Metamodels and Nonpoint Pollution Policy in Agriculture

Informed debate on agricultural nonpoint pollution requires evaluation of regional water quality in relation to management practices. It is prohibitive, in terms of cost and time, to run the site-specific process models for regional policy analysis. Therefore, a simplified and robust technique--metamodeling--is suggested to evaluate regional water quality. Data from an experimentally designed simulation of complex surface water and groundwater process models, PRZM and STREAM, are used to develop statistically validated metamodels. The estimated metamodels were integrated with a regional agricultural economic decision making model to evaluate the surface water and groundwater loadings of 16 major corn and sorghum herbicides. Spatial probability distributions are derived for herbicide concentrations exceeding the toxicity-weighted benchmark from the EPA. We estimate that 1.2 percent of the regional soils will lead to groundwater detection of atrazine exceeding 0.12 ?/L, which compares well with the findings of the EPA\u27s groundwater monitoring survey. We find no-till practices to significantly reduce the surface water concentration of atrazine and other herbicides with less impact on groundwater contamination suggesting indirect gains to soil conservation policies. But we also note that an atrazine ban could lead to increased soil erosion, even with the conservation compliance provisions fully incorporated

Introduction to metamodeling for reducing computational burden of advanced analyses with health economic models : a structured overview of metamodeling methods in a 6-step application process

Metamodels can be used to reduce the computational burden associated with computationally demanding analyses of simulation models, though applications within health economics are still scarce. Besides a lack of awareness of their potential within health economics, the absence of guidance on the conceivably complex and time-consuming process of developing and validating metamodels may contribute to their limited uptake. To address these issues, this paper introduces metamodeling to the wider health economic audience and presents a process for applying metamodeling in this context, including suitable methods and directions for their selection and use. General (i.e., non-health economic specific) metamodeling literature, clinical prediction modeling literature, and a previously published literature review were exploited to consolidate a process and to identify candidate metamodeling methods. Methods were considered applicable to health economics if they are able to account for mixed (i.e., continuous and discrete) input parameters and continuous outcomes. Six steps were identified as relevant for applying metamodeling methods within health economics, i.e. 1) the identification of a suitable metamodeling technique, 2) simulation of datasets according to a design of experiments, 3) fitting of the metamodel, 4) assessment of metamodel performance, 5) conduct the required analysis using the metamodel, and 6) verification of the results. Different methods are discussed to support each step, including their characteristics, directions for use, key references, and relevant R and Python packages. To address challenges regarding metamodeling methods selection, a first guide was developed towards using metamodels to reduce the computational burden of analyses of health economic models. This guidance may increase applications of metamodeling in health economics, enabling increased use of state-of-the-art analyses, e.g. value of information analysis, with computationally burdensome simulation models

Solving optimisation problems in metal forming using FEM: A metamodel based optimisation algorithm

During the last decades, Finite Element (FEM) simulations of metal forming processes have\ud become important tools for designing feasible production processes. In more recent years,\ud several authors recognised the potential of coupling FEM simulations to mathematical opti-\ud misation algorithms to design optimal metal forming processes instead of only feasible ones.\ud This report describes the selection, development and implementation of an optimisa-\ud tion algorithm for solving optimisation problems for metal forming processes using time\ud consuming FEM simulations. A Sequential Approximate Optimisation algorithm is pro-\ud posed, which incorporates metamodelling techniques and sequential improvement strate-\ud gies for enhancing the e±ciency of the algorithm. The algorithm has been implemented in\ud MATLABr and can be used in combination with any Finite Element code for simulating\ud metal forming processes.\ud The good applicability of the proposed optimisation algorithm within the ¯eld of metal\ud forming has been demonstrated by applying it to optimise the internal pressure and ax-\ud ial feeding load paths for manufacturing a simple hydroformed product. Resulting was\ud a constantly distributed wall thickness throughout the ¯nal product. Subsequently, the\ud algorithm was compared to other optimisation algorithms for optimising metal forming\ud by applying it to two more complicated forging examples. In both cases, the geometry of\ud the preform was optimised. For one forging application, the algorithm managed to solve\ud a folding defect. For the other application both the folding susceptibility and the energy\ud consumption required for forging the part were reduced by 10% w.r.t. the forging process\ud proposed by the forging company. The algorithm proposed in this report yielded better\ud results than the optimisation algorithms it was compared to

A Methodology for Fitting and Validating Metamodels in Simulation

This expository paper discusses the relationships among metamodels, simulation models, and problem entities. A metamodel or response surface is an approximation of the input/output function implied by the underlying simulation model. There are several types of metamodel: linear regression, splines, neural networks, etc. This paper distinguishes between fitting and validating a metamodel. Metamodels may have different goals: (i) understanding, (ii) prediction, (iii) optimization, and (iv) verification and validation. For this metamodeling, a process with thirteen steps is proposed. Classic design of experiments (DOE) is summarized, including standard measures of fit such as the R-square coefficient and cross-validation measures. This DOE is extended to sequential or stagewise DOE. Several validation criteria, measures, and estimators are discussed. Metamodels in general are covered, along with a procedure for developing linear regression (including polynomial) metamodels.

A User's Guide to the Brave New World of Designing Simulation Experiments

Many simulation practitioners can get more from their analyses by using the statistical theory on design of experiments (DOE) developed specifically for exploring computer models.In this paper, we discuss a toolkit of designs for simulationists with limited DOE expertise who want to select a design and an appropriate analysis for their computational experiments.Furthermore, we provide a research agenda listing problems in the design of simulation experiments -as opposed to real world experiments- that require more investigation.We consider three types of practical problems: (1) developing a basic understanding of a particular simulation model or system; (2) finding robust decisions or policies; and (3) comparing the merits of various decisions or policies.Our discussion emphasizes aspects that are typical for simulation, such as sequential data collection.Because the same problem type may be addressed through different design types, we discuss quality attributes of designs.Furthermore, the selection of the design type depends on the metamodel (response surface) that the analysts tentatively assume; for example, more complicated metamodels require more simulation runs.For the validation of the metamodel estimated from a specific design, we present several procedures.