Continuous and Discrete Model

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    Dr. Pratiksha Saxena

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    Numerical simulation approach

    Level of Aggregation Policies versus Decisions

    Aggregate versus Individuals

    Aggregate Dynamics versus Problem solving

    Difficulty of the formulation

    Nature of the system/problem

    Nature of the questionNature of preferred lenses

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    Advances in system development ultimately rely on well-constructed predictive models

    Applications: traditional fields such as electrical and mechanical engineering

    newer domains such as information and bio-technologies

    Using appropriate simulation software, we can derivesolutions to difficult problems using such models

    Success often depends on having a variety of modelingapproaches available to formulate the right model for theparticular issue at hand

    Therefore, a broad familiarity with different types ofmodels is desirable

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    1. Static or dynamic models

    2. Stochastic, deterministic or chaotic models

    3. Discrete or continuous change/models

    4. Aggregates or Individuals

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    Dynamic: State variables change over time

    (System Dynamics, Discrete Event, Agent-

    Based, Econometrics?) Static: Snapshot at a single point in time

    (Monte Carlo simulation, optimization

    models, etc.)

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    Deterministic modelis one whose behavior

    is entire predictable. The system is

    perfectly understood, then it is possible to

    predict precisely what will happen.

    Stochastic modelis one whose behavior

    cannot be entirely predicted.

    Chaotic modelis a deterministic model

    with a behavior that cannot be entirely

    predicted

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    Discrete model: the state variables change

    only at a countable number of points in time.

    These points in time are the ones at which

    the event occurs/change in state.Continuous: the state variables change in a

    continuous way, and not abruptly from one

    state to another (infinite number of states).

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    Continuous system models were the firstwidely employed models and aretraditionally described by ordinary andpartial differential equations.

    Such models originated in such areas asphysics and chemistry, electrical circuits,mechanics, and aeronautics.

    They have been extended to many new areassuch as bio-informatics, homeland security,and social systems.

    Continuous differential equation modelsremain an essential component in multi-formalism compositions.

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    A host of formalisms have emerged in the lastfew decades that greatly increase our ability toexpress features of the real world and employthem in engineering systems.

    Such formalisms include Neural Networks, FuzzyLogic Systems, Cellular Automata, Evolutionaryand Genetic Algorithms, among others.

    Hybrid models combine two or more formalisms,e.g., fuzzy logic control of continuousmanufacturing process.

    Most often, applications will require such hybridsto address the problem domain of interest.

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    Principal

    Interest

    AverageInterest Rate

    Noise

    SimulatedPrincipal

    Sim Interest

    EstimatedInterest Rate

    Noise Seed

    ObservedInterest Rate

    Continuous and Stochastic

    Continuous and Deterministic

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    Discrete and stochastic

    SimulatedPrincipal 1 0

    Sim Interest 1 0

    AveragePrincipal 0

    Averagingtime 0

    ObservedInterest Rate 0

    SimulatedPrincipal 1

    Sim Interest 1

    AveragePrincipal

    Averagingtime

    Observed

    Interest Rate

    Discrete and Deterministic

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    Aggregate model: we look for a more distant

    position. Modeler is more distant. Policy

    model. This view tends to be more

    deterministic. Individual model: modeler is taking a closer

    look of the individual decisions. This view

    tends to be more stochastic.

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    2 approaches:

    Time-slicing: move forward in our models in equal

    time intervals.

    Next-event technique: the model is only examined

    and updated when it is known that a state (or

    behavior) changes. Time moves from event to event.

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    Only from a more distant perspective in which

    events and decisions are deliberately blurred

    into patterns of behavior and policy structure

    will the notion that behavior is a consequence

    of feedback structure arise and be perceived

    to yield powerful insights.

    (Richardson, 1991)

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    5. Integration of variables directly evaluated

    by analog computers while Dc uses numerical

    approximation to solve it.

    6. DC can be programmed to any degree ofaccuracy as they use floating point

    representation of nubers and can tolerate

    extremely wide range of variations.

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    1. understand geology of place

    2.physical appereance of reservoir and

    continuity of flow

    3. objective of studyCollect results in concrete terms-material

    balance study, water cut, reservoir pressure

    4. data is gathered-water spread property

    called permeability, map of reservoir nadmeasurement of porosity

    5.initial simulation run made to calculate

    oroginal water at the site- input

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    From the expected growth pattern and

    seasonal fluctuations, curve of the projected

    demand

    Input-river inflow+rainfallNext simulation run to match the historical

    data for pressure, water cut, porosity,

    permeability

    This run takes maximum time(not constant) Seepage and evaporation losses

    Output by simulation run