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Data-driven approaches achieve remarkable results for modeling nonlinear electromechanical systems based on collected data. However, these models often neglect basic physical principles which determine the behavior of any real-world system. This omission is unfavorable in two ways: The models are not as data-efficient as they could be by incorporating physical prior knowledge, and the model itself might not be physically correct. 

In this talk, I will present our results on physics-enhanced Gaussian processes for learning of dynamical system with a focus on the class of electromechanical systems. I will propose Gaussian Process Port-Hamiltonian systems (GP-PHS) as a physics-informed, nonparametric Bayesian learning approach with uncertainty quantification. In contrast to many physics-informed techniques that impose physics by penalty, the proposed data-driven model is physically correct by design. The Bayesian nature of GP-PHS uses collected data to form a distribution over all possible Port-Hamiltonian systems instead of a single point estimate. The framework is in particular suitable for composable learning as its structure can be preserved under interconnection. Finally, the model can be used in a robust control setting to establish safe learning-based control.

Deep neural state-space models (SSMs) provide a powerful tool for modeling dynamical systems solely using operational data. Typically, neural SSMs are trained using data collected from the actual system under consideration, despite the likely existence of operational data from similar systems which have previously been deployed in the field. In this paper, we propose the use of model-agnostic meta-learning (MAML) for constructing deep encoder network-based SSMs, by leveraging a combination of archived data from similar systems (used to meta-train offline) and limited data from the actual system (used for rapid online adaptation). We demonstrate using numerical examples that meta-learning can result in more accurate neural SSM models than supervised- or transfer-learning, despite few adaptation steps and limited online data. We show that by surgically fine-tuning layers within the neural operator, we can achieve comparable performance to MAML while reducing online adaptation complexity. Furthermore, we demonstrate how one can employ meta-learning while incorporating physics-informed constraints, with use-cases from energy systems and buildings.

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The confluence of traditional system identification techniques with more modern machine learning based ones affords new opportunities for making the data-driven modeling techniques work well for industry-scale problems. Going beyond the physics-informed networks, our objective is to create engineering-friendly models. These are the models that not only facilitate the incorporation of physical knowledge, but are also easy to learn, and easy to augment, reduce or adapt to changing conditions. They are often no more complex than what the end use demands. They are also readily usable for control design and rapid prototyping. 

We present the latest developments in MATLAB that enable the creation of engineering-friendly models and their deployment in model-based design (MBD) workflows. We show functions and apps that facilitate this activity using MATLAB, Simulink®, System Identification Toolbox™, Deep Learning Toolbox™, Statistics and Machine Learning Toolbox™, and other related products.  

Accurate and efficient nonlinear dynamical systems models are essential understand, predict, estimate, and control complex natural and engineered systems.  In this talk, I will explore how machine learning may be used to develop these models purely from measurement data.  We explore the sparse identification of nonlinear dynamics (SINDy) algorithm, which identifies a minimal dynamical system model that balances model complexity with accuracy, avoiding overfitting.  This approach tends to promote models that are interpretable and generalizable, capturing the essential “physics” of the system.  We also discuss the importance of learning effective coordinate systems in which the dynamics may be expected to be sparse. This sparse modeling approach will be demonstrated on a range of challenging modeling and control problems, for example in fluid dynamics.