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Many recent efforts have been devoted to designing sophisticated deep learning structures, obtaining revolutionary results on benchmark datasets. The success of these deep learning methods mostly relies on an enormous volume of labeled…
Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional…
Generalization is one of the fundamental issues in machine learning. However, traditional techniques like uniform convergence may be unable to explain generalization under overparameterization. As alternative approaches, techniques based on…
Quantum sensors offer significant advantages over classical devices in spatial resolution and sensitivity, enabling transformative applications across materials science, healthcare, and beyond. Their practical performance, however, is often…
Physics-based and data-driven models for remaining useful lifetime (RUL) prediction typically suffer from two major challenges that limit their applicability to complex real-world domains: (1) incompleteness of physics-based models and (2)…
Physics-informed machine learning is gaining significant traction for enhancing statistical performance and sample efficiency through the integration of physical knowledge. However, current theoretical analyses often presume complete prior…
Model transformation tools assist system designers by reducing the labor--intensive task of creating and updating models of various aspects of systems, ensuring that modeling assumptions remain consistent across every model of a system, and…
The unprecedented amount of data generated from experiments, field observations, and large-scale numerical simulations at a wide range of spatio-temporal scales have enabled the rapid advancement of data-driven and especially deep learning…
Modern software systems are built to be used in dynamic environments using configuration capabilities to adapt to changes and external uncertainties. In a self-adaptation context, we are often interested in reasoning about the performance…
Operating complex real-world systems, such as soft robots, can benefit from precise predictive control schemes that require accurate state and model knowledge. This knowledge is typically not available in practical settings and must be…
Energy systems optimisation models are a leading tool for informing decisions in the energy transition. However, these models often remain opaque, and results are frequently presented without a clear discussion of their epistemic…
Deep Foundation Models (DFMs) offer unprecedented capabilities but their increasing complexity presents profound challenges to understanding their internal workings-a critical need for ensuring trust, safety, and accountability. As we…
In real-world scenarios, achieving domain adaptation and generalization poses significant challenges, as models must adapt to or generalize across unknown target distributions. Extending these capabilities to unseen multimodal…
Machine learning models that can generalize to unseen domains are essential when applied in real-world scenarios involving strong domain shifts. We address the challenging domain generalization (DG) problem, where a model trained on a set…
Recent physics foundation models claim general spatiotemporal forecasting ability, yet their evaluations often collapse performance into a single average score under a fixed training distribution. This makes it difficult to determine…
We study the fundamental problem of learning an unknown object from data using a prescribed model class. We introduce a unified framework that accommodates objects in arbitrary Hilbert spaces, general (possibly vector-valued) random linear…
Climate simulations, at all grid resolutions, rely on approximations that encapsulate the forcing due to unresolved processes on resolved variables, known as parameterizations. Parameterizations often lead to inaccuracies in climate models,…
Climate models play a critical role in understanding and projecting climate change. Due to their complexity, their horizontal resolution of about 40-100 km remains too coarse to resolve processes such as clouds and convection, which need to…
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…
In recent years, machine learning (ML) has become a key enabling technology for the sciences and industry. Especially through improvements in methodology, the availability of large databases and increased computational power, today's ML…