(278d) A Model-Based Methodology for Continuous Experimental Designs

Design of experiments (DoE) is a powerful paradigm to maximize the information content of experimental campaigns. The technique offers tremendous potential to accelerate the development of mathematical models, regardless of whether a mechanistic or statistical framework to modelling is adopted.

When applied to a statistical framework, the technique leads to a powerful and widely used experimental methodology for empirical process optimization. A valued feature of the methodology is that there exists a set of standard experimental designs which are simultaneously optimal for many statistical models suitable for modelling a wide range of problem settings, making them flexible and easy-to-use. Examples of such designs include factorial design and its derivatives (e.g. fractional factorial, Box-Behnken¹, central composite, and Plackett-Burman design). Although highly effective, this approach can still require significant resources and time to develop for large-scale systems. In addition, its applicability remains limited for dynamic systems and experimentation.

When applied to a mechanistic modelling framework, the technique leads to a systematic, optimization-based methodology known as model-based design of experiments (MBDoE). MBDoE is often applied to expedite the development of first-principles models, which have superior extrapolative capability compared to statistical models and may be transferrable to other similar systems. Such system-tailored experiments can offer large benefits compared to classical DoE, but they nonetheless come at the price of a much higher complexity and computational burden.

Despite being a mature field, optimal experimental design is still a very active area of research. For instance, there are contributions to extending classical DoE to optimize dynamic systems², novel optimality criteria^3,4,5, novel improvements of model-based designs to increase its effectiveness⁶, formulations for set-based^7,8 and Bayesian statistical frameworks⁹, and alternative numerical solution strategies for model-based designs ^10,11.

This talk will present a new numerical solution method for computing so-called continuous experimental designs (CED). CED is a central concept in convex design theory^12,13 where designs are akin to experimental recipes. As well as identifying which experiments are informative, a CED also specifies the optimal experimental effort to dedicate to each informative experiment which is considered a continuous variable. Because MBDoE formulations usually yield non-convex optimization problems, model-based designs are often sequentially constructed, with experiments designed one at a time. In practical applications where multiple experiments need to be designed, this then results in the solution of a series of non-convex optimization problems, riddled with local optima. By contrast, the proposed CED methodology introduces desirable numerical simplifications, such as making the optimization problem convex and allowing for simultaneously constructed (parallel design) experiments. It involves discretizing the experimental degrees-of-freedom into a set of candidate experiments. An information matrix is computed for each candidate. While conducting a sensitivity analysis is potentially costly for many candidates, this step can readily be vectorized on multiple CPUs. Then, a search is conducted over all the possible combinations of experimental effort in order to optimize a chosen information criterion (classically A, D or E optimality).

The talk will also introduce an open-source Python software implementing the CEP methodology. Computational results will be presented for a wide range of settings, from the classical statistical setting involving various response surface models to MBDoE for an industrial batch reactor system, as illustrated in the attached figure.

References

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10. Olofsson, S., Deisenroth, M. & Misener, R. Design of Experiments for Model Discrimination Hybridising Analytical and Data-Driven Approaches. in Proceedings of the 35th International Conference on Machine Learning (eds. Dy, J. & Krause, A.) 80, 3908–3917 (PMLR, 2018).
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13. Fedorov, V. V. & Hackl, P. Model-Oriented Design of Experiments. 125, (Springer New York, 1997).