of model parameters, a `direct' (or forward) problem aims at predicting the values of some observable quantities. In contrast, for given measurements of observable quantities, an `inverse' problem aims at obtaining the values of model parameters (Tarantola 1987). Over the past two decades, many inverse problems in meteorology have been solved using the adjoint models of corresponding meteorological prediction systems. These include the generation of singular vectors for ensemble prediction (e.g., Molteni et al. 1996); four-dimensional variational data assimilation (e.g., Lewis and Derber 1985; Le Dimet and Talagrand 1986; Courtier et al. 1994); forecast sensitivity to the initial conditions (Rabier et al. 1996; Pu et al. 1997a); and targeted observations (e.g., Rohaly et al. 1998; Pu et al. 1998). The four-dimensional variational data assimilation (4D-Var) using the adjoint model, in which

Abstract not found

In variational data assimilation (VDA) for meteorological and/or oceanic models, the assimilated fields are deduced by combining the model and the gradient of a cost functional measuring discrepancy between model solution and observation, via a first-order optimality system. However, existence and uniqueness of the VDA problem along with convergence of the algorithms for its implementation depend on the convexity of the cost function. Properties of local convexity can be deduced by studying the Hessian of the cost function in the vicinity of the optimum. This shows the necessity of second-order information to ensure a unique solution to the VDA problem.

Abstract. It is empirically established that multiobjective evolutionary algorithms do not scale well with the number of conflicting objectives. We here show that the convergence rate of all comparison-based multiobjective algorithms, for the Hausdorff distance, is not much better than the convergence rate of the random search, unless the number of objectives is very moderate, in a framework in which the stronger assumptions are (i) that the objectives are conflicting (ii) that lower bounding the computational cost by the number of comparisons is a good model. Our conclusions are (i) the relevance of the number of conflicting objectives (ii) the relevance of criteria based on comparisons with random-search for multi-objective optimization (iii) the very-hardness of more than 3-objectives optimization (iv) some hints about cross-over operators. 1

this report. We also thank Boyana Norris for her assistance in organizing the institute. Finally, we thank Gail Pieper for numerous suggestions that greatly improved the organization and readability of this report. ix Agenda

We present an estimate approach to compute the viscoplastic behavior of a polymer matrix compositeundo ddosit 13 thermomechanical environments. This investigation incorporates computational neural network as the tool for dr 14 termining the creep behavior of the composite. We propose a newsecondj,;#fl learning algorithm for training the 15 multilayer networks. Training in the neural network is generallyspecified as the minimization of an appropriate error 16 function with respect to parameters of the network (weightsand learning rates) correspond,; to excitoryand inhib- 17 itory connections. We propose here a technique for error minimizationbased on the use of thetruncated Newton (TN) 18 large-scale unconstrained minimization technique withquad#((W convergence rate. This technique o#ers a more so- phisticated use of thegrad#fiq informationcompared to simple steepestdeepes or conjugategradgat methodt In this 20 work we briefly specify the necessarydcessa for implementing the TNmethod for training the neural networks that predW, the viscoplastic behavior of the polymeric composite. Weprovid comparative experimental resultsand explicit 22 modd results to verify the e#ectiveness of the neuralnetworks-based modwo These results verify the superiority of the 23 present approachcompared to the explicit modicit scheme. Moreover,the presentstud ddnt,fiqWfix for the first 24 time the feasibility ofintrod,;xj the TNmethod,;xj quadod, convergence rate,to thefield of neural networks.

*A major focus in severe weather research for operational applications is the development of robust techniques to detect mesocyclones and tornadoes in real-time. Several factors limit the success

A new multiple-Doppler radar analysis technique is presented for the objective detection and characterization of tornado-like vortices. The technique consists of fitting radial wind data from two or more radars to a simple analytical model of a vortex and its near-environment. The model combines a uniform flow, linear shear flow, linear divergence flow (all of which comprise a broadscale flow), and modified combined Rankine vortex (representing the tornado). The vortex and its environment are allowed to translate. The parameters in the low-order model are determined by minimizing a cost function which accounts for the discrepancy between the model and observed radial winds. Since vortex translation is taken into account, the cost function can be evaluated over time as well as space, and thus the observations can be used at the actual times and locations they were acquired. The technique is first tested using analytically-simulated observations whose wind field and error characteristics are systematically varied. An ARPS (Advanced Regional Prediction System) high-resolution numerical simulation of a supercell and associated tornado is then used to emulate an observation data set. The method is tested with two virtual radars for several radar-sampling strategies. Finally, the technique is applied to a dataset of real dual-Doppler observations of a tornado that struck central Oklahoma on 8 May 2003. The method shows skill in retrieving the tornado path and radar-grid-scale features of the horizontal wind field in the vicinity of the tornado. The best results are obtained using a two-step procedure in which the broadscale flow is retrieved first. 1

A new multiple-Doppler radar analysis technique is presented for the objective detection and characterization of tornado-like vortices. The technique consists of fitting radial wind data from two or more radars to a simple analytical model of a vortex and its near-environment. The model combines a uniform flow, linear shear flow, linear divergence flow (all of which compose a broadscale flow), and a modified combined Rankine vortex (representing the tornado). The vortex and its environment are allowed to translate. The parameters in the low-order model are determined by minimizing a cost function that accounts for the discrepancy between the model and observed radial winds. Since vortex translation is taken into account, the cost function can be evaluated over time as well as space, and thus the observations can be used at the actual times and locations where they were acquired. The technique is first tested using analytically simulated observations whose wind field and error characteristics are systematically varied. An Advanced Regional Prediction System (ARPS) high-resolution numerical simulation of a supercell and associated tornado is then used to emulate an observation dataset. The method is tested with two virtual radars for several radarsampling strategies. Finally, the technique is applied to a dataset of real dual-Doppler observations of a tornado that struck central Oklahoma on 8 May 2003. The method shows skill in retrieving the tornado path and radar-grid-scale features of the horizontal wind field in the vicinity of the tornado. The best results are obtained using a two-step procedure in which the broadscale flow is retrieved first. 1.

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.