Physics-informed Machine Learning approaches for Structural Dynamics problems

In current times, Machine Learning has pervaded into every aspect of society. This also includes modern research activities. The classical approach to solving a structural dynamics problem is to utilise a time integration method involving time steps. The method has a large sensitivity to the choice of the time step thereby indicating loss of accuracy when utilising a large time step and an increase in computational power requirements when the time step is small. Thus, Machine Learning techniques are being utilised in order to mitigate the above stated problem. Physics-informed Machine Learning techniques have turned out to be quite promising as they help to combine both physical laws and constraints into the model apart from also considering any available measurement data. These approaches are favoured over traditional data-driven models which require substantial amounts of data that take considerable time and effort to gather and prepare. Physics-informed Machine Learning models have been proposed here to solve three distinct problems: (i) the Equation of Motion for a Structural Dynamics problem, (ii) identification of model parameters of the system given output measurements and (iii) identification of input forces on the system knowing the output responses. Compared to data-driven approaches which heavily depend on data, the Physics-informed approach applied to problem (i), can solve the problem in the absence of any data. The Physics-informed Machine Learning models have also been compared to their traditional counterparts and the computational efficiency of each has also been evaluated. Results indicate a good agreement with the traditional solutions.