  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.
