Finite Element Network Analysis: A Machine Learning based Computational Framework for the Simulation of Physical Systems

Abstract

This study introduces the concept of finite element network analysis (FENA) which is a physics-informed, machine-learning-based, computational framework for the simulation of complex 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 complex 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 mechanical system under static loading, the conceptual structure of the framework has broad applicability and could be extended to the most diverse field of 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.