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Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…

This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a differential advection operator and an integral collision…

We propose a kernel compression method for solving Distributed-Order (DO) Fractional Partial Differential Equations (DOFPDEs) at the cost of solving corresponding local-in-time PDEs. The key concepts are (1) discretization of the integral…

The goal of motion tomography is to recover a description of a vector flow field using information on the trajectory of a sensing unit. In this paper, we develop a predictor corrector algorithm designed to recover vector flow fields from…

In this paper, we introduce the Spectral Coefficient Learning via Operator Network (SCLON), a novel operator learning-based approach for solving parametric partial differential equations (PDEs) without the need for data harnessing. The…

Object segmentation is a key component in the visual system of a robot that performs tasks like grasping and object manipulation, especially in presence of occlusions. Like many other computer vision tasks, the adoption of deep…

The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…

We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…

Gaussian processes (GPs) are powerful probabilistic models that define flexible priors over functions, offering strong interpretability and uncertainty quantification. However, GP models often rely on simple, stationary kernels which can…

Estimating the dissipativity of nonlinear systems from empirical data is useful for the analysis and control of nonlinear systems, especially when an accurate model is unavailable. Based on a Koopman operator model of the nonlinear system…

We study post-training interpretability for Support Vector Machines (SVMs) built from truncated orthogonal polynomial kernels. Since the associated reproducing kernel Hilbert space is finite-dimensional and admits an explicit tensor-product…

A generalisation of Takens' delay-coordinate embedding theorem to stochastic systems, the Stochastic Embedding Sufficiency Theorem, is an inverse methodology enabling non-parametric recovery of both drift and diffusion fields from scalar…

We present several generative and predictive algorithms based on the RKHS (reproducing kernel Hilbert spaces) methodology, which, most importantly, are scale up efficiently with large datasets or high-dimensional data. It is well recognized…

This work considers stochastic optimization problems in which the objective function values can only be computed by a blackbox corrupted by some random noise following an unknown distribution. The proposed method is based on sequential…

Rapid, reliable, and accurate interpretation of medical time-series signals is crucial for high-stakes clinical decision-making. Deep learning methods offered unprecedented performance in medical signal processing but at a cost: they were…

Simulating parameter-dependent stochastic differential equations (SDEs) presents significant computational challenges, as separate high-fidelity simulations are typically required for each parameter value of interest. Despite the success of…

The one-class kernel spectral regression (OC-KSR), the regression-based formulation of the kernel null-space approach has been found to be an effective Fisher criterion-based methodology for one-class classification (OCC), achieving…

Semi-implicit distributions have shown great promise in variational inference and generative modeling. Hierarchical semi-implicit models, which stack multiple semi-implicit layers, enhance the expressiveness of semi-implicit distributions…

Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…