Scientific Models in the Computing Era

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In my very first class to introductory college physics, I was told that a good scientific model have a general descriptive power. While it is true, I found that it is a oversimplified statement after I was exposed to computational science and other fields outside physics.

Descriptive power is important, as in Shelling model in economics; but to many scientists and engineers, a model is devised because of its predictive power, which can be seen as one aspect of its descriptive power. Predictive power is a useful feature. All physics and engineering models have predictive power in a quantitative sense.

Physics models have to be descriptive in a sense that the models are describing physical things; but in the big data era, a lot of machine learning models are like black boxes, which means we care only about the meaning of inputs and outputs, but the content of the models do not necessarily carry a meaning. SVM and deep learning are good examples. (This in fact bothers some people.) But of course, in physics, there are a lot of phenomenological models that are between descriptive models and black boxes, such as the Ginzburg-Landau-Wilson (GLW) model widely used in magnets, superfluids, helimagnets, superconductors, liquid crystals etc. However, to be fair, some machine learning models are quite descriptive, such as clustering, Gaussian mixtures, MaxEnt etc.

A lot of traditional physics models are equation-based, but computational models are not. The reasons are evident. And of course, traditional physics models are mostly continuous while computational models are sometimes discrete. If the computational models are continuous and equation-based, they will be translated to discrete version for the computing machines to handle correctly.

However, whichever forms the models take, we, human beings, are essential to give the models meaning so that they are useful.

  • Allen B. Downey, “Think Complexity“, O’Reiley (2012).
  • Galit Shmueli, “To Explain or To Predict?” Statistical Science 25, pp. 289-310 (2010). [arXiv:1101.0891]
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