European Numerical Mathematics and
Advanced Applications Conference 2019
30th sep - 4th okt 2019, Egmond aan Zee, The Netherlands
15:45   MS2: Recent Advances in Model Order Reduction
Chair: Muhammad Umer Altaf
25 mins
A Nonintrusive POD-Adaptive Reduced Order Model for Coupled Nuclear Reactor applications
Fahad Alsayyari, Marco Tiberga, Zoltan Perko, Danny Lathouwers, Jan Leen Kloosterman
Abstract: High-fidelity models are often used to model complex coupled systems such as nuclear reactors. These models, however, are too expensive for parametric study applications such as uncertainty quantifications, optimization, and control. Proper Orthogonal Decomposition (POD) is an effective Reduced Order Modelling (ROM) technique to reduce the computational burden for large-scale nonlinear systems \cite{Benner2015}. POD can either be projection-based, which is code intrusive, or can be nonintrusively surrogate-based. Most practical nuclear applications use legacy codes which precludes the use of intrusive methods. An additional challenge for any POD approach is the exponential increase in the computational requirements with the increase in the dimensionality of the problem. In this work, we present an algorithm that integrates the nonintrusive POD approach with the sparse grids technique. We propose the use of the locally adaptive sparse grids \cite{Ma2009} to tackle the high dimensionality challenge. The adaptivity of the sparse grids guides the sampling scheme to generate the snapshots of the POD efficiently. Smolyak interpolant is used as a surrogate for the POD coefficients. The generation of the snapshots is controlled through a greediness parameter. In our approach, the produced ROM model can also be updated in the online phase by incorporating new snapshots. We demonstrate the performance of the algorithm by testing it on a simplified reactor physics problem (Figure~\ref{fig:simpl}), which showed an online time reduction by a factor of 10 compared to the reference model, and to a more complex system resembling the Molten Salt Fast Reactor (MSFR) (Figure~\ref{fig:msr})\cite{CNRS}. In both cases, the accuracy and the run time of the ROM model are compared with respect to the reference high-fidelity model.
25 mins
Subdomain Reduced-Order Modeling with Smooth Local Parameterization for Large-Scale Inversion Problems
Cong Xiao, Arnold Heemink, Hai Xiang Lin, Olwijn Leeuwenburgh
Abstract: Inversion problem is a major challenge for a large number of uncertain parameters. In general, if the adjoint model can be implemented, the adjoint-based minimization algorithm is one of the most efficient approaches nowadays to handle large-scale inversion problems. However, the implementation of the adjoint model requires an overwhelming programming effort, and the legacy code of forward simulation model is not always available. We have recently developed a non-intrusive subdomain reduced-order modeling, i.e., subdomain POD-TPWL, to assist an adjoint-based parameter estimation without the need of model intrusion. Here a RBF interpolation approach is integrated with domain decomposition to efficiently construct subdomain reduced-order model. The adjoint of this reduced-order model can be implemented very easy. From a computational point of view, a local parameterization where the parameters are defined in each subdomain separately is very attractive. In this study, we present one such local parameterization through integrating principle component analysis (PCA) and domain decomposition (DD) to independently represent the spatial parameter field within low-order parameter subspaces in each subdomain. This local parameterization allows us to perturb parameters in each subdomain simultaneously and the effects of all these perturbations can be computed with very few full-order model simulations. The performance of this SubDomain POD-TPWL with Local Parameterization, referred to LP-SD POD-TPWL, has been assessed through a benchmark reservoir model. The methodology has high scalability, since the number of sampling points depends primarily on the number of the local parameters in each subdomain and not on the dimension of the underlying full-order model. Activating more subdomains results in much less local parameter patterns and enables us to run fewer model simulations. For the cases studied in this work, to optimize 282 global PCA patterns, LP-SD POD-TPWL needs 90 full-order model simulations, among them, 32 simulations are used to collect the snapshots for POD, 49 simulations are used to construct the initial subdomain reduced-order model, and the remaining 9 simulations are used to update the reduced-order model in 9 outer-loops.
25 mins
Reduced Order Variational Data Assimilation for Estimating Soil Moisture Profile
Leila Farhadi, Parisa Heidary, Muhammad Umer Altaf
Abstract: Spatially distributed soil moisture profiles are required for watershed applications such as drought and flood prediction, crop irrigation scheduling, pest management, and determining mobility with lightweight vehicles. Soil moisture is highly variable in space and time owing to the dynamics in soil hydraulic properties. Therefore, measurement and simulation of soil moisture pattern are of particular importance. Satellite-based soil moisture can be obtained from passive microwave, active microwave, and optical sensors, although the coarse spatial resolution of passive microwave and the inability to obtain vertically resolved information from optical sensors limit their usefulness for watershed-scale applications. In a synthetic study the potential of using surface soil moisture measurements obtained from different satellite platforms to retrieve soil moisture profiles and soil hydraulic properties, will be explored using reduced order variational data assimilation procedures and a 1D mechanistic soil water model. Adjoint techniques namely variational data assimilation (4DVAR) is a well-known method for estimation of the unknown parameters of a physical system. This method improves a model consistency with available data by minimizing a cost function measuring the model–data misfit with respect to some model inputs and parameters. Associated with this type of method, however, are difficulties related to the coding of the adjoint model, which is needed to compute the gradient of the 4DVAR cost function. Proper orthogonal decomposition (POD) is a model reduction technique that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called POD modes. Two distinct approaches for POD in 4DVAR will be explored in this study. In the first approach, an optimization algorithm is applied in order to minimize the cost function entirely in the POD-reduced space. The second approach uses POD to approximate only the adjoint model. The accuracy and feasibility of the proposed approaches will be investigated through a synthetic study. The effect of assimilation strategy, measurement frequency, accuracy in surface soil moisture measurements, and soils differing in textural and hydraulic properties will be investigated. The approach will be able to assess the value of periodic space-borne observations of surface soil moisture for soil moisture profile estimation and for identifying the adequate conditions (e.g. temporal resolution and measurement accuracy) for remotely sensed soil moisture data assimilation.