Related papers: Learning functions, operators and dynamical system…
In this article, we develop a kernel-based framework for constructing dynamic, pathdependent trading strategies under a mean-variance optimisation criterion. Building on the theoretical results of (Muca Cirone and Salvi, 2025), we…
We employ so-called quantum kernel estimation to exploit complex quantum dynamics of solid-state nuclear magnetic resonance for machine learning. We propose to map an input to a feature space by input-dependent Hamiltonian evolution, and…
The role of response operators is well established in quantum mechanics. We investigate their use for universal quantum machine learning models of response properties in molecules. After introducing a theoretical basis, we present and…
The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics. While recent deep learning approaches have been useful in…
In this paper, we push forward the idea of machine learning systems whose operators can be modified and fine-tuned for each problem. This allows us to propose a learning paradigm where users can write (or adapt) their operators, according…
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…
We review recent studies dealing with the generation of machine learning models of molecular and solid properties. The models are trained and validated using standard quantum chemistry results obtained for organic molecules and materials…
Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently proposed method MEKA (Si et al., 2014) effectively employs two common assumptions in Hilbert spaces: the low-rank property of an…
A systematic mathematical framework for the study of numerical algorithms would allow comparisons, facilitate conjugacy arguments, as well as enable the discovery of improved, accelerated, data-driven algorithms. Over the course of the last…
An adaptive observer is designed for online estimation of Hilbert-Schmidt operators from online measurement of the state for some class of nonlinear infinite-dimensional dynamical systems. Convergence is ensured under detectability and…
Learning mappings between infinite-dimensional function spaces has achieved empirical success in many disciplines of machine learning, including generative modeling, functional data analysis, causal inference, and multi-agent reinforcement…
Data-driven spectral analysis of Koopman operators is a powerful tool for understanding numerous real-world dynamical systems, from neuronal activity to variations in sea surface temperature. The Koopman operator acts on a function space…
Kernel methods are powerful for machine learning, as they can represent data in feature spaces that similarities between samples may be faithfully captured. Recently, it is realized that machine learning enhanced by quantum computing is…
Improvement of statistical learning models in order to increase efficiency in solving classification or regression problems is still a goal pursued by the scientific community. In this way, the support vector machine model is one of the…
Learning-based simulators show great potential for simulating particle dynamics when 3D groundtruth is available, but per-particle correspondences are not always accessible. The development of neural rendering presents a new solution to…
This is a survey article on Mercer's Theorem in its most general form and its relations with the theory of reproducing kernel Hilbert spaces and the spectral theory of compact operators. We provide a modern introduction to the basics of the…
This article develops iterative machine learning (IML) for output tracking. The input-output data generated during iterations to develop the model used in the iterative update. The main contribution of this article to propose the use of…
The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynamical information from a partial observation; and then…
Obtaining reliable, adaptive confidence sets for prediction functions (hypotheses) is a central challenge in sequential decision-making tasks, such as bandits and model-based reinforcement learning. These confidence sets typically rely on…
Current meta-learning approaches focus on learning functional representations of relationships between variables, i.e. on estimating conditional expectations in regression. In many applications, however, we are faced with conditional…