Data Collaboration

The Data Collaboration methodology puts models, theory, and data on the same footing. It does not change the way experimentation is done, but requires a different approach to analyzing even one s own observations and, as a consequence, places new standards on data reporting. In this approach, measured data, its estimated uncertainty, and a model of the 

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The answer to the second question is a set of parameter values as of yet unfalsified by the experimental data. If the unfalsified set is found to be empty, then the underlying reaction model and/or the experimental data may be considered invalidated. The unfalsified set is often hard to describe explicitly, hence additional questions (in the form of constrained optimizations) are typically posed to probe the extent and implications of the unfalsified parameter set. We refer to the approach of applying constrained optimization to query the unfalsified set as Data Collaboration. ... 

The use of a simple polynomial form as a surrogate model decreases the computational cost of the objective function evaluation by orders of magnitude. Not only does it make the solution of the inverse problem possible for large-scale dynamic models, but it also allows one to use more elaborate numerical methods of optimization, enables a rigorous statistical analysis of confidence regions [30,31], and ties in closely with a more general approach to model analysis. Data Collaboration, discussed later in the text. 

The concept of a dataset lays down the foundation for the Data Collaboration methodology. We associate with experiment E a dataset unit, which consists of the measured value, de, reported uncertainty in the measurements, /g and Ue, and a mathematical model. Me. The model Me is defined as the functional relation between the model active variables, x, and the prediction for dg, yielding leties together data, model, and uncertainty. A dataset, D, is a collection of such dataset units Ue = de, Ug, le, M ). In the present Data Collaboration methodology, the models are the statistical surrogates developed in computer experiments, namely Mg = e(x), and so Ug = dg, Ug, le, i e) and D = C/g. ... 

The Data Collaboration approach casts problems as constrained optimization over the feasible region, drawn on the entire knowledge... 

All the questions posed in the Data Collaboration framework appear as constrained optimization problems [72]. Typically, there are both inequality and equality constraints. If /, g, and h are functions, then a constrained optimization problem is of the form... 

In what follows, we illustrate the general mathematical strategy of Data Collaboration using as an example our main problem, that of model prediction [69] given a dataset comprised of Ny> dataset units (i.e., Ad quadratic models S with the respective coefficient matrices M,), obtain a prediction interval for an arbitrary quadratic model sq. The computational problem we thus focus on is an indefinite quadratic program for X = [xi, X2,..., x ] e R",... 

The framework of Data Collaboration supports a rigorous numerical approach to dataset consistency, which provides a combined way to look at system uncertainties originating from either rate parameters or experimental observations [70]. The measure of dataset consistency... 

We also performed toy thought experiments [68] to gauge the information loss by doing traditional analysis without the benefit of Data Collaboration at the raw data level. We considered a measure of information gained as a result of the data processing as a relative... 

We can compare how I changes depending on the mode of data analysis. Specifically, we defined the information loss, L, due to not using Data Collaboration as... 

This example illustrates the need (and payoff) for fully collaborative environments in which models and data can be shared, allowing sophisticated global optimization-based tools to reason quantitatively with the community information. Examples of questions that one can address through Data Collaboration by considering set-intersection assertions about the feasible region within the parameter space are ... 

Some of these questions can be answered with the methodology available today, and some require further development. To enable Data Collaboration in its full mode one of the upcoming challenges is creation of an infrastructure able to create and curate the dataset by engaging the entire scientihc community [46]. 

The methodology of Solution Mapping was developed while one of us (MF) was working on various projects supported by DOE, NASA, AFOSR, and GRI. The work on Data Collaboration and preparation of this manuscript were supported by NSF, under Grant Nos. CTS-0113985 and CHE-0535542. 

Feeley, R., Frenklach, M., Onsum, M., Russi, T., Arkin, A., Packard, A. Model discrimination using data collaboration. J. Phys. Chem. A 110, 6803-6813 (2006)... 

Another sign of development is that a growing number of thermokinetic parameters are accompanied by estimations of their accuracy. In the best cases, these uncertainty estimates are based not on the error analysis of a single experiment but reflect the comparison of several independent experimental or theoretical studies and therefore incorporate systematic errors of the various methods. In the past, such evaluations were performed by human experts, but as the dataset grows, perhaps a new paradigm for this process is required. Data collaboration approaches have been suggested which could place this task in the hands of wide communities (and computer software), rather than small groups of experts. 

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