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Koopman operator theory has emerged as a leading data-driven approach that relies on a judicious choice of observable functions to realize global linear representations of nonlinear systems in the lifted observable space. However,…

In this paper we present a discussion of the basic aspects of the well-known problem of prediction and inference in physics, with specific attention to the role of models, the use of data and the application of recent developments in…

Neural operators have proven to be a promising approach for modeling spatiotemporal systems in the physical sciences. However, training these models for large systems can be quite challenging as they incur significant computational and…

This thesis makes considerable contributions to the realm of machine learning, specifically in the context of open-world scenarios where systems face previously unseen data and contexts. Traditional machine learning models are usually…

Constrained mechanical systems occur in many applications, such as modeling of robots and other multibody systems. In this case, the motion is governed by a system of differential-algebraic equations (DAE), often with large and sparse…

The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…

Thanks to novel, powerful brain activity recording techniques, we can create data-driven models from thousands of recording channels and large portions of the cortex, which can improve our understanding of brain-states neuromodulation and…

Deep neural networks, and in particular recurrent networks, are promising candidates to control autonomous agents that interact in real-time with the physical world. However, this requires a seamless integration of temporal features into…

Neural operators have emerged as powerful tools for learning nonlinear mappings between function spaces, enabling real-time prediction of complex dynamics in diverse scientific and engineering applications. With their growing adoption in…

In data-driven modelling of complex dynamic processes, it is often desirable to combine different classes of models to enhance performance. Examples include coupled models of different fidelities, or hybrid models based on physical…

In this paper, we propose a novel algorithm for learning the Koopman operator of a dynamical system from a \textit{small} amount of training data. In many applications of data-driven modeling, e.g. biological network modeling,…

Learning identifiable representations and models from low-level observations is helpful for an intelligent spacecraft to complete downstream tasks reliably. For temporal observations, to ensure that the data generating process is provably…

Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable…

Standard machine learning is unable to accommodate inputs which do not belong to the training distribution. The resulting models often give rise to confident incorrect predictions which may lead to devastating consequences. This problem is…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

It is a growing direction to utilize unintended memorization in ML models to benefit real-world applications, with recent efforts like user auditing, dataset ownership inference and forgotten data measurement. Standing on the point of ML…

To predict rare extreme events using deep neural networks, one encounters the so-called small data problem because even long-term observations often contain few extreme events. Here, we investigate a model-assisted framework where the…

Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…