Finite element network analysis: A machine learning based computational framework for the simulation of physical systems

摘要

This paper introduces the concept of finite element network analysis (FENA) which is a physics-informed, machine-learning-based, computational framework for the simulation of physical systems. The framework leverages the extreme computational speed of trained neural networks and the unique transfer knowledge property of bidirectional recurrent neural networks (BRNN) to provide a uniquely powerful and flexible computing platform. One of the most remarkable properties of this framework consists in its ability to simulate the response of physical systems, made of multiple interconnected components, by combining individually pre-trained network models that do not require any further training following the assembly phase. This remarkable result is achieved via the use of key concepts such as transfer knowledge and network concatenation. Although the computational framework is illustrated and numerically validated for the case of a 1D elastic bar under static loading, the conceptual structure of the framework is extremely general and it suggests potential extensions to a broad spectrum of applications in computational science. The framework is numerically validated against the solution provided by traditional finite element analysis and the results highlight the outstanding performance of this new concept of computational platform. (C) 2021 Elsevier Ltd. All rights reserved.