Data-driven modelling of dynamical systems from data streams
Creators: name: Falconer, Stephen
Publisher: name: University of Surrey
Year: 2024

description: In the modern era, most systems of interest are too complex to be amenable to traditional deriv-
description: ations from first principles. As such, data-driven methods have experienced a surge in popularity,
description: and are revolutionizing the way we model, predict and control dynamical systems Many of these
description: data-driven methods employ neural networks within their architecture, which undergo a compu-
description: tationally expensive training phase to optimize a model over a fixed dataset. Dynamical systems
description: however are often continuously generating new data in the form of a data stream, and to maintain
description: the most accurate and up-to-date models, this new data must be incorporated in some way into
description: the model. Regularly retraining the model is often computationally infeasible, hence there is a need
description: for techniques capable of efficiently modelling dynamical systems directly from data streams.<br>
description: <br>
description: Existing methods for modelling linear dynamical systems from data streams often adapt the
description: existing data-driven modelling technique dynamic mode decomposition (DMD), and adapt it for
description: the streaming data case. These methods often suffer from either developing models that are
description: insensitive to information in new measurements and unable to track a changing system, or being
description: overly responsive to new data and hence highly unstable in the presence of measurement noise. We
description: show how DMD can be combined with the data assimilation technique ensemble Kalman filtering
description: (EnKF), in what we refer to as the DMDEnKF, to effectively update the current state and model
description: estimates of a system as new data becomes available. We demonstrate that this approach is able
description: to track time varying dynamical systems in synthetic examples, and when applied to real world
description: seasonal influenza-like illness data from the USA Centers for Disease Control and Prevention, find
description: the DMDEnKF’s performance in short-term forecasting to be comparable to the best mechanistic
description: models in the ILINet competition.<br>
description: <br>
description: Many dynamical systems of interest are nonlinear, so when modelling these systems DMD
description: based frameworks have limited applicability, as they produce linear models. Data-driven modelling
description: techniques exist for nonlinear dynamical systems, however they are limited by poor dimensional
description: scaling, high sensitivity to abstract user-specified parameters, or being difficult to train. One such
description: method is the Koopman autoencoder, which generates a low-dimensional latent space and model
description: of a nonlinear system directly from data. We propose small alterations to Koopman autoencoders
description: to make them easier to train, then show how their reduced order latent space and model of the
description: system can be efficiently updated as new data becomes available using the EnKF, in a technique
description: we call the KAE EnKF. We demonstrate this approach is able to effectively track and forecast
description: time-varying, nonlinear dynamical systems in synthetic examples. We then apply the KAE EnKF
description: to a real video of a pendulum, and achieve a significant improvement over current state-of-the-art
description: methods, in generating effective latent space reconstructions, accurate short-term forecasts, and
description: efficient adaptations to externally forced changes to the pendulum’s frequency.<br>