What's in the Box? Systematic Approaches for Inferring Algebraic Models From Experimental Data Or Simulations

We address the problem of discovering algebraic relationships that are hidden in a set of data, an experimental process, or a simulation model.  The problem lies at the interfaces between statistical experimental design and machine learning.  We summarize our experience with systematic approaches [1, 2] that rely on optimization techniques to identify algebraic models that are simple and accurate, while minimizing the amount of data (experiments or simulations) that are required in order to draw inferences.  We also describe software implementations of these approaches.

Key words: machine learning, optimization, computing

References:

1. Zhang, Y. and N. V. Sahinidis, Uncertainty quantification in CO2 sequestration using surrogate models from polynomial chaos expansion, Industrial & Engineering Chemistry Research, 52, 3121−3132, 2013.
2. Cozad, A., N. V. Sahinidis, and D. Miller, Learning surrogate models for simulation-based optimization, to be submitted, 2013.