Physics Informed Machine Learning for Quenching

Although the idea of building digital twins for complex infrastructure and systems is well established, its realisation remains very challenging due to the need to combine advanced computational modelling, data for calibration and sensor integration to obtain models with true predictive value for decision support. The perspectives of using digital twins for predictive maintenance, operational optimization, and risk analysis are substantial and the potential for impact significant, from safety, planning, and financial points of view. Digital twins rely on mathematical and numerical modelling, reduced order models in combination with machine learning techniques, deep understanding of the underlying physics and the knowledge on the availability of data. The main purpose of this project is to understand the the importance of reduced models in combination with machine learning tools in the development of digital twin technologies but focusing more exactly on their limitations when applied to a precise case study (quenching). Secondly, one needs to understand how to combine advanced model and data driven technologies to improve the knowledge of the physics and the added value of machine learning depending the available data.

Unlike in image processing for example, for many complex scientific and engineering problems there is usually a limited availability of experimental data and for this reason using data driven machine learning (ML) tools and algorithms (working under the assumption of the availability of a large amount of data) is not an option. For this reason, a new paradigm has emerged recently giving rise to a new scientific field, i.e. physics informed machine learning (PIML) consisting in a combination of the physical models, small data and machine learning tools.

Taking into account the knowledge of the physical models, in this case we need high-fidelity data but smaller amount in comparison with only data driven ML. On the other side, we need physical models which will reinforce the learning. Based on the common numerical experience we have two types of physical (mathematical) models: (i) high confidence ones - given with high confidence due to "simple" procedures to obtain them. (ii) limited confidence ones - are very complex to obtain. These are empirical and semi-empirical models (e.g. nucleation sides density). Their behaviour might be of chaotic nature. Physical models of high confidence class are directly applicable to reinforce ML and should be fully respected by the predictions and learning algorithms. The physical models with limited confidence can be used for the ML reinforcement but can be violated (even by 50%). The limited confidence physical models can be further studied using mathematical modelling, experiments and possibly machine learning itself. As an example, the Euler-Euler approach to multiphase flows gives a good base for PIML. It provides a large number of physical models which can be used for ML but a large number of them would be classified to be applicable with limited confidence.

In this project we would like to apply these ideas to quenching in order to improve the overall mathematical and numerical models using available data, empirical laws but also existing models. This relies on the fact that current models are based primarily on experimental observations. Those models need extra parameters, such as minimum and maximum bubble diameter, reference temperature, material properties, surface angle, etc. The existing models therefore lack generality and are developed for specific conditions, e.g. high pressures.

In the whole process, besides the practical aspect, methodological aspects will be tackled/improved, i.e. numerical modelling of non-linear PDEs, fast solution methods in the optimisation process, test of different neural networks their combination with reduced order modelling for non-linear problems (which remains a challenge).