Gianmarco Ducci, Maryke Kouyate, Karsten Reuter, Christoph Scheurer
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引用次数: 0
Abstract
Sparse data-driven approaches enable the approximation of governing laws of physical processes with parsimonious equations. While significant effort has been made in this field over the last decade, data-driven approaches generally rely on the paradigm of imposing a fixed base of library functions. In order to promote sparsity, finding the optimal set of basis functions is a necessary condition but a challenging task to guess in advance. Here, we propose an alternative approach that consists of optimizing the very library of functions while imposing sparsity. The robustness of our results is not only evaluated by the quality of the fit of the discovered model but also by the statistical distribution of the residuals with respect to the original noise in the data. In order to avoid choosing one metric over the other, we would rather rely on a multi-objective genetic algorithm (NSGA-II) for systematically generating a subset of optimal models sorted in a Pareto front. We illustrate how this method can be used as a tool to derive microkinetic equations from experimental data.
期刊介绍:
The Journal of Chemical Physics publishes quantitative and rigorous science of long-lasting value in methods and applications of chemical physics. The Journal also publishes brief Communications of significant new findings, Perspectives on the latest advances in the field, and Special Topic issues. The Journal focuses on innovative research in experimental and theoretical areas of chemical physics, including spectroscopy, dynamics, kinetics, statistical mechanics, and quantum mechanics. In addition, topical areas such as polymers, soft matter, materials, surfaces/interfaces, and systems of biological relevance are of increasing importance.
Topical coverage includes:
Theoretical Methods and Algorithms
Advanced Experimental Techniques
Atoms, Molecules, and Clusters
Liquids, Glasses, and Crystals
Surfaces, Interfaces, and Materials
Polymers and Soft Matter
Biological Molecules and Networks.