Modeling

1
Modeling Simulation

• Topical Lecture
• CS 101
• Arif Zaman

2
Modeling

• Create a model
• Usually a simplified description
• Using a few rules
• Solve the model
• Using algebra, calculus, differential equations
• Using simulation
• Improve the model
• Adding more parameters, equations

3
Physics

• Physics was spectacularly successful.
• F m a G m1m2 /r 2explains sun-moon-planets-st
  ars-galaxies
• But not quite right, so we add
• Friction (static and dynamic)
• Rotation
• Collision
• Rigid and non-rigid bodies

4
Physics Envy

• Economics
• Psychology
• Sociology
• Biology
• Political Science
• Agriculture
• Chemistry
• and even Physics

• No simple equations
• No exact equations
• Probability needed
• Interactions of 1000s of individuals cant be
  accurately modeled by a simple composite number.

5
Computers to the Rescue

• Benefits
• Numerical solutions to complex differential
  equations that have no closed form solutions
• Possible to model millions of individuals

• Loss
• No longer able to understand the model, or to
  solve it (e.g. Two-body problem is an ellipse).
• Solution may take a long time to find.

6
Flock of Birds (Boids)

• Nothing random other than starting point
• According to rules.
• Add Response to threat
• Another example of flocking
• Herd behavior of animals
• Note that many things modeled here.

• Separation steer to avoid crowding local
  flockmates
• Alignment steer towards the average heading of
  local flockmates
• Cohesion steer to move toward the average
  position of local flockmates
• http//www.red3d.com/cwr/ boids/ Craig Reynolds

7
Water

• Hydrodynamics
• Computers use Finite Element or Finite Difference
  Methods to solve with voxels.
• Simplifications are needed to be able to do this
  in any reasonable amount of time. (4-7 mins per
  frame)
• Nick Foster Ronald Fedkiw http//www.cis.upenn.e
  du/fostern/

• Navier-Stokes (1800) used PDEs to solve.
• u(x,y,z,t) is velocity,v is viscosity, ? is
  density, p is the pressure vectorg is the
  gravity vector.

8
The Forest for the Trees

• For each tree there are curves
• Tree growth rate (as a function of light)
• Tree transparency
• Spread of seeds
• Death rate as a function of growth.
• Disasters or logging. http//www.sciencemag.org/fe
  ature/data/deutschman/index.htm

9
With no logging
Total tree density climbs quickly from the sparse
initial conditions, reaching a peak around year
200. Fast-growing species like black cherry,
white pine, and red oak reach the canopy first.
As the light reaching the forest floor declines,
these species seedlings fail to recruit into the
canopy, and the more shade-tolerant species
(mainly beech, hemlock, and, to a lesser extent,
yellow birch) increase in relative abundance. By
the end of the 1000-year simulation, beech
reaches almost 100 dominance in the forest.
10
With periodic logging
the same suite of species (white pine, red oak,
and black cherry) dominate the early growth. But
continued opening of the canopy leads to enhanced
performance of yellow birch. Yellow birch has the
longest dispersal and high growth in moderate
light, which allows it to expand quickly
throughout the forest. Beech and hemlock are
common and show little sign of being
displaced. The apparent paradox of higher density
in disturbed simulations
11
NASA and Muslims

• Rely on simulation of solar system to predict the
  times for prayer, the visibility and location of
  the moon.
• Solar system simulation (including several 100
  asteroids) can be done extremely accurately, in a
  reasonable amount of time on a home computer.

12
Small time-step problem

• Take small time steps
• Everything moves, sore-compute forces.
• This approach does not work well. Errors
  accumulate. Linear Algebra and Numerical Analysis
  come to the rescue.

13
Weather Prediction

• Far harder than anyone suspected.
• Chaotic (a butterfly in China affects a
  hurricane in Louisiana).
• NEC Earth Simulator (now 4 after three years as
  1) is 640 processors, each with 8 vector
  arithmetic processors. Each processor is 8Gflop,
  total 10Tb memory.
• NOAA feeds 2 million observations/day for weather
  prediction.
• Currently 1-3 day is so so, trying for 7 days.

14
Fire

• To understand why two firefighters died.
• To understand what to do in case of fire.
• For firefighters.
• For residents.

15
Simulations can help in

• Training and teaching
• Providing cheaper, less dangerous labs
• Policy planning
• Design and prototyping
• Design of Pseudo-experiments.
• Movie/Game making
• Prediction and approximation

• Flight simulator
• Space flight simulation
• Business Game
• Nuclear power plant emergency
• War Games
• Medical Simulation
• Car, aircraft, wing design
• Political planning

16
Simulation in the News

• Diet and Health
• Cell Biology
• Trauma Injuries of the Eye
• New Orleans Hurricane

17
Diet, Smoking and Heart Disease

• Researchers in Turkey constructed a computer
  model of the adult population of England and
  Wales, looking at the effect of reducing smoking,
  cholesterol, and blood pressure in those with and
  without heart disease. This showed that primary
  prevention has a four fold bigger impact on
  mortality than secondary prevention.

18
A Living Cell

• Researchers are taking on a project that will
  attempt to create a detailed computer model of a
  living cell that includes all of the cell's genes
  and proteins, their function and their
  relationships to one another.
• The researchers will use Saccharomyces
  cerevisiae, a single-celled yeast, which, they
  say, shares many genetic traits with humans,
  making it a useful model.
• The work is part of a 4.88 million grant from
  the National Science Foundation.
• Over the next five years, Keck Graduate Institute
  of Applied Life Sciences will lead a team of
  biochemists and computer scientists including a
  team from the University of Rochester Medical
  Center to build the computer model of gene and
  protein function within the cell, and then test
  predictions against real-world experiments.

19
Eye Injuries

• Stitzel and his colleagues have been working on
  the computer simulation model for several years
  and already have reported that the model tracks
  the actual results of a series of experiments in
  which foam particles, BBs and baseballs strike
  the human eye. The model predicts when the globe
  of the eye will rupture from high-speed blunt
  trauma.
• In an accompanying editorial, Paul F. Vinger,
  M.D., of Concord, Mass., said the Virginia
  Tech-Wake Forest center's project to create the
  computer simulation "is a formidable undertaking
  that is bound to change the course of eye trauma
  research."
• He said that when the model predictions were
  compared with actual results, there was
  "excellent correlation between the calculated and
  experimental results."

20
New Orleans Hurricane

• As the hurricane hit, John Pardue sat in his home
  in Baton Rouge, nervously tracking the storms
  progress on his computer for three hours until
  the power was cut. As director of the Louisiana
  Water Resources Research Institute and an expert
  in the detection of levee flaws, he and his team
  had produced a computer model showing the
  calamitous consequences of a major hurricane
  striking the New Orleans region.
• The model was widely applauded when first
  developed five years ago, yet the federal
  government effectively refused to act on the
  warnings. Critically, the major civil engineering
  works needed to build a new sea wall which would
  have greatly limited the hurricanes devastating
  effect, did not transpire.
• We knew that it was going to be catastrophic,
  Pardue says. It was not a surprise it was in
  the New York Times, National Geographic,
  Scientific American. This exact scenario water
  will be 20 feet high in parts of the city, people
  will die, all the things that have happened. Its
  eerie because weve been thinking about this for
  a number of years, and to see it unfold before
  your eyes is just unbelievable.

21
Assignment

• Write a simulator for your self.
• Send your sim to class, and you can sleep-in
  every morning!