Jrising at 03:31, 25 August 2013

2013-08-25T03:31:16Z

Jrising at 20:54, 18 October 2012

2012-10-18T20:54:51Z

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	"Maps" are dimension-aware functions in space-time, often tied to data streams (e.g., IRI tsvs, geotiffs).		"Maps" are dimension-aware functions in space-time, often tied to data streams (e.g., IRI tsvs, geotiffs).
	Maps of different resolutions can be manipulated transparently. Example:		Maps of different resolutions can be manipulated transparently. Example:
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	<slide title="Case Study: Hydrological Modeling">		<slide title="Case Study: Hydrological Modeling">
	[[File:Bhakramap.png]]		[[File:Bhakramap.png]]

	[[File:Netmap_ext.png]]		[[File:Netmap_ext.png]]
	</slide>		</slide>

Jrising at 20:49, 18 October 2012

2012-10-18T20:49:31Z

New page

<slide header="none" center="both">
= Open World Project =
Friday Forum

Oct. 19, 2012

 

James Rising, Upmanu Lall,

Bruce Shaw, Pierre Gentine
</slide>

<slide title="Talk Plan">
* Other Projects of Interest
* Motivation and Vision
* Core Elements
* Case Study Projects
* Climate Behaviors
* Fisheries Model
* Next Steps
</slide>

<slide title="Other Projects of Interest">
* [http://www.existencia.org/carbon/ Carbon Transition Working Group]
* [http://sdresearch.wikischolars.columbia.edu/jar2234+Peruvian+Fisheries Peruvian Spatial Fisheries]
* [http://sdresearch.wikischolars.columbia.edu/Ocean+Health Ocean Health Metric]
* [http://sdresearch.wikischolars.columbia.edu/jar2234+Marine+Protected+Areas Empirical Benefits from Marine Protected Areas]
* [http://existencia.org/weaver/ Web-Weaver Data Extractor]
* [http://cantovario.com CantoVario]
* [http://openworld.existencia.org/index.php?title=Friday_Forum_Presentation Slider Extension]
</slide>

<slide title="Introduction" fs="2em">
Many of the human behaviors that drive climate change and
environmental degradation are deeply embedded in our society,
economy, and government, and are mutually reinforcing. Better
modeling of human-natural systems can help in many ways:
* Analyzing feedback loops can help identify '''leverage points''', where small policy changes can have pervasive impacts.
* Allowing models at diverse scales and contexts to interact can help scientists '''integrate knowledge'''.
* Interactive models can facilitate '''communication''' with policymakers and make complex problems intelligible.

The Open Model is a modeling framework aimed at these issues.
</slide>

<slide title="Applicability" fs="2em">
* Systemically intractable due over-determined, reinforcing drives, and spatially heterogeneous.
* Environmental and public health issues: environmental degradation, agricultural practices in poor countries, obesity, substance abuse, groundwater use, fishery management, passenger transport
* Rebound effects and cross-border shifts (e.g., carbon leakage)

 

<center>'''Something for everyone!'''</center>
</slide>

<slide title="Why bigger models?">
* '''Accuracy?''' Debatable
* '''Precision?''' Marginally better
* '''As a platform?''' If it's popular

* ''Interaction of the components''
* ''Finer tipping points''
</slide>

<slide title="Core Elements">
* Amalgamated Modeling
* Multiple Network Maps
* Networked System Dynamics
* Computational Tools
* Open Interface
* Smart Variables

[[File:Elements.png|200px|center]]
</slide>

<slide title="Amalgamated Modeling" fs="1.8em">
Amalgamated modeling allows models to interact, specialize, and "overlap".

Every model is incomplete; applies to a constrained context.
:'''Let's embrace partial models!'''
Want a "plugin architecture", where models can easily be allowed to interact

Coupling causes feedback, and models are defined at different scales.
:'''Need a new way to couple models!'''

Allow overlapping-- models inform different variables, at different scales.
</slide>

<slide title="Amalgamated Modeling">
[[File:Blobs.png]]
</slide>

<slide title="Bayesian Coupling">
[[File:Amalgelt.png]]
</slide>

<slide title="Bayesian Coupling">
For a variable <math>\theta</math> described by multiple models, each
model provides both a PDF across values at a given time <math>t</math>
when run in isolation, <math>p(\theta, \bar{S}^i)</math>, and a
distribution that includes feedback effects, <math>p(\theta, \tilde{S}^i)</math>. The final distribution is
<math>
p(\theta | \cdot) \propto p(\theta) \prod_i p(\theta |
\bar{S}^i)^\lambda p(\theta, \tilde{S}^i)^{1-\lambda}
</math>

[[File:Amalgcombo.png|center]]
</slide>

<slide title="Amalgamation Challenges">
* How do I test it?
* Efficient probability function calculations
* Smooth or spectrally-informed transitions?
* What does downsampling contribute?
* How to ensure that different scales add up?

[[File:Trialestimate.png|200px]]
</slide>

<slide title="Multiple Networks">
Models use multiple networks simultaneously
* Different paths on which stocks flow
* Disaggregations into structured classes
* Capturing network properties
</slide>

<slide title="Multiple Networks in Ohio">
[[File:Ohionet.png]]
</slide>

<slide title="Networked System Dynamics">
Spatial variation matters; let's combine "systems" and "space"!

[[File:ssdarch-mod.png|200px]]

* Systems need to be able to vary over space
* Ensure that the separate blocks match the aggregate
</slide>

<slide title="Disaggregating System Models">
[[File:Popmod-vensim.png|center]]

[[File:Popmod.png|center]]
</slide>

<slide title="Networked System Dynamics">
[[File:Netstocks.png]]
</slide>

<slide title="Networked System Dynamics">
[[File:Ohiomod.png]]
</slide>

<slide title="Self-Similar Networks">
[[File:Selfsimodel.jpeg|center]]
</slide>

<slide title="Networking Challenges">
* What is a full language of networked system dynamics?
* Can a model only apply to part of a network?
* How to ensure that missing models "fail gracefully"?
</slide>

<slide title="Computational Tools">
* Evaluate model performance
* Identify driving feedback loops
* Identify tipping and leverage points
* Construct simplified models for communication
* System Regression: construct models from data
</slide>

<slide title="Integrating Data" fs="2em">
* Calibration
* Validation
* Filling in missing models
:'''We need a smart (context-aware and incomplete-welcoming) data library!'''
</slide>

<slide title="Open Interface" fs="2em">
[[File:Climatepred.png|right|200px]]

For researchers:
* Exploring the model
* Running tests
* Contributing models

For policy-makers:
* Interact with the model
* Visualize results
* Outline scenarios
</slide>

<slide title="Smart Variables: Dimensions">
* <math>3</math> vs. <math>3</math> [tonnes] vs. <math>1350487537</math> [seconds since Jan. 1, 1970]
* Dimensional analysis at the heart of science
* Automatic model checking, unit conversion
</slide>

<slide title="Smart Variables: Maps" fs="2em">
"Maps" are dimension-aware functions in space-time, often tied to data streams (e.g., IRI tsvs, geotiffs).
Maps of different resolutions can be manipulated transparently. Example:

<syntaxhighlight lang="cpp">
GeographicMap<double>& degreeDayMelt = (degreeDayFactor + degreeDaySlope * elevation)
* (snowCover / 100) * (surfaceTemp - ZERO_CELSIUS) * (surfaceTemp >= ZERO_CELSIUS);
</syntaxhighlight>

* elevation is a static map at <math>1 km</math> resolution
* surfaceTemp is a daily varying map at <math>.25^\circ</math> resolution, read from the file 1 day at a time
* snowCover is a weekly varying map at <math>.33^\circ</math> resolution, reconstructed for past years
</slide>

<slide title="Smart Variables: Relations">
Variables can represent relationships or differential equations between other variables.

Example (the heat equations):
<syntaxhighlight lang="cpp">
q = -k * Grad(u);
Diff(u) = (-1 / c_p * rho) * Div(q);
</syntaxhighlight>

The equations themselves are saved within <code>q</code> and <code>Diff(u)</code>, so the model can be run.
</slide>

<slide title="Networked Equations Language">
Custom '''Modeling Language''' combines a units-aware equation-like syntax with networks and GIS.

<syntaxhighlight lang="cpp">
capacity = 1e10 [tons];
rate = 0.0077 [tons/year];
biomass = Stock(1e7 [tons]);
catches = TimeSeries("catches.tsv", [tons/year]);
biomass += rate * biomass *
(1 - biomass / capacity) - catches;

print(biomass[0:100], "\t");
</syntaxhighlight>
</slide>

<slide title="Toolbox">
Transparently combine Matlab, R, shell scripting, Mathematica and other code.

[[File:Toolbox.png]]
</slide>

<slide title="Case Study: Networked Economics">
Step 1: Reconstruct Solow Growth (with some random shocks):

* <math>\frac{d L}{d t} = \lambda L(t)</math>
* <math>Y(t) = K(t)^\alpha L(t)^{1-\alpha} \epsilon(t)</math>
* <math>\frac{d K}{d t} = s Y(t) - \delta K(t)</math>

[[File:Solow.png|200px]]
</slide>

<slide title="Case Study: Networked Economics">
Step 2: Make a "distributed" analog to Solow growth:

* Multiple firms, with individual capital stocks
* Separate growth and decay: <math>g[t] = s Y[t]</math>, <math>d[t] = \delta K[t]</math>
* If <math>g[t] \ge d[t]</math>, growth: <math>K[t+1] = K[t] + g[t]</math>
* If <math>g[t] < d[t]</math>, stagnation: <math>K[t+1] = K[t]</math>
** And probability of collapse, so expected value follows Solow
** <math>K[t+1] = K[t] + g[t] - d[t] = (1 - P(c)) K[t] \implies P(c) = (d[t] - g[t]) / K[t]</math>
* Firms can make connections to each other, which increase "technology" (specialization) factor

[[File:Smallworld.png]]

* But when collapse, connections severed, capital goes to 0
</slide>

<slide title="Case Study: Networked Economics">
[[File:Distrib.png]]

[[File:Economies.png]]
</slide>

<slide title="Case Study: Hydrological Modeling">
[[File:Bhakramap.png]]
[[File:Netmap_ext.png]]
</slide>

<slide title="Extensions">
* Memetic propagation of models
* Integration with climate models
* Importing Vensim models
</slide>

<slide title="Model for Climate Behaviors">
[[File:Architecture.png]]
</slide>

<slide title="How Many Variables?">
{|
| World3/2000 || 283
|-
| System Dynamics National Model || 2000+
|-
| Encyclopedia of World Problems and Human Potential || 56,135
|-
|  environmental feedback loops || 2,675
|}
</slide>
<slide title="Multimanaged Fisheries Project">
[[File:Food_web_600.jpg]]
</slide>

<slide title="Multimanaged Fisheries Project">
* Plug-in different "fish" and "policy" modules
* <math>g_t^i = r^i s_t^i (1 - \frac{s_t^i / K_t^i})</math>
* <math>K_t^i = \sum_{j \in q(i)} w^{ij} s_t^i</math>
</slide>

File:Elements.png - Revision history

Jrising at 03:31, 25 August 2013

Jrising at 20:54, 18 October 2012

Jrising at 20:49, 18 October 2012