The modeling and identification of dynamical systems is of great importance in a large range of domains including physics, engineering, biology, and chemistry. Applications range from model-based control of autonomous systems and perception of dynamical objects to the understanding of complex reaction processes in chemical reactors. Whereas classical models of physical systems are typically based on first principles, there is a recent shift to more data-driven modeling of complex dynamics to capture more details in a more efficient manner. However, this paradigmatic shift introduces new questions regarding the efficiency, interpretability, and physical correctness of the model, that is, the learned model respects physical principles such as preservation of the constraints, volume, and energy. Including physical principles in a data-driven approach is beneficial in several ways: the models are meaningful as they respect the postulates of physics, come with increased interpretability, and can be more data-efficient as satisfaction of physical axioms, which results in a meaningful inductive bias for the outputs of the model. Data-driven models require only minimal prior knowledge to model complex dynamics, and they are not limited to a finite set of parameters, as happens with typical system identification methods.
Probably, the most widely studied data-driven technique for modeling dynamical systems, together with Gaussian Mixture Models and Hidden Markov Models, is the theory of Gaussian Processes (GPs) due to its characteristic of describing the dynamics with small training datasets and high probabilities. This technique is based on Bayesian methods. The Bayesian methodology is a probabilistic construction allowing the combination of new information with existent information: by using Bayes’ theorem, current knowledge is combined with the information of new data to improve the knowledge. An alternative to the Bayesian approach for learning-based modeling of dynamical systems is the use of Neural Networks (NNs) and Reinforce Learning (RL). In the last years there were advances on the use of RL to learn dynamical systems and design controllers driven by data. Nevertheless, for complex nonlinear dynamics as the coordinated motion of multiple mechanical systems, the training with RL does not provide an uncertainty quantification of the prediction outputs and can have difficulty generalizing from sparse data. For this reason, in this mini course we focus on modeling with Gaussian Process Regression (GPR), a supervised learning technique based on GPs, so that the online learning provides a quantified uncertainty of the prediction and also provides training and update of predictions in real time in comparison with classical NNs and RL. This uncertainty calculation is very valuable because it provides probabilistic safety guarantees for the system, that is, it provides probabilistic error bounds for the predictions using GPs that can be used, for instance, as ultimate bounds for the tracking error of autonomous vehicles to reach a desired trajectory wichi is the main application we will explore in the mini course.
Schedule to be defined
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