Theory-inspired machine learning—towards a synergy between knowledge and data

Abstract

Most engineering domains abound with models derived from first principles that have beenproven to be effective for decades. These models are not only a valuable source of knowledge, but they also form the basis of simulations. The recent trend of digitization has complemented these models with data in all forms and variants, such as process monitoring time series, measured material characteristics, and stored production parameters. Theory-inspired machine learning combines the available models and data, reaping the benefits of established knowledge and the capabilities of modern, data-driven approaches. Compared to purely physics- or purely data-driven models, the models resulting from theory-inspired machine learning are often more accurate and less complex, extrapolate better, or allow faster model training or inference. In this short survey, we introduce and discuss several prominent approaches to theory-inspired machine learning and show how they were applied in the fields of welding, joining, additive manufacturing, and metal forming.

Machine Learning and Meteorological Normalization for Assessment of Particulate Matter Changes during the COVID-19 Lockdown in Zagreb, Croatia

“…In the future, the authors aim to shift the focus towards PM composition and source apportionment regarding changes during the lockdown which helps understand the contributions. Furthermore, the authors intend to apply recent in-house research on the intersection of physics-based and machine learning based models (so call physics-inspired machine learning) such as seen in recent research [ 45 , 74 ] where models’ accuracy profits from the combination of the two worlds.…”

A unified ML framework for solubility prediction across organic solvents

“…This work refers to mechanistic, data-driven and hybrid modelling – it is worth noting the meaning of this terminology. Mechanistic modelling refers to descriptions of phenomena in a system based on theory and first principles: 5 in the context of solubility, mechanistic models are generally derived from the laws of thermodynamics. In contrast, data-driven approaches do not innately carry the context of their applied domain, instead fitting a general form to a set of input data to create a model that can be re-applied: linear regression is one of the simplest examples, but this also captures ML methods.…”

A PINN approach for traffic state estimation and model calibration based on loop detector flow data

“…Our neural network is fully connected feed-forward consisting of 8 hidden layers with 20 neurons in each layer, with tanh as the activation function. The activation functions and the connecting structure of neurons in the PINN are designed to conduct the differential operations in (2), see [5, Fig. 1] for a visual representation of the employed PINN architecture.…”

“…Physics-informed neural networks (PINNs) have recently been introduced as an alternative method of solving nonlinear differential equations [1], [2]. Compared to purely physics-or purely data-driven models, this approach allows to combine data and physical constraints in the same computing framework.…”