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2 2021

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Using FreeFEM open software for modelling the vibrations of piezoelectric devices

Moszyński Marek

Vibrations in Physical Systems

2021

Vol. 32, nr 1

art. no. 2021112

Modelling vibrations of piezoelectric transducers has been a topic discussed in the literature for many decades. The first models - so-called one-dimensional - describe the vibrations only near operating frequency and near its harmonics. Attempts to introduce two-dimensional models were related to the possibility of one transducer working at several frequencies, including both thickness vibrations and those resulting from the transducer horizontal dimensions. In recent decades, thanks to the use of the finite element method and its derivatives, and the progress related to the increase in processor speed and memory availability, the implementation of models based on three-dimensional modelling is possible using software on personal computers. As the implementation of finite element method algorithms is characterized by high complexity, several professional software packages have been created on the commercial market, among which only a few implement the piezoelectric equations. In this context, this article presents how to use open source software along with developed programming language for intuitive definition of piezoelectric equations and its solution.

Physics-guided neural networks (PGNNs) to solve differential equations for spatial analysis

Borzyszkowski Bartłomiej, Damaszke Karol, Romankiewicz Jakub, Świniarski Marcin, Moszyński Marek

Bulletin of the Polish Academy of Sciences. Technical Sciences

2021

Vol. 69, nr 6

art. no. e139391

Numerous examples of physically unjustified neural networks, despite satisfactory performance, generate contradictions with logic and lead to many inaccuracies in the final applications. One of the methods to justify the typical black-box model already at the training stage involves extending its cost function by a relationship directly inspired by the physical formula. This publication explains the concept of Physics-guided neural networks (PGNN), makes an overview of already proposed solutions in the field and describes possibilities of implementing physics-based loss functions for spatial analysis. Our approach shows that the model predictions are not only optimal but also scientifically consistent with domain specific equations. Furthermore, we present two applications of PGNNs and illustrate their advantages in theory by solving Poisson’s and Burger’s partial differential equations. The proposed formulas describe various real-world processes and have numerous applications in the area of applied mathematics. Eventually, the usage of scientific knowledge contained in the tailored cost functions shows that our methods guarantee physics-consistent results as well as better generalizability of the model compared to classical, artificial neural networks.