Physics-Enhanced Machine Learning: a position paper for dynamical systems investigations

This position paper takes a broad look at Physics-Enhanced Machine Learning (PEML) -- also known as Scientific Machine Learning -- with particular focus to those PEML strategies developed to tackle dynamical systems' challenges. The need to go beyond Machine Learning (ML) strategies is driven by: (i) limited volume of informative data, (ii) avoiding accurate-but-wrong predictions; (iii) dealing with uncertainties; (iv) providing Explainable and Interpretable inferences. A general definition of PEML is provided by considering four physics and domain knowledge biases, and three broad groups of PEML approaches are discussed: physics-guided, physics-encoded and physics-informed. The advantages and challenges in developing PEML strategies for guiding high-consequence decision making in engineering applications involving complex dynamical systems, are presented.

A switching Gaussian process latent force model for the identification of mechanical systems with a discontinuous nonlinearity

An approach for the identification of discontinuous and nonsmooth nonlinear forces, as those generated by frictional contacts, in mechanical systems that can be approximated by a single-degree-of-freedom model is presented. To handle the sharp variations and multiple motion regimes introduced by these nonlinearities in the dynamic response, the partially-known physics-based model and noisy measurements of the system's response to a known input force are combined within a switching Gaussian process latent force model (GPLFM). In this grey-box framework, multiple Gaussian processes are used to model the unknown nonlinear force across different motion regimes and a resetting model enables the generation of discontinuities. The states of the system, nonlinear force and regime transitions are inferred by using filtering and smoothing techniques for switching linear dynamical systems. The proposed switching GPLFM is applied to a simulated dry friction oscillator and an experimental setup consisting in a single-storey frame with a brass-to-steel contact. Excellent results are obtained in terms of the identified nonlinear and discontinuous friction force for varying: (i) normal load amplitudes in the contact; (ii) measurement noise levels and (iii) number of samples in the datasets. Moreover, the identified states, friction force and sequence of motion regimes are used for evaluating: (1) uncertain system parameters; (2) the friction force-velocity relationship and (3) the static friction force. The correct identification of the discontinuous nonlinear force and the quantification of any remaining uncertainty in its prediction enable the implementation an accurate forward model able to predict the system's response to different input forces.

Natural Language Processing for Systems Engineering: Automatic Generation of Systems Modelling Language Diagrams

The design of complex engineering systems is an often long and articulated process that highly relies on engineers' expertise and professional judgment. As such, the typical pitfalls of activities involving the human factor often manifest themselves in terms of lack of completeness or exhaustiveness of the analysis, inconsistencies across design choices or documentation, as well as an implicit degree of subjectivity. An approach is proposed to assist systems engineers in the automatic generation of systems diagrams from unstructured natural language text. Natural Language Processing (NLP) techniques are used to extract entities and their relationships from textual resources (e.g., specifications, manuals, technical reports, maintenance reports) available within an organisation, and convert them into Systems Modelling Language (SysML) diagrams, with particular focus on structure and requirement diagrams. The intention is to provide the users with a more standardised, comprehensive and automated starting point onto which subsequently refine and adapt the diagrams according to their needs. The proposed approach is flexible and open-domain. It consists of six steps which leverage open-access tools, and it leads to an automatic generation of SysML diagrams without intermediate modelling requirement, but through the specification of a set of parameters by the user. The applicability and benefits of the proposed approach are shown through six case studies having different textual sources as inputs, and benchmarked against manually defined diagram elements.

Cyclical Variational Bayes Monte Carlo for Efficient Multi-Modal Posterior Distributions Evaluation

Statistical model updating is frequently used in engineering to calculate the uncertainty of some unknown latent parameters when a set of measurements on observable quantities is given. Variational inference is an alternative approach to sampling methods that has been developed by the machine learning community to estimate posterior approximations through an optimization approach. In this paper, the Variational Bayesian Monte Carlo (VBMC) method is investigated with the purpose of dealing with statistical model updating problems in engineering involving expensive-to-run models. This method combines the active-sampling Bayesian quadrature with a Gaussian-process based variational inference to yield a non-parametric estimation of the posterior distribution of the identified parameters involving few runs of the expensive-to-run model. VBMC can also be used for model selection as it produces an estimation of the model's evidence lower bound. In this paper, a variant of the VBMC algorithm is developed through the introduction of a cyclical annealing schedule into the algorithm. The proposed cyclical VBMC algorithm allows to deal effectively with multi-modal posteriors by having multiple cycles of exploration and exploitation phases. Four numerical examples are used to compare the standard VBMC algorithm, the monotonic VBMC, the cyclical VBMC and the Transitional Ensemble Markov Chain Monte Carlo (TEMCMC). Overall, it is found that the proposed cyclical VBMC approach yields accurate results with a very reduced number of model runs compared to the state of the art sampling technique TEMCMC. In the presence of potential multi-modal problems, the proposed cyclical VBMC algorithm outperforms all the other approaches in terms of accuracy of the resulting posterior.

Machine Learning based optimization for interval uncertainty propagation with application to vibro-acoustic models

Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These approaches employ a machine learning based optimization strategy, the so-called Bayesian optimization, for evaluating the upper and lower bounds of a generic response variable over the set of possible responses obtained when each interval variable varies independently over its range. The lack of knowledge caused by not evaluating the response function for all the possible combinations of the interval variables is accounted for by developing a probabilistic description of the response variable itself by using a Gaussian Process regression model. An iterative procedure is developed for selecting a small number of simulations to be evaluated for updating this statistical model by using well-established acquisition functions and to assess the response bounds. In both approaches, an initial training dataset is defined. While one approach builds iteratively two distinct training datasets for evaluating separately the upper and lower bounds of the response variable, the other builds iteratively a single training dataset. Consequently, the two approaches will produce different bound estimates at each iteration. The upper and lower bound responses are expressed as point estimates obtained from the mean function of the posterior distribution. Moreover, a confidence interval on each estimate is provided for effectively communicating to engineers when these estimates are obtained for a combination of the interval variables for which no deterministic simulation has been run. Finally, two metrics are proposed to define conditions for assessing if the predicted bound estimates can be considered satisfactory.