EMMLi: A maximum likelihood approach to the analysis of modularity.

Quantile hydrologic model selection and structure deficiency assessment is applied in three case studies. The performance of quantile model selection problem is rigorously evaluated using a model structure on the French Broad river basin data set. The case study shows that quantile model selection encompasses model selection strategies based on summary statistics and that it is equivalent to maximum likelihood estimation under certain likelihood functions. It also shows that quantile model predictions are fairly robust. The second case study is of a parsimonious hydrological model for dry land areas in Western India. The case study shows that an intuitive improvement in the model structure leads to reductions in asymmetric loss function values for all considered quantiles. The asymmetric loss function is a quantile specific metric that is minimized to obtain a quantile specific prediction model. The case study provides evidence that a quantile-wise reduction in the asymmetric loss function is a robust indicator of model structure improvement. Finally a case study of modeling daily streamflow for the Guadalupe River basin is presented. A model structure that is least deficient for the study area is identified from nine different model structures based on quantile structural deficiency assessment. The nine model structures differ in interception, routing, overland flow and base flow conceptualizations. The three case studies suggest that quantile model selection and deficiency assessment provides a robust mechanism to compare deficiencies of different model structures and helps to identify better model structures. In addition to its novelty, quantile hydrologic model selection is a frequentist approach that seeks to complement existing Bayesian approaches to hydrological model uncertainty.

This paper proposes a new methodology for constructing groundwater models. The proposed methodology, which determines simultaneously both model structure and model parameters, is based on the following ideas: (1) When solving the inverse problem, different model structures always produce different model parameters; (2) since the number of possible model structures of an aquifer is infinite, the number of possible representative parameters is also infinite; (3) to obtain a set of appropriate representative model parameters, we must have an appropriate model structure; and (4) an appropriate model structure should be determined not only by observation data and prior information but also by the accuracy requirements of model applications. In this proposed methodology we start with a homogeneous model structure and, step by step, gradually increase the complexity of the model structure. At each level of complexity we calculate not only the fitting residual of parameter identification but also the error of model structure to determine if a more complex model structure is needed. The model structure error of using one model structure to replace another model structure is defined by a maximum‐minimum (max‐min) problem that is based on the distance between the two models and is measured in parameter, observation, and prediction (or decision) spaces. This proposed methodology is used to solve a hypothetical remediation design problem in which the true hydraulic conductivity is a random field with a certain trend. We have found that for the example problem, virtually identical pumping policy is obtained when a five‐zone model with an optimized zonation pattern is used to represent the nonstationary random field. We have also found that observation errors have minimum impact on management solution in comparison with structure errors. To calculate the model structure error for this example, the inverse solution is coupled with a management problem. We have also developed an effective iteration method to handle nonlinear water quality constraints.

<p>Recent investigations have shown it is possible to simultaneously calibrate model structures and model parameters to identify appropriate models for a given task (Spieler et al., 2020). However, this is computationally challenging, as different model structures may use a different number of parameters. While some parameters may be shared between model structures, others might be relevant for only a few structures, which theoretically requires the calibration of conditionally active parameters. Additionally, shared model parameters might cause different effects in different model structures, causing their optimal values to differ across structures. In this study, we tested how two current “of the shelf” mixed-integer optimization algorithms perform when having to handle these peculiarities during the automatic model structure identification (AMSI) process recently introduced by Spieler et al. (2020).</p><p>To validate the current performance of the AMSI approach, we conduct a benchmark experiment with a model space consisting of 6912 different model structures.  First, all model structures are independently calibrated and validated for three hydro-climatically differing catchments using the CMA-ES algorithm and KGE as the objective function. This is referred to as standard calibration procedure. We identify the best performing model structure(s) based on validation performance and analyze the range of performance as well as the number of structures performing in a similar range. Secondly, we run AMSI on all three catchments to automatically identify the most feasible model structure based on the KGE performance. Two different mixed-integer optimization algorithms are used – namely DDS and CMA-ES. Afterwards, we compare the results to the best performing models of the standard calibration of all 6912 model structures.</p><p>Within this experimental setup, we analyze if the best performing model structure(s) AMSI identifies are identical to the best performing structures of the standard calibration and if there are differences in performance when using different optimization algorithms for AMSI. We also validate if AMSI can identify the best performing model structures for a catchment at a fraction of the computational cost than the standard calibration procedure requires by using “off the shelf” mixed-integer optimization algorithms.</p><p> </p><p> </p><p> </p><p>Spieler, D., Mai, J., Craig, J. R., Tolson, B. A., & Schütze, N. (2020). Automatic Model Structure Identification for Conceptual Hydrologic Models. Water Resources Research, 56(9). https://doi.org/10.1029/2019WR027009</p>

Choosing (an) adequate model structure(s) for a given purpose, catchment, and data situation is a critical task in the modeling chain. However, despite model intercomparison studies, hypothesis testing approaches with modular modeling frameworks, and continuous efforts in model development and improvement, there are still no clear guidelines for identifying a preferred model structure. By introducing a framework for Automatic Model Structure Identification (AMSI), we support the process of identifying (a) suitable model structure(s) for a given task. The proposed AMSI framework employs a combination of the modular hydrological model RAVEN and the heuristic global optimization algorithm dynamically dimensioned search (DDS). It is the first demonstration of a mixed‐integer optimization algorithm applied to simultaneously optimize model structure choices (integer decision variables) and parameter values (continuous decision variables) in hydrological modeling. The AMSI framework is thus able to sift through a vast number of model structure and parameter choices for identifying the most adequate model structure(s) for representing the rainfall‐runoff behavior of a catchment. We demonstrate the feasibility of the approach by reidentifying given model structures that produced a specific hydrograph and show the limits of the current setup via a real‐world application of AMSI on 12 MOPEX catchments. Results show that the AMSI framework is capable of inferring feasible model structure(s) reproducing the rainfall‐runoff behavior of a given catchment. However, it is a complex optimization problem to identify model structure and parameters simultaneously. The variance in the identified structures is high due to near equivalent diagnostic measures for multiple model structures, reflecting substantial model equifinality. Future work with AMSI should consider the use of hydrologic signatures, case studies with multiple types of observation data, and the use of mixed‐integer multiobjective optimization algorithms.

<p>Recent studies have introduced methods to simultaneously calibrate model structure choices and parameter values to identify an appropriate (conceptual) model structure for a given catchment. This can be done through mixed-integer optimization to identify the graph structure that links dominant flow processes (Spieler et al., 2020) or, likewise, by continuous optimization of weights when blending multiple flux equations to describe flow processes within a model (Chlumsky et al., 2021). Here, we use the combination of the mixed-integer optimization algorithm DDS and the modular modelling framework RAVEN and refer to it as Automatic Model Structure Identification (AMSI) framework.</p><p>This study validates the AMSI framework by comparing the performance of the identified AMSI model structures to two different benchmark ensembles. The first ensemble consists of the best model structures from the brute force calibration of all possible structures included in the AMSI model space (7488+). The second ensemble consists of 35+ MARRMoT structures representing a structurally more divers set of models than currently implemented in the AMSI framework. These structures stem from the MARRMoT Toolbox introduced by Knoben et al. (2019) providing established conceptual model structures based on hydrologic literature.</p><p>We analyze if the model structure(s) AMSI identifies are identical to the best performing structures of the brute force calibration and comparable in their performance to the MARRMoT ensemble. We can conclude that model structures identified with the AMSI framework can compete with the structurally more divers MARRMoT ensemble. In fact, we were surprised to see how well we do with a simple two storage structure over the 12 tested MOPEX catchments (Duan et al.,2006). We aim to discuss several emerging questions, such as the selection of a robust model structure, Equifinality in model structures, and the role of structural complexity.</p><p> </p><p>Spieler et al. (2020). https://doi.org/10.1029/2019WR027009</p><p>Chlumsky et al. (2021). https://doi.org/10.1029/2020WR029229</p><p>Knoben et al. (2019). https://doi.org/10.5194/gmd-12-2463-2019</p><p>Duan et al. (2006). https://doi.org/10.1016/j.jhydrol.2005.07.031</p>

An evaluation of the impact of model structure on hydrological modelling uncertainty for streamflow simulation

The growth of social networking platforms such as Facebook and Twitter has bridged communication channels between people to share their thoughts and sentiments. However, along with the rapid growth and rise of the Internet, the idea of anonymity has also been introduced wherein user identities are easily falsified and hidden. Hence, presenting difficulty for businesses to give accurate advertisements to specific account demographics. As such, this study searched for the best model to identify gender and age group of Filipino social media accounts through analyzing post contents. Two model structures for the classifier namely, the stacked/combined structure and the parallel structure were experimented on. Different types of features including those based on socio-linguistics, grammar, characters and words were considered. The results show that different model structures, features, feature reduction and classification algorithms apply to age classification and gender classification. For Facebook and Twitter, the best model for classifying age was Support Vector Classifier (SVC) with least absolute shrinkage and selection operator (Lasso) on a parallel model structure for Facebook, while a combined model structure is best for Twitter. For gender classification, the best model for Facebook used Ridge Classifier (RC), while the best model for Twitter used SVC, both utilizing Lasso on a parallel model structure. The features that were dominant in age classification for both Facebook and Twitter were word-based, socio-linguistic features and post time, while socio-linguistic features, specifically netspeak, were important in gender classification for both platforms. Based on the differences of the features affecting the performance of the models, Facebook and Twitter data must be analyzed separately as the posts found in these two platforms differ significantly.

To explore the significance of alternative model structures and their inadequacies, hydrological modeling frameworks that allow quick implementation and comparison of alternative structures were already developed, mostly in a lumped mode. These systems allow testing the suitability of different model components and combining them in a modular fashion. Components can be modified or added if none of the available components fulfils the problem-specific requirements. It is, however, important to highlight that there is no general superior model structure for all spatial resolutions used. So, combining this flexible handling of structural components with varying the spatial resolution is necessary to adapt the model building process to specific conditions of the system, the available data and the objectives of the study. The next important step is to define effective strategies to diagnose and compare competitive model structures. Only then one can propose model structure improvements. There are several approaches described in the literature that help model diagnosis, like sensitivity analysis, parameter optimisation and uncertainty analysis, but these are mostly used to evaluate one specific structure or compare only a limited number of different structures and are typically not used in conjunction, but rather individually. By changing either specific processes or spatial resolution, while fixing the remainder of the model structure, rigorous testing of the model structure is possible, by addressing the effect of individual model components or spatial resolution. We present a tool to diagnose alternative model structures and address the effect of individual model components. The tool allows improving the evaluation and selection process of appropriate model structures out of the possible combinations coming from these flexible model structures to ensure the model represents the dominant processes of the system with the required rigour. The presented strategy uses both uncertainty and sensitivity analysis in a Monte-Carlo based framework. Regional sensitivity analysis allows identifying and comparing critical parameters among the different structures for different objective functions. Uncertainty analysis quantifies output uncertainty and parameter identifiability for different likelihood functions among the different structures. Comparing the posterior distribution of the parameters with the initial sampled distribution defines how these are conditioned by the model evaluation process. Since working with flexible structures, analysis can be done on both common and non-common components and associated parameters of the different model structures in a lumped or distributed mode. Structural components can be changed one at a time or a predefined set of model structures can be compared, using the combination of the above mentioned techniques. Selection criteria are assessed and linked to specific objectives (looking to specific flow regimes, specific objective functions or adapted metrics like flow duration curves). Moreover, it expresses the significant effect of the selected objective function(s) and the importance of using multiple evaluation criteria supporting the research question instead of only trying to reproduce the observed hydrograph.

Although the use of possible worlds in semantics has been very fruitful and is now widely accepted, there is a puzzle about the standard definition of validity in possible-worlds semantics that has received little notice and virtually no comment. A sentence of an intensional language is typically said to be valid just in case it is true at every world under every model on every model structure of the language. Each model structure contains a set of possible worlds, and models are defined relative to model structures, assigning truth-values to sentences at each world countenanced by the model structure. The puzzle is why more than one model structure is used in the definition of validity. There is presumably just one class of all possible worlds and just one model structure defined on this class that does correctly the things that model structures are supposed to do. (These include, but need not be limited to, specifying the set of individuals in each world as well as various accessibility relations between worlds.) Why not define validity simply as truth at every world under every model on this one model structure? What is the point of bringing in more model structures than just this one? We investigate these questions in some detail and conclude that for many intensional languages the puzzle points to a genuine difficulty: the standard definition of validity is insufficiently motivated. We begin (Section 1) by showing that a plausible and natural account of validity for intensional languages can be based on a single model structure, and that validity so defined is analogous in important respects to the standard account of validity for extensional languages. We call this notion of validity validity!, and in Section 2 we contrast it with the standard notion, which we call validity2. Several attempts are made to discover a rationale for the almost universal acceptance of validity2, but in most of these attempts we come up empty-handed. So in Section 3 we investigate validity! for some intensional languages. Our investigation includes providing axiomatizations for several propositional and predicate logics, most of which are provably complete. The completeness proofs are given in the Appendix, which also contains a sketch of a compactness proof for one of the predicate logics.

The advent of hydrological modeling frameworks that support multiple model structures using the same software enables both model structure and model parameters to be calibrated and assessed. To date, the identification of optimal model structure has typically been performed manually. Here, a continuous (rather than discrete) treatment of model structure is used, which enables simultaneous automatic calibration of model structure and parameters using a conventional real‐valued decision variable optimization algorithm (the dynamically dimensioned search algorithm, DDS). The method, referred to herein as blended model structure calibration (BMSC), relies upon the calculation of each hydrologic flux (e.g., for infiltration) as a weighted average of fluxes generated from multiple process algorithm options. This method is applied to 12 lumped MOPEX catchment models and compared to the calibration of 108 fixed model structures, representing all possible permutations of fixed model structures with the given process options in this study. The BMSC method consistently identified near‐optimal model structure (as evaluated using average model rank performance) at significantly lower computational cost than calibrating the collective of fixed structure models. The BMSC method also provides a useful tool in identifying dominant processes and model structures in catchments.

Comparison of two types of population pharmacokinetic model structures of paclitaxel

We will generalize the projective model structure in the category of unbounded complexes of modules over a commutative ring to the category of unbounded complexes of quasi-coherent sheaves over the projective line. Concretely we will define a locally projective model structure in the category of complexes of quasi-coherent sheaves on the projective line. In this model structure the cofibrant objects are the dg-locally projective complexes. We also describe the fibrations of this model structure and show that the model structure is monoidal. We point out that this model structure is necessarily different from other known model structures such as the injective model structure and the locally free model structure.

In a paper from 2002, Hovey introduced the Gorenstein projective and Gorenstein injective model structures on R-Mod, the category of R-modules, where R is any Gorenstein ring. These two model structures are Quillen equivalent and in fact there is a third equivalent structure we introduce: the Gorenstein flat model structure. The homotopy category with respect to each of these is called the stable module category of R. If such a ring R has finite global dimension, the graded ring R[x]/(x2) is Gorenstein and the three associated Gorenstein model structures on R[x]/(x2)-Mod, the category of graded R[x]/(x2)-modules, are nothing more than the usual projective, injective and flat model structures on Ch(R), the category of chain complexes of R-modules. Although these correspondences only recover these model structures on Ch(R) when R has finite global dimension, we can set R = ℤ and use general techniques from model category theory to lift the projective model structure from Ch(ℤ) to Ch(R) for an arbitrary ring R. This shows that homological algebra is a special case of Gorenstein homological algebra. Moreover, this method of constructing and lifting model structures carries through when ℤ[x]/(x2) is replaced by many other graded Gorenstein rings (or Hopf algebras, which lead to monoidal model structures). This gives us a natural way to generalize both chain complexes over a ring R and the derived category of R and we give some examples of such generalizations.

Abstract. The use of flexible hydrological model structures for hypothesis testing requires an objective and diagnostic method to identify whether a rainfall-runoff model structure is suitable for a certain catchment. To determine if a model structure is realistic, i.e. if it captures the relevant runoff processes, both performance and consistency are important. We define performance as the ability of a model structure to mimic a specific part of the hydrological behaviour in a specific catchment. This can be assessed based on evaluation criteria, such as the goodness of fit of specific hydrological signatures obtained from hydrological data. Consistency is defined as the ability of a model structure to adequately reproduce several hydrological signatures simultaneously while using the same set of parameter values. In this paper we describe and demonstrate a new evaluation Framework for Assessing the Realism of Model structures (FARM). The evaluation framework tests for both performance and consistency using a principal component analysis on a range of evaluation criteria, all emphasizing different hydrological behaviour. The utility of this evaluation framework is demonstrated in a case study of two small headwater catchments (Maimai, New Zealand, and Wollefsbach, Luxembourg). Eight different hydrological signatures and eleven model structures have been used for this study. The results suggest that some model structures may reveal the same degree of performance for selected evaluation criteria while showing differences in consistency. The results also show that some model structures have a higher performance and consistency than others. The principal component analysis in combination with several hydrological signatures is shown to be useful to visualise the performance and consistency of a model structure for the study catchments. With this framework performance and consistency are evaluated to identify which model structure suits a catchment better compared to other model structures. Until now the framework has only been based on a qualitative analysis and not yet on a quantitative analysis.

This paper outlines a method of choosing a model structure which can describe the dynamics of a manipulator. The model structure is based on a "Black Box" approach, therefore the model does not attempt to determine physical parameters such as moments of inertia or link masses. The model structure is used to estimate parameters which best fit the selected model structure to the observed input/output data sequence. The manipulator dynamics are written as a fourier series expansion. The fourier coefficients are identified by a least squares algorithm. This paper will present a parameter selection criteria which will determine the model structure one should choose. The tracking accuracy of controllers based on different model structures will be compared. The model structures are chosen based on a parameter selection criteria. It is demonstrated that simple model structures can be used to model the nonlinear dynamics of a robotic manipulator.