Category: Vensim

A System Zoo

I just picked up a copy of Hartmut Bossel’s excellent System Zoo 1, which I’d seen years ago in German, but only recently discovered in English. This is the first of a series of books on modeling – it covers simple systems (integration, exponential growth and decay), logistic growth and variants, oscillations and chaos, and some interesting engineering systems (heat flow, gliders searching for thermals). These are high quality models, with units that balance, well-documented by the book. Every one I’ve tried runs in Vensim PLE so they’re great for teaching.

I haven’t had a chance to work my way through the System Zoo 2 (natural systems – climate, ecosystems, resources) and System Zoo 3 (economy, society, development), but I’m pretty confident that they’re equally interesting.

You can get the models for all three books, in English, from the Uni Kassel Center for Environmental Systems Research – it’s now easy to find a .zip archive of the zoo models for the whole series, in Vensim .mdl format, on CESR’s home page: www2.cesr.de/downloads.

To tantalize you, here are some images of model output from Zoo 1. First, a phase map of a bistable oscillator, which was so interesting that I built one with my kids, using legos and neodymium magnets:

Continue reading “A System Zoo”

Delay Sandbox

There’s a handy rule of thumb for estimating how much of the input to a first order delay has propagated through as output: after three time constants, 95%. (This is the same as the rule for estimating how much material has left a stock that is decaying exponentially – about a 2/3 after one lifetime, 85% after two, 95% after three, and 99% after five lifetimes.)

I recently wanted rules of thumb for other delay structures (third order or higher), so I built myself a simple model to facilitate playing with delays. It uses Vensim’s DELAY N function, to make it easy to change the delay order.

Here’s the structure:

Continue reading “Delay Sandbox”

Theil Statistics

Source: Created by Rogelio Oliva, 1995; Updated by Tom Fiddaman, 2009 2011 – slight improvement to numerical robustness.

See Sterman, J. D. 1984. Appropriate Summary Statistics for Evaluating the Historical Fit of System Dynamics Models. Dynamica 10 (2): 51-66.

Units balance: Yes

Format: Vensim; requires an advanced version

Files:

D-4584 Theil Statistics documentation– D-memo documentation

Theil_2011.mdl – Theil Statistics model

Theil_2011.vpm – published binary version; includes data.vdf so it’ll run right out of the box

Dummy_data.mdl – dummy data generator creating input to Theil model

Vensim Compiled Simulation on the Mac

Speed freaks on Windows have long had access to 2 to 5x speed improvements from compiled simulations. Now that’s available on the Mac in the latest Vensim release.

Here’s how to do it, in three easy steps:

  • Get a Mac.
  • Get the gcc compiler. The only way I know to get this is to sign up as an Apple Developer (free) and download Xcode (I grabbed 3.2.2, which is much smaller than the 3.2.6+iOS SDK, but version shouldn’t matter much). There may be other ways, but this was easy.
  • Get Vensim DSS. After you install (checking the Install external function and compiled simulation support to: box), launch the program and go to Vensim DSS>Preferences…>Startup and set the Compiled simulation path to /Users/Shared/Vensim/comp. Now move to the advanced tab and set the compilation options to Query or Compile (you may want to skip this for normal Simulation, and just do it for Optimization and Sensitivity, where speed really counts).

OK, so I cheated a little on the step count, but it really is pretty easy. It’s worth it, too: I can run World3 1000 times in about 8 seconds interpreted; compiled gets that down to about 2.

Update: It turns out that an installer bug prevents 5.10d on the Mac from installing a needed file; you can get it here.

The Rise and Fall of the Saturday Evening Post

Replicated by David Sirkin and Julio Gomez from Hall, R. I. 1976. A system pathology of an organization: The rise and fall of the old Saturday Evening Post. Administrative Science Quarterly 21(2): 185-211. (JSTOR link). Just updated for newer Vensim versions.

This is one of the classic models on the Desert Island Dynamics list.

There are some units issues, preserved from the original by David and Julio. As I update it, I also wonder if there are some inconsistencies in the accounting for the subscription pipeline. Please report back here if you find anything interesting.

satevepost2011b.mdl

satevepost2011b.vmf

Boiling Water Reactor Dynamics

Replicated from “Hybrid Simulation of Boiling Water Reactor Dynamics Using A University Research Reactor” by James A. Turso, Robert M. Edwards, Jose March-Leuba, Nuclear Technology vol. 110, Apr. 1995.

This is a simple 5th-order representation of the operation of a boiling water reactor around its normal operating point, which is subject to interesting limit cycle dynamics.

The original article documents the model well, with the exception of the bifurcation parameter K and a nonlinear term, for which I’ve identified plausible values by experiment.

TursoNuke1.mdl

Monday tidbits- tools, courses

I neglected to cross-post an interesting new Vensim model documentation tool that’s in my model library.

Shameless commerce dept.: I’m teaching Vensim courses in Palo Alto in April and Bozeman in June. Following the June offering, Ventana’s Bill Arthur will be teaching “SMLOD” – Small Models with Lots of Data – a deep technical dive into the extraction of insight from large datasets.

Fibonacci Rabbits

This is a small, discrete time model that explores the physical interpretation of the Fibonacci sequence. See my blog post about this model for details.

Fibonacci2.vpm This runs with Vensim PLE, but users might want to use the Model Reader in order to load the included .cin file with non-growing eigenvector settings.

Optimizing Vensim models

Danger – another technical post, mainly relevant to users of advanced Vensim versions.

The title has a double meaning: I’m talking about optimizing the speed of a model, which is most often needed for optimization problems.

Here’s the challenge: you have a model, and you think you understand it. You’d like to calibrate it to data, do some policy optimization to identify good decision rules, and do some Monte Carlo simulation to identify sensitive parameters and robust policies. All of those things take thousands or even millions of model runs. Or, maybe you’d just like to make a slightly sluggish model fast enough to run interactively with Synthesim.

Here’s what you can do:

  • Run compiled. Probably your best bet is to use MS Visual c++ 2010 Express, which is free, or an old copy of MSVC 6. Some of the versions in between apparently have problems. You may need to change Vensim’s mdl.bat file to match the specific paths of your software. You might succeed with free tools, like gcc+, but I haven’t tried – I’d be interested to hear of such adventures. Update: You now want Visual Studio with the C/C++ workload. For recent versions of Vensim, it’s actually mdldp64.bat that contains the active compile script. It usually works right out of the box.
  • Use the INITIAL() statement as much as you can. In particular, be sure that any data-retrieval functions like GET DATA AT TIME are wrapped in an initial if possible (they’re comparatively slow).
  • Consider using data equations for input calculations that are not part of the feedback structure of the model. Data equations get executed once, at the start of a group of optimization/sensitivity/Synthesim simulations, rather than with each iteration. However, don’t use data equations where parameters you plan to change are involved, because then your changes won’t propagate through the results. If you want to save startup time too, move complex data calculations into an offline data model.
  • Switch any sparse array summary calculations from SUM, VMIN, VMAX, and PROD functions to VECTOR SELECT or VECTOR ELM MAP. Update: I’m no longer sure this is worth the trouble.
  • Update: Calculate vector sums only once. For example, instead of writing share[k] = quantity[k]/SUM(quantity[k!]), calculate the sum separately, so that share[k] = quantity[k]/total quantity and  total quantity = SUM(quantity[k!]).
  • Get rid of any extraneous structure that’s not related to your payoff or other variables of interest. If you still want the information, move it to a separate model that reads the main model’s .vdf for postprocessing. Update: you can put it in a submodel and load it, or not, as needed.
  • Consider whether your payoff is separable. In other words, if your model boils down to payoff = part1(parameter1) + part2(parameter2), you can optimize sequentially for parameter1 and parameter2, since they don’t interact. Vensim’s algorithm is designed for the worst case – parameters that interact, multiple optima, discontinuities, etc. You can automate a sequential set of optimizations with a command script.
  • Consider transforming some of your optimization parameters. For example, if you are fitting to data for a stock with a first order outflow, that outflow can be written as stock/tau or stock*delta, where tau and delta are the lifetime and fractional loss rate, respectively. Mathematically, it makes no difference whether you use the tau or delta approach, but in some practical cases it might. For example, if you think delta might be near zero (a long lifetime), you might do better to optimize over delta = [0,1] than tau = [1,1e9].
  • If you’re looking for hardware improvements, clock speed matters more than multicores and cache. Update: for optimization, MCMC and sensitivity runs, multiple cores help a lot in v10+.

These options are in the order that I thought of them, which means that they’re very roughly in order of likely improvement per unit effort.

Unfortunately, it’s often the case that all of this will get you a 10x improvement, and you need 1000x. Unless you have a supercomputer or massive parallel grid at your disposal, the only real remedy is to simplify your model. Fortunately, that’s not necessarily a bad thing.

Update: One more thing to try: if you’re doing single simulations with a large model, the bottleneck may be the long disk write of the output .vdf file. In that case, you can use a savelist (.lst) to restrict the number of variables stored to just the output you’re interested in. However, you should occasionally do a run without a savelist, and browse through the model results to be sure that things are OK. Consider writing some Reality Checks to enforce quality control on things you won’t be looking at.

Update 2: Another suggestion, via Hazhir Rahmandad: when using the ALLOC functions (DEMAND AT PRICE, etc.), choose simple demand/supply function shapes, like triangular, rather than complex shapes like exponential. The allocation functions iterate to equilibrium internally, and this can be time consuming. Avoiding the use of FIND ZERO and SIMULTANEOUS where possible is also helpful – often a lookup or polynomial approximation to the solution of simultaneous equations will suffice.