A Model Falsification Approach to Learning in Non-Stationary Environments for Experimental Design

Andrea Murari,Emmanuele Peluso,Michela Gelfusa,Teddy Craciunescu,Michele Lungaroni

doi:10.1038/s41598-019-54145-7

Abstract

The application of data driven machine learning and advanced statistical tools to complex physics experiments, such as Magnetic Confinement Nuclear Fusion, can be problematic, due the varying conditions of the systems to be studied. In particular, new experiments have to be planned in unexplored regions of the operational space. As a consequence, care must be taken because the input quantities used to train and test the performance of the analysis tools are not necessarily sampled by the same probability distribution as in the final applications. The regressors and dependent variables cannot therefore be assumed to verify the i.i.d. (independent and identical distribution) hypothesis and learning has therefore to take place under non stationary conditions. In the present paper, a new data driven methodology is proposed to guide planning of experiments, to explore the operational space and to optimise performance. The approach is based on the falsification of existing models. The deployment of Symbolic Regression via Genetic Programming to the available data is used to identify a set of candidate models, using the method of the Pareto Frontier. The confidence intervals for the predictions of such models are then used to find the best region of the parameter space for their falsification, where the next set of experiments can be most profitably carried out. Extensive numerical tests and applications to the scaling laws in Tokamaks prove the viability of the proposed methodology.

Highlights

Once the experiments have explored the new region of the operational space and new data are collected, the process can be repeated until convergence on a sufficiently specific model for the interpretation of the phenomena under study
Since the available models have been derived in conditions different from the ones of the final applications, the i.i.d assumptions cannot be invoked
It is worth mentioning that practically the same methodology can be adopted to fine tune the analysis of existing databases

Summary

Introduction

Once the most advantageous operational region to investigate is selected, experiments are performed, new data are collected and the process can be repeated. Given the limitations of the databases available, typically the Fitness Functions does not manage to converge on a single individual model, clearly outperforming all the others.

Results

Conclusion