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Deep learning continues to revolutionize an ever-growing number of critical application areas including healthcare, transportation, finance, and basic sciences. Despite their increased predictive power, model transparency and human…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
Branchable databases are evolving from developer tools to infrastructure for agentic workloads characterized by speculative mutations and non-linear state exploration. Traditional RDBMS mechanisms such as nested transactions do not provide…
Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure.…
Design, control, and estimation for dynamic systems require accurate and analytically tractable models. However, modern engineered systems contain components that are described with heterogeneous modeling paradigms, as well as subsystems…
Big data and machine learning are driving comprehensive economic and social transformations and are rapidly re-shaping the toolbox and the methodologies of applied scientists. Machine learning tools are designed to learn functions from data…
Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…
The increasing availability of data and advancements in computational intelligence have accelerated the adoption of data-driven methods (DDMs) in product development. However, their integration into product development remains fragmented.…
Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…
Recently, there has been a growing interest in applying machine learning methods to problems in engineering mechanics. In particular, there has been significant interest in applying deep learning techniques to predicting the mechanical…
Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such…
Representing and predicting high-dimensional and spatiotemporally chaotic dynamical systems remains a fundamental challenge in dynamical systems and machine learning. Although data-driven models can achieve accurate short-term forecasts,…
Tabular foundation models such as TabPFN and TabICL already produce full predictive distributions, yet prevailing regression benchmarks evaluate them almost exclusively via point-estimate metrics (RMSE, $R^2$). This discards precisely the…
Deep learning has revolutionized medical image analysis, playing a vital role in modern clinical applications. However, the deployment of large-scale models in real-world clinical settings remains challenging due to high computational…
With the rapid development of more complex robots, Fault Detection and Diagnosis (FDD) becomes increasingly harder. Especially the need for predetermined models and historic data is problematic because they do not encompass the dynamic and…
Composable AI offers a scalable and effective paradigm for tackling complex AI tasks by decomposing them into sub-tasks and solving each sub-task using ready-to-use well-trained models. However, systematically evaluating methods under this…
While the disciplines of physics and engineering sciences in many cases have taken advantage from accurate time-series prediction of system behaviour by applying ordinary differential equation systems upon precise basic physical laws such…
Engineering design optimization seeks to automatically determine the shapes, topologies, or parameters of components that maximize performance under given conditions. This process often depends on physics-based simulations, which are…
Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…
Physics-informed deep learning models have emerged as powerful tools for learning dynamical systems. These models directly encode physical principles into network architectures. However, systematic benchmarking of these approaches across…