  We propose a novel surrogate modelling approach to efficiently and accurately
approximate the response of complex dynamical systems driven by time-varying
exogenous excitations over extended time periods. Our approach, namely manifold
nonlinear autoregressive modelling with exogenous input (mNARX), involves
constructing a problem-specific exogenous input manifold that is optimal for
constructing autoregressive surrogates. The manifold, which forms the core of
mNARX, is constructed incrementally by incorporating the physics of the system,
as well as prior expert- and domain- knowledge. Because mNARX decomposes the
full problem into a series of smaller sub-problems, each with a lower
complexity than the original, it scales well with the complexity of the
problem, both in terms of training and evaluation costs of the final surrogate.
Furthermore, mNARX synergizes well with traditional dimensionality reduction
techniques, making it highly suitable for modelling dynamical systems with
high-dimensional exogenous inputs, a class of problems that is typically
challenging to solve. Since domain knowledge is particularly abundant in
physical systems, such as those found in civil and mechanical engineering,
mNARX is well suited for these applications. We demonstrate that mNARX
outperforms traditional autoregressive surrogates in predicting the response of
a classical coupled spring-mass system excited by a one-dimensional random
excitation. Additionally, we show that mNARX is well suited for emulating very
high-dimensional time- and state-dependent systems, even when affected by
active controllers, by surrogating the dynamics of a realistic
aero-servo-elastic onshore wind turbine simulator. In general, our results
demonstrate that mNARX offers promising prospects for modelling complex
dynamical systems, in terms of accuracy and efficiency.
