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Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide…
Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…
Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work,…
Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…
Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as…
This paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller. The Koopman operator allows a nonlinear system to be rewritten as an infinite-dimensional linear system by viewing it in…
The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…
Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…
In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian…
In this paper, a novel Koopman-type inverse operator for linear time-invariant non-minimum phase systems with stochastic disturbances is proposed. This operator employs functions of the desired output to directly calculate the input.…
Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…
In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In…
This work presents a data-driven Koopman operator-based modeling method using a model averaging technique. While the Koopman operator has been used for data-driven modeling and control of nonlinear dynamics, it is challenging to accurately…
We propose a new approach to inverse reinforcement learning (IRL) based on the deep Gaussian process (deep GP) model, which is capable of learning complicated reward structures with few demonstrations. Our model stacks multiple latent GP…
Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in…
Reinforcement Learning (RL) has made significant strides in various domains, and policy gradient methods like Proximal Policy Optimization (PPO) have gained popularity due to their balance in performance, training stability, and…
Koopman operator theory has found significant success in learning models of complex, real-world dynamical systems, enabling prediction and control. The greater interpretability and lower computational costs of these models, compared to…
Koopman operator theory provides a powerful framework for representing nonlinear dynamics through a linear operator acting on lifted observables, enabling the use of linear control techniques for nonlinear systems. However, Koopman models…
Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are probabilistic and non-parametric…
Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…