Optimization of Designed Experiments Based on Multiple Criteria Utilizing a Pareto Frontier

Lattice Thermal Conductivity Prediction Using Symbolic Regression and Machine Learning

Prediction models of lattice thermal conductivity (κ_L) have wide applications in the discovery of thermoelectrics, thermal barrier coatings, and thermal management of semiconductors. However, κ_L is notoriously difficult to predict. Although classic models such as the Debye-Callaway model and the Slack model have been used to approximate the κ_L of inorganic compounds, their accuracy is far from being satisfactory. Herein we propose a genetic programming-based symbolic regression (SR) approach for finding analytical κ_L models and compare them with multilayer perceptron neural networks and random forest regression models using a hybrid cross-validation (CV) approach including both K-fold CV and holdout validation. Four formulae have been discovered by our SR approach that outperform the Slack formula as evaluated on our dataset. Through the analysis of our models' performance and the formulae generated, we found that the trained formulae successfully reproduce the correct physical law that governs the lattice thermal conductivity of materials. We also systematically show that currently extrapolative prediction over datasets with different distributions as the training set remains to be a big challenge for both SR and machine learning-based prediction models.

Chemometrics-assisted optimization of liquid chromatography-quadrupole-time-of-flight mass spectrometry analysis for targeted metabolomics

Mass spectrometry-based metabolomics is characterized by a vast number of variables leading to a great degree of complexity. In this work, we aimed to simplify this process with a stepped chemometric optimization of the both funnel technology (funnel exit DC, FDC; funnel RF LP, FLC; funnel RF HP, FRP) and ion source parameters (Octopolo, Oct; and Fragmentor, Frag) of a quadrupole-time of flight (qTOF) for a human urinary metabolites. The workflow comprised a Box-Behnken experimental design with 47 experiments followed by the identification and quantification of a set of metabolites using high-resolution full-scan MS mode and feature extraction with an inclusion list. Metabolite peak areas were grouped according to abundance (high and low) and modeled by Random Forest regression (variance explained >85%). The full three-level factorial design consisting in 243 experiments was predicted and top 10 solutions for desirability function and those comprising the Pareto front were extracted and investigated. To guarantee the quality of results, we compared the Pareto front solutions with those achieved by standard instrumental parameters suggested by the manufacturer. A set of five solutions were identified that increased the mean peak area by 56-59% and 17%, for high- and low-abundance metabolites, respectively. The optimal parameters were determined to be: FLP, 100 V; FDC, 40 and 30 V; Frag, 275 and 400 V; and Oct, 600 and 800 V. The methodology applied throughout this work represents a flexible strategy to optimize instrumental parameters and exploit the performance of a qTOF MS detector.

Trade-Off Analysis in High-Throughput Materials Exploration

This Research Article presents a strategy to identify the optimum compositions in metal alloys with certain desired properties in a high-throughput screening environment, using a multiobjective optimization approach. In addition to the identification of the optimum compositions in a primary screening, the strategy also allows pointing to regions in the compositional space where further exploration in a secondary screening could be carried out. The strategy for the primary screening is a combination of two multiobjective optimization approaches namely Pareto optimality and desirability functions. The experimental data used in the present study have been collected from over 200 different compositions belonging to four different alloy systems. The metal alloys (comprising Fe, Ti, Al, Nb, Hf, Zr) are synthesized and screened using high-throughput technologies. The advantages of such a kind of approach compared to the limitations of the traditional and comparatively simpler approaches like ranking and calculating figures of merit are discussed.

Efficient prediction designs for random fields

For estimation and predictions of random fields, it is increasingly acknowledged that the kriging variance may be a poor representative of true uncertainty. Experimental designs based on more elaborate criteria that are appropriate for empirical kriging (EK) are then often non-space-filling and very costly to determine. In this paper, we investigate the possibility of using a compound criterion inspired by an equivalence theorem type relation to build designs quasi-optimal for the EK variance when space-filling designs become unsuitable. Two algorithms are proposed, one relying on stochastic optimization to explicitly identify the Pareto front, whereas the second uses the surrogate criteria as local heuristic to choose the points at which the (costly) true EK variance is effectively computed. We illustrate the performance of the algorithms presented on both a simple simulated example and a real oceanographic dataset. © 2014 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.