2024 AIChE Annual Meeting

(119h) A Novel Tunable Space-Filling Adaptive Sampling Strategy Based on Delaunay Triangulation

Authors

Steven Sachio, Imperial College London
Maria Papathanasiou, Imperial College London
A surrogate is a model able to approximate high-fidelity models with significant computational time reduction and their usage in chemical engineering applications is rapidly becoming widespread [1, 2]. The majority of current research on surrogate modeling harnesses machine-learning tools to achieve high accuracy. This approach, however, requires a copious amount of training data. Hence, the design of computer experiments for data generation from high-fidelity models is key, especially for balancing the trade-off between computational time saved through their use and time invested in their development [3]. Common techniques such as the quasi-random Sobol' sequence [4] or the maximin-optimized Latin Hypercube sampling [5] offer a valuable approach for sampling design space with good space-filling qualities [6]. However, such methods do not account for the topology of the target high-fidelity model inside the design space [7]. Adaptive sampling, on the other hand, does include such information in the sampling loop, thus offering advantages in terms of surrogate accuracy and high-fidelity sampling efficiency, by reducing the total amount of samples needed while maximizing the knowledge gained from the model [8]. These strategies excel in managing complex and non-linear problems in low-dimensional spaces but struggle with the curse of dimensionality in higher-dimensional domains, leading to diminishing returns or even negative effects, particularly if the strategies lack intrinsic space-filling qualities or overly prioritize exploitation over a balanced approach [9].

In the context of feasibility analysis and design space identification with surrogate modeling the demand for effective adaptive sampling strategies is significant. Although many studies have been conducted on this matter with promising results [10, 11, 12, 13] there remain challenges to be tackled, especially related to a lack of methods with innate space-filling capabilities with swiftly tunable exploration to exploitation balance and that do not necessarily require a surrogate model during sampling. The latter characteristic is particularly crucial to exploiting the capabilities of parallel computing during data generation, since the need for training a surrogate after each adaptive iteration could break the parallelizability of the routine making it a serious bottleneck.

In this work, we present a method that effectively addresses these challenges by integrating the adaptive sampling strategy in space-filling techniques. Specifically, iterative Delaunay triangulations for point collocation, both for exploration and exploitation, are used. For the initial sampling, the proposed method is seeded with a few samples of a space-filling design of experiments, such as an optimized Latin Hypercube. However, to effectively enable the Delaunay triangulation, the hypercube corners must also be sampled. For this, a 2n full-factorial sampling, where n is the problem dimensionality, is performed. After the initial seeding, a Delaunay triangulation mesh is created and the areas of each triangle forming the mesh are calculated. The areas of triangles with a vertex within a constraint are multiplied by a weight factor and the triangle with the biggest weighted area is selected. The next adaptive sample point is thus positioned at the barycenter of the selected triangle, to homogeneously fill the void space. The steps of mesh formation, area calculation, weighing, selection, and sampling effectively form an adaptive iteration. The program is repeated until a target stop criterion is met.

To validate the method's space-filling qualities, the algorithm is assessed in a full-explorative run against two widely utilized one-shot designs of experiments: Latin Hypercube and Sobol' sequence sampling. The capabilities of the presented approach are tested and assessed on the benchmark modified Branin function [14] and on the continuous capture process for monoclonal antibodies production [6, 15]. The method demonstrates the potential for enhancing design space identification advancing adaptive sampling-methods towards wider exploration of the space. This work addresses relevant gaps in adaptive sampling strategies suited for feasibility analysis while also keeping an approach for broader applications in different process systems engineering scenarios, with the potential for advancing the efficiency and efficacy of surrogate model utilization.

Acknowledgements:
Funding from the UK Engineering & Physical Sciences Research Council (EPSRC) for the i-PREDICT:
Integrated adaPtive pRocEss DesIgn and ConTrol (Grant reference: EP/W035006/1) is gratefully acknowledged.
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