Modeling

Models

Models are crucial in the learning cycle from combinatorial experimentation and materials informatics for two reasons.  First, they represent a succinct and mathematically workable means to analyze and engineer materials.  As indicated above, empirical models may be extracted from combinatorial experimentation combined with informatics approaches which enrich the value of the data through filtering, analysis, and various means of prioritization of the data. These models can then become the basis for achieving desired materials performance characteristics.  Since real materials problems are profoundly multivariate in terms of input parameters and performance figures of merit, complex dependencies of these parameters must be dealt with as mathematical models, e.g. response surface models which approximate the behavior of the materials system over a broad parameter space.

Second, model development drives understanding by relating the expanded sets of empirical data from combinatorial experimentation to fundamental physical parameters and phenomena.  Theoretical work in materials science, chemistry, and solid state physics may lead to models which predict materials properties and structure, and such work can be accomplished at various levels, from ab-initio molecular orbital or band structure calculations to basic considerations from chemical bonding.  Or models may address physics fundamentals through data mining, either extracting unexpected correlations that generate new ideas, or inferring the relationship between materials data and legacy databases of derived parameters such as electronegativity or pseudopotential radius.

It should also be recognized that many modeling outputs will be multi-level and/or multi-scale in character.  For example, in a modeling system fundamental physical parameters (e.g., valence) might be related to equilibrium properties of a material, while the kinetics involved in a materials synthesis process may substantially determine which equilibrium state is realized; such situations can result in multi-level, heterogeneous components to the larger model.  Furthermore, the properties of materials can depend on behavior occurring at different length scales, e.g., continuum mechanics and adhesion of a thin film on a MEMS scale, coupled with microstructural effects determined on a nanoscale.

Model refinement

While informatics techniques such as PCA can be used to develop response surface models from empirical data, iteration and refinement of such models can add further value.  Empirical data is accompanied by uncertainties from both experimental reproducibility and measurement error.  Different forms of analytical expressions, implying different underlying mechanisms, give rise to differing accuracy in how well the model represents the data.  Methodologies differ for PCA, neural network, and other model derivation methods. As more fundamental, physics-based models are generated, they must be compared with experimental data for validation and refinement; this can be accomplished by carrying out virtual design-of-experiments in which the physics-based model is used to generate combinatorial predictions that can be directly compared with experimental data.  Taken together, these examples underscore the fact that model development is an iterative process, not only with experiment but even within the context of existing empirical data and different types of models.