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

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