Coarse Representation Research Articles

Deformation Recovery: Localized Learning for Detail-Preserving Deformations

We introduce a novel data-driven approach aimed at designing high-quality shape deformations based on a coarse localized input signal. Unlike previous data-driven methods that require a global shape encoding, we observe that detail-preserving deformations can be estimated reliably without any global context in certain scenarios. Building on this intuition, we leverage Jacobians defined in a one-ring neighborhood as a coarse representation of the deformation. Using this as the input to our neural network, we apply a series of MLPs combined with feature smoothing to learn the Jacobian corresponding to the detail-preserving deformation, from which the embedding is recovered by the standard Poisson solve. Crucially, by removing the dependence on a global encoding, every point becomes a training example, making the supervision particularly lightweight. Moreover, when trained on a class of shapes, our approach demonstrates remarkable generalization across different object categories. Equipped with this novel network, we explore three main tasks: refining an approximate shape correspondence, unsupervised deformation and mapping, and shape editing. Our code is made available at https://github.com/sentient07/LJN.

Linear-regression-based algorithms can succeed at identifying microbial functional groups despite the nonlinearity of ecological function.

Microbial communities play key roles across diverse environments. Predicting their function and dynamics is a key goal of microbial ecology, but detailed microscopic descriptions of these systems can be prohibitively complex. One approach to deal with this complexity is to resort to coarser representations. Several approaches have sought to identify useful groupings of microbial species in a data-driven way. Of these, recent work has claimed some empirical success at de novo discovery of coarse representations predictive of a given function using methods as simple as a linear regression, against multiple groups of species or even a single such group (the ensemble quotient optimization (EQO) approach). Modeling community function as a linear combination of individual species' contributions appears simplistic. However, the task of identifying a predictive coarsening of an ecosystem is distinct from the task of predicting the function well, and it is conceivable that the former could be accomplished by a simpler methodology than the latter. Here, we use the resource competition framework to design a model where the "correct" grouping to be discovered is well-defined, and use synthetic data to evaluate and compare three regression-based methods, namely, two proposed previously and one we introduce. We find that regression-based methods can recover the groupings even when the function is manifestly nonlinear; that multi-group methods offer an advantage over a single-group EQO; and crucially, that simpler (linear) methods can outperform more complex ones.

A Pressure-Based Model of IV Fluid Therapy Kinetics.

The kinetics of intravenous (IV) fluid therapy and how it affects the movement of fluids within humans and animals is an ongoing research topic. Clinical researchers have in the past used a mathematical model adopted from pharmacokinetics that attempts to mimic these kinetics. This linear model is based on the ideas that the body tries to maintain fluid levels in various compartments at some baseline targets and that fluid movement between compartments is driven by differences between the actual volumes and the targets. Here a nonlinear pressure-based model is introduced, where the driving force of fluid movement out of the blood stream is the pressure differences, both hydrostatic and oncotic, between the capillaries and the interstitial space. This model is, like the linear model, a coarse representation of fluid movement on the whole body scale, but, unlike the linear model, it is based on some of the body's biophysical processes. The abilities of both models to fit data from experiments on both awake and anesthetized cats was analyzed. The pressure-based model fit the data better than the linear model in all but one case, and was deemed statistically significantly better in a third of the cases.

Testing the Sensitivity of a WRF-Based Great Lakes Regional Climate Model to Cumulus Parameterization and Spectral Nudging

Abstract The Weather Research and Forecasting (WRF) Model is used to dynamically downscale ERA-Interim global reanalysis data to test its performance as a regional climate model (RCM) for the Great Lakes region (GLR). Four cumulus parameterizations and three spectral nudging techniques applied to moisture are evaluated based on 2-m temperature and precipitation accumulation in the Great Lakes drainage basin (GLDB). Results are compared to a control simulation without spectral nudging, and additional analysis is presented showing the contribution of each nudged variable to temperature, moisture, and precipitation. All but one of the RCM test simulations have a dry precipitation bias in the warm months, and the only simulation with a wet bias also has the least precipitation error. It is found that the inclusion of spectral nudging of temperature dramatically improves a cold-season cold bias, and while the nudging of moisture improves simulated annual and diurnal temperature ranges, its impact on precipitation is complicated. Significance Statement Global climate models are vital to understanding our changing climate. While many include a coarse representation of the Great Lakes, they lack the resolution to represent effects like lake effect precipitation, lake breeze, and surface air temperature modification. Therefore, using a regional climate model to downscale global data is imperative to correctly simulate the land–lake–atmosphere feedbacks that contribute to regional climate. Modeling precipitation is particularly important because it plays a direct role in the Great Lakes’ water cycle. The purpose of this study is to identify the configuration of the Weather Research and Forecasting Model that best simulates precipitation and temperature in the Great Lakes region by testing cumulus parameterizations and methods of nudging the regional model toward the global model.

Prior semantic-embedding representation learning for on-the-fly FG-SBIR

In fine-grained sketch-based image retrieval (FG-SBIR) framework, sketch drawing is a time-consuming and skill-intensive process that greatly restricts its practical application. Our study aims to enhance the early-stage retrieval efficiency by utilizing partial sketches with a minimum number of strokes in the on-the-fly FG-SBIR framework. Nevertheless, partial sketches with few strokes usually lack global information and consist only of sparse local details. This lack of detail results in ambiguous semantic content and indistinct differences among images, which consequently impairs early-stage retrieval. To acquire an efficient representation for these sketches, we propose a multi-granularity feature representation model that utilizes prior knowledge embedding to deal with the sketch drawing process. In the first stage,we design a triplet network to learn the joint a coarse representation embedding space that is common between the complete sketch and the image. In the second stage, We enhanced the semantic representation of sketches by utilizing prior knowledge, which aids in supplementing missing fine-grained features. This was achieved by formalizing the prior knowledge and integrating it into the feature vector obtained in the initial stage, thereby acquiring the final representation of a subset of sketches. Experiments conducted on two public datasets indicate that our method outperforms the state-of-the-art baseline during the early retrieval phase. In practical applications, our approach has also achieved good results.

Geo-guided deep learning for spatial downscaling of solute transport in heterogeneous porous media

Resolving solute transport in heterogeneous porous media is a complex task, because of the sparse experimental data and the high computational cost of numerical simulations. This work proposes a unique two-stage deep learning architecture comprising a dual-branch autoencoder and a geo-guided super-resolution generative adversarial network (Gg-SRGAN) to address this dual challenge. The dual-branch autoencoder addresses the issue of sparsity by constructing a continuous, but coarse representation of concentration and pressure profiles from a sparse, discontinuous profile with up to 85% missing data points. The Gg-SRGAN is then employed to generate a finer representation of field variables from the outputs generated by the dual-branch autoencoder (i.e., downscaling). We train and test our framework using six solute transport cases with varying levels of heterogeneity and compare the results with standalone methods, namely the vanilla autoencoder and vanilla SRGAN, in addition to ground truth profiles generated by the finite element method (FEM). The comparisons are performed based on several statistical metrics, such as absolute point error (APE), mean squared error (MSE), peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and learned perceptual image patch similarity (LPIPS). The first four cases are used for training, evaluation, and testing. The last two cases are utilized for blind testing to determine the generalizability of the framework. Our results show that the dual-branch autoencoder outperforms the vanilla autoencoder, and the Gg-SRGAN outperforms the SRGAN during both the training and evaluation phases. Moreover, the proposed framework can successfully construct the fine representation of concentration profiles, compared to FEM, using the coarse representation of the pressure, concentration, and domain permeability fields. When tested using the two blind test cases, the proposed dual-branch autoencoder and Gg-SRGAN exhibit superior performance compared to their counterparts in terms of all evaluation metrics.

Physics-Informed Deep Learning Approach for Reintroducing Atomic Detail in Coarse-Grained Configurations of Multiple Poly(lactic acid) Stereoisomers.

Multiscale modeling of complex molecular systems, such as macromolecules, encompasses methods that combine information from fine and coarse representations of molecules to capture material properties over a wide range of spatiotemporal scales. Being able to exchange information between different levels of resolution is essential for the effective transfer of this information. The inverse problem of reintroducing atomistic degrees of freedom in coarse-grained (CG) molecular configurations is particularly challenging as, from a mathematical point of view, it is an ill-posed problem; the forward mapping from the atomistic to the CG description is typically defined via a deterministic operator ("one-to-one" problem), whereas the reversed mapping from the CG to the atomistic model refers to creating one representative configuration out of many possible ones ("one-to-many" problem). Most of the backmapping methods proposed so far balance accuracy, efficiency, and general applicability. This is particularly important for macromolecular systems with different types of isomers, i.e., molecules that have the same molecular formula and sequence of bonded atoms (constitution) but differ in the three-dimensional configurations of their atoms in space. Here, we introduce a versatile deep learning approach for backmapping multicomponent CG macromolecules with chiral centers, trained to learn structural correlations between polymer configurations at the atomistic level and their corresponding CG descriptions. This method is intended to be simple and flexible while presenting a generic solution for resolution transformation. In addition, the method is aimed to respect the structural features of the molecule, such as local packing, capturing therefore the physical properties of the material. As an illustrative example, we apply the model on linear poly(lactic acid) (PLA) in melt, which is one of the most popular biodegradable polymers. The framework is tested on a number of model systems starting from homopolymer stereoisomers of PLA to copolymers with randomly placed chiral centers. The results demonstrate the efficiency and efficacy of the new approach.

Hybrid Base Complex: Extract and Visualize Structure of Hex-dominant Meshes.

Hex-dominant mesh generation has received significant attention in recent research due to its superior robustness compared to pure hex-mesh generation techniques. In this work, we introduce the first structure for analyzing hex-dominant meshes. This structure builds on the base complex of pure hex-meshes but incorporates the non-hex elements for a more comprehensive and complete representation. We provide its definition and describe its construction steps. Based on this structure, we present an extraction and categorization of sheets using advanced graph matching techniques to handle the non-hex elements. This enables us to develop an enhanced visual analysis of the structure for any hex-dominant meshes.We apply this structure-based visual analysis to compare hex-dominant meshes generated by different methods to study their advantages and disadvantages. This complements the standard quality metric based on the non-hex element percentage for hex-dominant meshes. Moreover, we propose a strategy to extract a cleaned (optimized) valence-based singularity graph wireframe to analyze the structure for both mesh and sheets. Our results demonstrate that the proposed hybrid base complex provides a coarse representation for mesh element, and the proposed valence singularity graph wireframe provides a better internal visualization of hex-dominant meshes.

Forecasting the spread of an invasive forest‐defoliating insect

AbstractAimBiological invasions are an escalating environmental challenge due to their substantial ecological and socio‐economic consequences. Accurate near‐term forecasts of future areas occupied by an invasive species could enhance the efficiency and efficacy of invasion monitoring and management but spread forecasting models have been developed and tested for few invasive species thus far.LocationNortheastern USA.MethodsWe developed a quantitative model to forecast 1‐year‐ahead occupancy of Lymantria dispar dispar, an expanding invasive forest insect introduced into the eastern United States in 1869 that causes large‐scale defoliation of forests. We validated and tested the model using historical distribution and density data from a large‐scale network of pheromone‐baited traps. We first assessed how forecast accuracy depended on trap catch density thresholds for determining occupancy and on the spatial scale of local connectivity measures. Next, we tested how increasing the computational complexity and biological detail encoded in the models affected prediction accuracy.ResultsModels using lower occupancy thresholds and measuring connectivity over shorter distances tended to perform best. A simple model using only coarse and generic representations of habitat suitability and local diffusive spread potential performed at least as well as more complex models. Our best models achieved total accuracy and true‐positive rates exceeding 95%.ConclusionsOur baseline model illustrates the utility of a mechanistic model to forecast year‐to‐year occupancy dynamics of L. dispar. Near‐term spread forecasting can be a valuable tool for invasion management, even for species without detailed a priori ecological knowledge.

Comparing Shape Representations for the Aesthetic Judgement of 3D Shape Pairs.

Visual aesthetics of 3D shapes is a fundamental perceptual attribute. In this paper, we explore the question of how different shape representations affect the aesthetic judgments of shape pairs. Specifically, we compare human responses to perceptual aesthetics judgements on 3D shapes in pairs presented in different 3D shape representation such as voxels, points, wireframe, and polygon. In contrast to our own previous work [8] that explores this question for a few shape classes, this paper analyzes a larger number of shape classes. Our key finding is that human aesthetics judgements on relatively low resolution of points or voxels are comparable to polygon meshes, which implies that humans can often make their aesthetics decisions based on relatively coarse representations of the shapes. Our results have implications towards the data collection process of pairwise aesthetics data and the further use of such data in shape aesthetics and 3D modeling problems.

Data-driven stochastic spectral modeling for coarsening of the two-dimensional Euler equations on the sphere

A resolution-independent data-driven subgrid-scale model in coarsened fluid descriptions is proposed. The method enables the inclusion of high-fidelity data into the coarsened flow model, thereby enabling accurate simulations also with the coarser representation. The small-scale model is introduced at the level of the Fourier coefficients of the coarsened numerical solution. It is designed to reproduce the kinetic energy spectra observed in high-fidelity data of the same system. The approach is based on a control feedback term reminiscent of continuous data assimilation implemented using nudging (Newtonian relaxation). The method relies solely on the availability of high-fidelity data from a statistically steady state. No assumptions are made regarding the adopted discretization method or the selected coarser resolution. The performance of the method is assessed for the two-dimensional Euler equations on the sphere for coarsening factors of 8 and 16 times. Applying the method at these significantly coarser resolutions yields good results for the mean and variance of the Fourier coefficients and leads to improvements in the empirical probability density functions of the attained vorticity values. Stable and accurate large-scale dynamics can be simulated over long integration times and are illustrated by capturing long-time vortex trajectories.

Minimal Coarse-Grained Model for Immunoglobulin G: Diffusion and Binding under Crowding.

Immunoglobulin G (IgG) is the most common type of antibody found in blood and extracellular fluids and plays an essential role in our immune response. However, studies of the dynamics and reaction kinetics of IgG-antigen binding under physiological crowding conditions are scarce. Herein, we develop a coarse-grained model of IgG consisting of only six beads that we find minimal for a coarse representation of IgG's shape and a decent reproduction of its flexibility and diffusion properties measured experimentally. Using this model in Brownian dynamics simulations, we find that macromolecular crowding affects only slightly the IgG's flexibility, as described by the distribution of angles between the IgG's arms and stem. Our simulations indicate that, contrary to expectations, crowders slow down the translational diffusion of an IgG less strongly than they do for a smaller Ficoll 70, which we relate to the IgG's conformational size changes induced by crowding. We also find that crowders affect the binding kinetics by decreasing the rate of the first binding step and enhancing the second binding step.

Num2vec: Pre-Training Numeric Representations for Time Series Forecasting in the Sensing System

Time series forecasting in the sensing system aims to predict future values based on historical records that sensors have collected. Previous works, however, usually focus on improving model structure or algorithm for better performance but the perspective of learning proper numeric representations is overlooked. The inappropriate and coarse numeric representations are not expressive enough to capture the intrinsic characteristics of numbers, which will obviously degrade the prediction performance. In this article, we propose Num2vec, an algorithmic framework to learn numeric representations. Specifically, Num2vec lists three main logic characteristics of numbers: arithmetic, direction, and periodicity. By representing numbers into a transition space, Num2vec can translates numbers agilely to different Internet of Things tasks through selecting the corresponding characteristics. According to such a design, Num2vec enjoys flexible numeric representations to fit different Internet of Things time series tasks. Extensive experiments on four real-world datasets show that the approach achieves the best performance when compared with state-of-the-art baselines.

Evaluating the influence of anatomical accuracy and electrode positions on EEG forward solutions

Generating realistic volume conductor models for forward calculations in electroencephalography (EEG) is not trivial and several factors contribute to the accuracy of such models, two of which are its anatomical accuracy and the accuracy with which electrode positions are known. Here, we investigate effects of anatomical accuracy by comparing forward solutions from SimNIBS, a tool which allows state-of-the-art anatomical modeling, with well-established pipelines in MNE-Python and FieldTrip. We also compare different ways of specifying electrode locations when digitized positions are not available such as transformation of measured positions from standard space and transformation of a manufacturer layout.Substantial effects of anatomical accuracy were seen throughout the entire brain both in terms of field topography and magnitude with SimNIBS generally being more accurate than the pipelines in MNE-Python and FieldTrip. Topographic and magnitude effects were particularly pronounced for MNE-Python which uses a three-layer boundary element method (BEM) model. We attribute these mainly to the coarse representation of the anatomy used in this model, in particular differences in skull and cerebrospinal fluid (CSF). Effects of electrode specification method were evident in occipital and posterior areas when using a transformed manufacturer layout whereas transforming measured positions from standard space generally resulted in smaller errors.We suggest modeling the anatomy of the volume conductor as accurately possible and we hope to facilitate this by making it easy to export simulations from SimNIBS to MNE-Python and FieldTrip for further analysis. Likewise, if digitized electrode positions are not available, a set of measured positions on a standard head template may be preferable to those specified by the manufacturer.

Coupled mesoscale–microscale modeling of air quality in a polluted city using WRF-LES-Chem

Abstract. To perform realistic high-resolution air quality modeling in a polluted urban area, the Weather Research and Forecasting (WRF) model is used with an embedded large-eddy simulation (LES) module and online chemistry. As an illustration, a numerical experiment is conducted in the megacity of Hong Kong, which is characterized by multi-type inhomogeneous pollution sources and complex topography. The results from the multi-resolution simulations at mesoscale and LES scales are evaluated by comparing them with ozone sounding profiles and surface observations. The comparisons show that both mesoscale and LES simulations reproduce the mean concentrations of the chemical species and their diurnal variations at the background stations well. However, the mesoscale simulations largely underestimate the NOx concentrations and overestimate O3 at the roadside stations due to the coarse representation of the traffic emissions. The LES simulations improve the agreement with the measurements near the road traffic, and the LES with the highest spatial resolution (33.3 m) provides the best results. The large-eddy simulations show more detailed structures in the spatial distributions of chemical species than the mesoscale simulations, highlighting the capability of LES to resolve high-resolution photochemical transformations in urban areas. Compared to the mesoscale model results, the LES simulations show similar evolutions in the profiles of the chemical species as a function of the boundary layer development over a diurnal cycle.

On the genes, genealogies, and geographies of Quebec.

Population genetic models only provide coarse representations of real-world ancestry. We used a pedigree compiled from 4 million parish records and genotype data from 2276 French and 20,451 French Canadian individuals to finely model and trace French Canadian ancestry through space and time. The loss of ancestral French population structure and the appearance of spatial and regional structure highlights a wide range of population expansion models. Geographic features shaped migrations, and we find enrichments for migration, genetic, and genealogical relatedness patterns within river networks across regions of Quebec. Finally, we provide a freely accessible simulated whole-genome sequence dataset with spatiotemporal metadata for 1,426,749 individuals reflecting intricate French Canadian population structure. Such realistic population-scale simulations provide opportunities to investigate population genetics at an unprecedented resolution.

Backward masking reveals coarse-to-fine dynamics in human V1

Natural images exhibit luminance variations aligned across a broad spectrum of spatial frequencies (SFs). It has been proposed that, at early stages of processing, the coarse signals carried by the low SF (LSF) of the visual input are sent rapidly from primary visual cortex (V1) to ventral, dorsal and frontal regions to form a coarse representation of the input, which is later sent back to V1 to guide the processing of fine-grained high SFs (i.e., HSF). We used functional resonance imaging (fMRI) to investigate the role of human V1 in the coarse-to-fine integration of visual input. We disrupted the processing of the coarse and fine content of full-spectrum human face stimuli via backward masking of selective SF ranges (LSFs: <1.75cpd and HSFs: >1.75cpd) at specific times (50, 83, 100 or 150 ms). In line with coarse-to-fine proposals, we found that (1) the selective masking of stimulus LSF disrupted V1 activity in the earliest time window, and progressively decreased in influence, while (2) an opposite trend was observed for the masking of stimulus’ HSF. This pattern of activity was found in V1, as well as in ventral (i.e. the Fusiform Face area, FFA), dorsal and orbitofrontal regions. We additionally presented subjects with contrast negated stimuli. While contrast negation significantly reduced response amplitudes in the FFA, as well as coupling between FFA and V1, coarse-to-fine dynamics were not affected by this manipulation. The fact that V1 response dynamics to strictly identical stimulus sets differed depending on the masked scale adds to growing evidence that V1 role goes beyond the early and quasi-passive transmission of visual information to the rest of the brain. It instead indicates that V1 may yield a ‘spatially registered common forum’ or ‘blackboard’ that integrates top-down inferences with incoming visual signals through its recurrent interaction with high-level regions located in the inferotemporal, dorsal and frontal regions.

Damage preserving transformation for materials with microstructure

The failure of heterogeneous materials with microstructures is a complex process of damage nucleation, growth and localisation. This process spans multiple length scales and is challenging to simulate numerically due to its high computational cost. One option is to use domain decomposed multi-scale methods with dynamical refinement. If needed, these methods refine coarse regions into a fine-scale representation to explicitly model the damage in the microstructure. However, damage evolution is commonly restricted to fine-scale regions only. Thus, they are unable to capture the full complexity and breath of the degradation process in the material. In this contribution, a generic procedure that allows to account for damage in all representations is proposed. The approach combines a specially designed orthotropic damage law, with a scheme to generate pre-damaged fine-scale microstructures. Results indicate that the damage approximation for the coarse representation works well. Furthermore, the generated fine-scale damage patterns are overall consistent with explicitly simulated damage patterns. Minor discrepancies occur in the generation but subsequently vanish when explicit damage evolution continuous; for instance under increased load. The presented approach provides a methodological basis for adaptive multi-scale simulation schemes with consistent damage evolution.

A Hybrid Embedded Discrete Fracture Model and Dual-Porosity, Dual-Permeability Workflow for Hierarchical Treatment of Fractures in Practical Field Studies

Summary Natural fracture systems comprise numerous small features and relatively few large ones. At field scale, it is impractical to treat all fractures explicitly. We represent the largest fractures using an embedded discrete fracture model (EDFM) and account for smaller ones using a dual-porosity, dual-permeability (DPDK) idealized representation of the fracture network. The hybrid EDFM + DPDK approach uses consistent discretization schemes and efficiently simulates realistic field cases. Further speedup can be obtained using aggregation-based upscaling. Capabilities to visualize and post-process simulation results facilitate understanding for effective management of fractured reservoirs. The proposed approach embeds large discrete fractures as EDFM within a DPDK grid (which contains both matrix and idealized fracture continua for smaller fractures) and captures all connections among the triple media. In contrast with existing EDFM formulations, we account for discrete fracture spacing within each matrix cell via a new matrix-fracture transfer term and use consistent assumptions for classical EDFM and DPDK calculations. In addition, the workflow enables coarse EDFM representations using flow-based cell-aggregation upscaling for computational efficiency. Using a synthetic case, we show that the proposed EDFM + DPDK approach provides a close match of simulation results from a reference model that represents all fractures explicitly, while providing runtime speedup. It is also more accurate than previous standard EDFM and DPDK models. We demonstrate that the matrix-fracture transfer function agrees with flow-based upscaling of high-resolution fracture models. Next, the automated workflow is applied to a waterflooding study for a giant carbonate reservoir, with an ensemble of stochastic fracture realizations. The overall workflow provides the computational efficiency needed for performance forecasts in practical field studies, and the 3D visualization allows for the derivation of insights into recovery mechanisms. Finally, we apply a finite-volume tracer-based flux post-processing scheme on simulation results to analyze production allocation and sweep for understanding expected waterflood performance.

Analysis of LBLOCA of APR1400 with 3D RPV model using TRACE

It is very difficult to capture the multi-dimensional phenomena such as asymmetric flow and temperature distributions with the one-dimensional (1D) model, obviously, due to its inherent limitation. In order to overcome such a limitation of the 1D representation, many state-of-the-art system codes have equipped a three-dimensional (3D) component for multi-dimensional analysis capability. In this study, a standard multi-dimensional analysis model of APR1400 (Advanced Power Reactor 1400) has been developed using TRACE (TRAC/RELAP Advanced Computational Engine). The entire reactor pressure vessel (RPV) of APR1400 has been modeled using a single 3D component. The fuels in the reactor core have been described with detailed and coarse representations, respectively, to figure out the impact of the fuel description. Using both 3D RPV models, a comparative analysis has been performed postulating a double-ended guillotine break at a cold leg. Based on the results of comparative analysis, it is revealed that both models show no significant difference in general plant behavior and the model with coarse fuel model could be used for faster transient analysis without reactor kinetics coupling. The analysis indicates that the asymmetric temperature and flow distributions are captured during the transient, and such nonuniform distributions contribute to asymmetric quenching behaviors during blowdown and reflood phases. Such asymmetries are directly connected to the figure of merits in the LBLOCA analysis. Therefore, it is recommended to employ a multi-dimensional RPV model with a detailed fuel description for a realistic safety analysis with the consideration of the spatial configuration of the reactor core.