Regularising NARX models with multi-task learning

A Nonlinear Auto-Regressive with eXogenous inputs (NARX) model can be used to describe time-varying processes; where the output depends on both previous outputs and current/previous external input variables. One limitation of NARX models is their propensity to overfit and result in poor generalisation for future predictions. The proposed method to help to overcome the issue of overfitting is a NARX model which predicts outputs at both the current time and several lead times into the future. This is a form of multi-task learner (MTL); whereby the lead time outputs will regularise the current time output. This work shows that for high noise level, MTL can be used to regularise NARX with a lower Normalised Mean Square Error (NMSE) compared to the NMSE of the independent learner counterpart.

When is an SHM problem a Multi-Task-Learning problem?

Multi-task neural networks learn tasks simultaneously to improve individual task performance. There are three mechanisms of multi-task learning (MTL) which are explored here for the context of structural health monitoring (SHM): (i) the natural occurrence of multiple tasks; (ii) using outputs as inputs (both linked to the recent research in population-based SHM (PBSHM)); and, (iii) additional loss functions to provide different insights. Each of these problem settings for MTL is detailed and an example is given.