New Mexico Computer Science For All Designing and Running Simulations Maureen Psaila-Dombrowski

Models vs. Simulations Model ▫The actual program ▫The abstraction of the real world ▫Captures the elements of the system and the behavior of the elements being modeled Simulation ▫Running the model to simulate the passage of time ▫Exploring the behavior of the modeled system over time. ▫In studying complex systems, sometime unexpected patterns emerge that weren’t explicitly programmed into the model.

Simulations on Your Computer Why?  Once the model is developed ▫Can run many trials ▫Can run many parameters  Can develop models for situations where experimentation is difficult ▫Too dangerous ▫Too expensive ▫Too time intensive

Deterministic vs. Stochastic Two types of simulation models: ▫Deterministic simulation models:  Provide single outputs for each set of inputs  No Randomness involved ▫Stochastic simulation models  Can produce somewhat different outputs for each set of inputs  Randomness IS involved  Agent-based models of Complex Adaptive Systems have Randomness -> they are stochastic  Look at the probability distribution of possible outcomes.

How to run a Simulation Simple parameter sweeping (one dimension) ▫Hold all other variables constant ▫Set min, max, and increment for one variable. ▫Sweep one variable (from min to max value) Repetition – Because the models are stochastic ▫Repetitions at each setting ▫Take the average? What output do you want?

Ant Foraging Model Food piles Ants wander around looking for food Ant finds a piece of food ▫Carries the food back to the nest ▫Drops a chemical as it moves – trail  Chemical evaporation  Chemical diffusion Other ants find the chemical trail, ▫Follow the chemical to food ▫Carries the food back to the nest ▫Reinforce chemical trail Repeated until there is no more food in that pile.

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Ant Foraging Experiment/Simulation Three Parameters ▫Number of ants (0-200) ▫Diffusion rate (0-99)  How quickly the chemical diffuses  How wide the trail is ▫Evaporation rate (0-99)  How fast the chemical evaporates  How long the trail lasts

Ant Foraging Experiment/Simulation NEED TO KNOW WHAT OUTPUT DATA you are collecting…. Is it food left after # ticks? Is it ticks before all food is found?

Parameter Sweeping Picking Sample Points (where and how many) ▫Make sense  no ants does not make sense ▫Must represent the variable or parameter being explored  Extremes are not enough ▫2 points = line…. assumption  Must use points in the middle ▫More points if behavior is complicated

Ant Simulation – Parameter Sweeping Parameter Sweeping ▫Ants (3 sample points)  50, 100, 200 ▫Diffusion rate (4 sample points)  0, 33, 66, 99 ▫Evaporation rate (4 sample points)  0, 33, 66, 99 Total Number of sampling points ▫3 x 4 x 4 ▫48 sample points

Repetitions Stochastic model Must run repetitions at each sample point How many repetitions? ▫How random is the process? ▫Up to the experimenter – YOU!

Ant Simulation - Repetitions I get to decide ▫Run the model to see how random ▫5 repetitions How many experiments? (number of sample points) x (number of repetitions) ( 48 ) x ( 5) = 240 Can Limit Experiments ▫Fix the number of ants to 100 (number of sample points) x (number of repetitions) ( 4 x 4 ) x ( 5) = 80

What Output? Simulation Output depends on the model ▫Number of ticks ▫Number of agents ▫Number of patches of color Epidemic model ▫Ticks until everyone infected ▫Number of agents infected after number of ticks Ants Model ▫Amount of food left after # ticks ▫Ticks before all food is found ▫Ticks before all found gathered

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Stopping Forever Button Forever GO button can go forever Want an accurate measurement Automatically Stop the Forever GO button ▫Conditional Stop at the TOP of GO procedure to go if condition? [ stop ]... end

Show Stop in program

Table of Results

Graph of Results

Computer Simulation Write-up: Must include enough  replication ▫Description of problem of interest and abstraction ▫Description of Model  Assumptions/Simplifications  Variables/Parameters ▫Description of Simulation  Parameter Sweeping  Repetitions ▫Description of Results  Verbal Description  Tables/Graphs ▫Discussion of Results/Conclusions

Summary Model – The program that captures the elements of the system being modeled and the behavior of those elements Simulation - Running the model to explore the behavior of the modeled system over time. Deterministic simulation models: Provide single outputs for each set of inputs because No Randomness involved Stochastic simulation models: produce different outputs for each set of inputs because Randomness IS involved  Agent-based models of Complex Adaptive Systems have Randomness -> they are stochastic  Look at the probability distribution of possible outcomes. How to perform a Stochastic Simulation  Parameter Sweeping  Repetition When you write up simulation results  must include enough detail for simulation to be repeated and explained