Dynamic Bayesian Networks as a Probabilistic Metamodel for Combat Simulations

Simulation modeling is used in many situations. Simulation meta-modeling is used to estimate a simulation model result by representing the space of simulation model responses. Metamodeling methods are particularly useful when the simulation model is not particularly suited to real-time or mean real-time use. Most metamodeling methods provide expected value responses while some situations need probabilistic responses. This research establishes the viability of Dynamic Bayesian Networks for simulation metamodeling, those situations needing probabilistic responses. A bootstrapping method is introduced to reduce simulation data requirement for a DBN, and experimental design is shown to benefit a DBN used to represent a multi-dimensional response space. An improved interpolation method is developed and shown beneficial to DBN metamodeling applications. These contributions are employed in a military modeling case study to fully demonstrate the viability of DBN metamodeling for Defense analysis application

Evolutionary model type selection for global surrogate modeling

Due to the scale and computational complexity of currently used simulation codes, global surrogate (metamodels) models have become indispensable tools for exploring and understanding the design space. Due to their compact formulation they are cheap to evaluate and thus readily facilitate visualization, design space exploration, rapid prototyping, and sensitivity analysis. They can also be used as accurate building blocks in design packages or larger simulation environments. Consequently, there is great interest in techniques that facilitate the construction of such approximation models while minimizing the computational cost and maximizing model accuracy. Many surrogate model types exist ( Support Vector Machines, Kriging, Neural Networks, etc.) but no type is optimal in all circumstances. Nor is there any hard theory available that can help make this choice. In this paper we present an automatic approach to the model type selection problem. We describe an adaptive global surrogate modeling environment with adaptive sampling, driven by speciated evolution. Different model types are evolved cooperatively using a Genetic Algorithm ( heterogeneous evolution) and compete to approximate the iteratively selected data. In this way the optimal model type and complexity for a given data set or simulation code can be dynamically determined. Its utility and performance is demonstrated on a number of problems where it outperforms traditional sequential execution of each model type

Emulating dynamic non-linear simulators using Gaussian processes

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models of the climate or the functioning of the human brain. The models we are interested in are highly non-linear and exhibit tipping points, bifurcations and chaotic behaviour. However, each simulation run could be too time-consuming to perform analyses that require many runs, including quantifying the variation in model output with respect to changes in the inputs. Therefore, Gaussian process emulators are used to approximate the output of the code. To do this, the flow map of the system under study is emulated over a short time period. Then, it is used in an iterative way to predict the whole time series. A number of ways are proposed to take into account the uncertainty of inputs to the emulators, after fixed initial conditions, and the correlation between them through the time series. The methodology is illustrated with two examples: the highly non-linear dynamical systems described by the Lorenz and Van der Pol equations. In both cases, the predictive performance is relatively high and the measure of uncertainty provided by the method reflects the extent of predictability in each system

Statistical metamodeling of dynamic network loading

Dynamic traffic assignment models rely on a network performance module known as dynamic network loading (DNL), which expresses flow propagation, flow conservation, and travel delay at a network level. The DNL defines the so-called network delay operator, which maps a set of path departure rates to a set of path travel times (or costs). It is widely known that the delay operator is not available in closed form, and has undesirable properties that severely complicate DTA analysis and computation, such as discontinuity, non-differentiability, non-monotonicity, and computational inefficiency. This paper proposes a fresh take on this important and difficult issue, by providing a class of surrogate DNL models based on a statistical learning method known as Kriging. We present a metamodeling framework that systematically approximates DNL models and is flexible in the sense of allowing the modeler to make trade-offs among model granularity, complexity, and accuracy. It is shown that such surrogate DNL models yield highly accurate approximations (with errors below 8%) and superior computational efficiency (9 to 455 times faster than conventional DNL procedures such as those based on the link transmission model). Moreover, these approximate DNL models admit closed-form and analytical delay operators, which are Lipschitz continuous and infinitely differentiable, with closed-form Jacobians. We provide in-depth discussions on the implications of these properties to DTA research and model applications

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

Automated Construction of Dynamic Bayesian Networks in Simulation Metamodeling

Tässä työssä esitellään uusi lähestymistapa dynaamisten Bayes-verkkojen (dynamic Bayesian networks, DBNs) automatisoituun konstruointiin simulaatiometamallinnuksessa. DBN-metamallien avulla tutkitaan diskreetillä tapahtumasimuloinnilla (discrete event simulation, DES) luotua simulointidataa. Lähestymistavan avulla kyetään konstruoimaan DBN-metamalleja helposti ja nopeasti tuntematta Bayes-verkkojen toimintaa lähemmin. Aiemmin konstruoitujen DBN-metamallien mahdollisia puutteita voidaan korjata vaivattomasti luomalla uusia paranneltuja metamalleja. Tämä menettely parantaa DBN-metamallien tarkkuutta ja käytettävyyttä. DES on stokastinen simulointimuoto, joka mahdollistaa mallin muuttujien arvojen aikakehityksen tarkastelun. Simulointimetamalleilla tutkitaan simulointimallien ominaisuuksia kuvaamalla niiden sisäänmenojen ja ulostulojen välistä yhteyttä. DBN-metamalleissa DBN kuvaa DES-mallin aikariippuvien muuttujien yhteisjakauman, minkä avulla voidaan tarkastella muuttujien reuna- ja ehdollisten todennäköisyysjakaumien aikakehitystä. Tämä mahdollistaa erilaiset mitä-jos -analyysit, joita ei voida toteuttaa pelkillä sisäänmeno-ulostulokuvauksilla. Tässä työssä esiteltävä lähestymistapa DBN-metamallien automatisoituun konstruointiin koostuu koesuunnittelusta, simulointidatan esikäsittelystä, muuttujakohtaisten ajanhetkien valinnasta DBN:ää varten, DBN:n luomisesta sekä metamallin validoinnista. Automatisoidun mallintamislähestymistavan lisäksi tässä työssä esitellään DBN:ien muuttujakohtaiset aikaskaalat, joiden avulla kyetään konstruoimaan tarkempia DBN:iä kasvattamatta niiden kokoa. Esitettyyn lähestymistapaan perustuen kehitetään DBN-metamallien konstruointityökalu. Työssä havainnollistetaan esitetyn lähestymistavan ja konstruointityökalun käyttökelpoisuutta kahdella esimerkkitapauksella, jotka liittyvät ilmataistelua ja ilmatukikohdan toimintaa kuvaaviin simulointimalleihin.This thesis introduces an automated approach for constructing dynamic Bayesian networks (DBNs) in simulation metamodeling. DBN metamodels permit studies dealing with simulation data produced by discrete event simulation (DES) models. The new approach allows easier and faster construction of such metamodels without requiring detailed knowledge of the methodology of Bayesian networks. Deficiencies in previously created DBN metamodels are thus readily corrected by creating new refined models. This increases the overall accuracy and usability of DBN metamodels. DES is an event based form of stochastic simulation that enables the study of the time evolution of the variables of the underlying system. Simulation metamodels are used to investigate the properties of simulation models by describing their behavior in the form of input-output mappings. In DBN metamodels, a DBN represents the joint probability distribution of the time-dependent variables of a DES model. The utilization of DBNs in metamodeling, unlike the use of input-output mappings, therefore enables investigations involving time-dependent variables. Unconditional and conditional time evolutions, i.e., the evolution over time of marginal or conditional probability distributions, can be studied. This allows for various forms of what-if analysis. The automated approach to the construction of DBN metamodels presented in this thesis includes design of experiment, preprocessing of the simulation data, selection of the variable specific time instants for the DBN, creation of the DBN, and validation of the DBN. In addition, this thesis introduces the concept of multiple time scales in DBNs which allows for more accurate DBNs without increasing their size. An implementation of the approach, a tool for constructing DBN metamodels, is also presented. Constructing DBN metamodels with the tool verifies the practicality of the automated approach. The use of the approach and the tool is illustrated by two example simulation studies dealing with air combat and the operation of an air base

Estimating performance indexes of a baggage handling system using metamodels

In this study, we develop some deterministic metamodels to quickly and precisely predict the future of a technically complex system. The underlying system is essentially a stochastic, discrete event simulation model of a big baggage handling system. The highly detailed simulation model of this is used for conducting some experiments and logging data which are then used for training artificial neural network metamodels. Demonstrated results show that the developed metamodels are well able to predict different performance measures related to the travel time of bags within this system. In contrast to the simulation models which are computationally expensive and expertise extensive to be developed, run, and maintained, the artificial neural network metamodels could serve as real time decision aiding tools which are considerably fast, precise, simple to use, and reliable.<br /

Automatic surrogate model type selection during the optimization of expensive black-box problems

The use of Surrogate Based Optimization (SBO) has become commonplace for optimizing expensive black-box simulation codes. A popular SBO method is the Efficient Global Optimization (EGO) approach. However, the performance of SBO methods critically depends on the quality of the guiding surrogate. In EGO the surrogate type is usually fixed to Kriging even though this may not be optimal for all problems. In this paper the authors propose to extend the well-known EGO method with an automatic surrogate model type selection framework that is able to dynamically select the best model type (including hybrid ensembles) depending on the data available so far. Hence, the expected improvement criterion will always be based on the best approximation available at each step of the optimization process. The approach is demonstrated on a structural optimization problem, i.e., reducing the stress on a truss-like structure. Results show that the proposed algorithm consequently finds better optimums than traditional kriging-based infill optimization

From multiscale modeling to metamodeling of geomechanics problems

In numerical simulations of geomechanics problems, a grand challenge consists of overcoming the difficulties in making accurate and robust predictions by revealing the true mechanisms in particle interactions, fluid flow inside pore spaces, and hydromechanical coupling effect between the solid and fluid constituents, from microscale to mesoscale, and to macroscale. While simulation tools incorporating subscale physics can provide detailed insights and accurate material properties to macroscale simulations via computational homogenizations, these numerical simulations are often too computational demanding to be directly used across multiple scales. Recent breakthroughs of Artificial Intelligence (AI) via machine learning have great potential to overcome these barriers, as evidenced by their great success in many applications such as image recognition, natural language processing, and strategy exploration in games. The AI can achieve super-human performance level in a large number of applications, and accomplish tasks that were thought to be not feasible due to the limitations of human and previous computer algorithms. Yet, machine learning approaches can also suffer from overfitting, lack of interpretability, and lack of reliability. Thus the application of machine learning into generation of accurate and reliable surrogate constitutive models for geomaterials with multiscale and multiphysics is not trivial. For this purpose, we propose to establish an integrated modeling process for automatic designing, training, validating, and falsifying of constitutive models, or "metamodeling". This dissertation focuses on our efforts in laying down step-by-step the necessary theoretical and technical foundations for the multiscale metamodeling framework. The first step is to develop multiscale hydromechanical homogenization frameworks for both bulk granular materials and granular interfaces, with their behaviors homogenized from subscale microstructural simulations. For efficient simulations of field-scale geomechanics problems across more than two scales, we develop a hybrid data-driven method designed to capture the multiscale hydro-mechanical coupling effect of porous media with pores of various different sizes. By using sub-scale simulations to generate database to train material models, an offline homogenization procedure is used to replace the up-scaling procedure to generate path-dependent cohesive laws for localized physical discontinuities at both grain and specimen scales. To enable AI in taking over the trial-and-error tasks in the constitutive modeling process, we introduce a novel “metamodeling” framework that employs both graph theory and deep reinforcement learning (DRL) to generate accurate, physics compatible and interpretable surrogate machine learning models. The process of writing constitutive models is simplified as a sequence of forming graph edges with the goal of maximizing the model score (a function of accuracy, robustness and forward prediction quality). By using neural networks to estimate policies and state values, the computer agent is able to efficiently self-improve the constitutive models generated through self-playing. To overcome the obstacle of limited information in geomechanics, we improve the efficiency in utilization of experimental data by a multi-agent cooperative metamodeling framework to provide guidance on database generation and constitutive modeling at the same time. The modeler agent in the framework focuses on evaluating all modeling options (from domain experts’ knowledge or machine learning) in a directed multigraph of elasto-plasticity theory, and finding the optimal path that links the source of the directed graph (e.g., strain history) to the target (e.g., stress). Meanwhile, the data agent focuses on collecting data from real or virtual experiments, interacts with the modeler agent sequentially and generates the database for model calibration to optimize the prediction accuracy. Finally, we design a non-cooperative meta-modeling framework that focuses on automatically developing strategies that simultaneously generate experimental data to calibrate model parameters and explore weakness of a known constitutive model until the strengths and weaknesses of the constitutive law on the application range can be identified through competition. These tasks are enabled by a zero-sum reward system of the metamodeling game and robust adversarial reinforcement learning techniques