Related papers: Extracting Interaction Kernels for Many-Particle S…

In this work, we present a multiscale kinetic framework for consensus-based image segmentation. By interpreting an image as a system of interacting particles, each pixel is characterised by its spatial position and an internal feature…

Spectral densities encode essential information about system-environment interactions in open-quantum systems, playing a pivotal role in shaping the system's dynamics. In this work, we leverage machine learning techniques to reconstruct key…

The use of machine learning algorithms is an attractive way to produce very fast detector simulations for scattering reactions that can otherwise be computationally expensive. Here we develop a factorised approach where we deal with each…

In this paper, we consider particle systems with interaction and Brownian motion. We prove that when the initial data is from the sampling of Chorin's method, i.e., the initial vertices are on lattice points $hi\in \mathbb{R}^d$ with mass…

In this paper, we present a probabilistic analysis of a dynamical particle model for the self-adaptive immune response to cancer, as proposed by the first author in a previous work. The model is motivated by the interplay between immune…

The energy spectrum of two short-range interacting particles in a harmonic potential trap has previously been related to free-space scattering phase shifts. But the existing formula for this purpose is exact only in the limit of an…

Empirical data can often be considered as samples from a set of probability distributions. Kernel methods have emerged as a natural approach for learning to classify these distributions. Although numerous kernels between distributions have…

Particle-mesh methods, such as the particle-in-cell (PIC) method, cannot retain exact pairwise interaction at sub-cell scales. For dense nonneutral relativistic electron bunches, this makes it difficult to accurately capture the…

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…

The possibility to apply phase-space methods to many-body interacting systems might provide accurate descriptions of correlations with a reduced numerical cost. For instance, the so--called stochastic mean-field phase-space approach, where…

In this paper, we discuss a framework for teaching bimanual manipulation tasks by imitation. To this end, we present a system and algorithms for learning compliant and contact-rich robot behavior from human demonstrations. The presented…

We present a new phase field crystal model for structural transformations in multi-component alloys. The formalism builds upon the two-point correlation kernel developed in Greenwood et al. for describing structural transformations in pure…

We use numerical simulations to study the phase behavior of a system of purely repulsive soft dumbbells as a function of size ratio of the two components and their relative degree of deformability. We find a plethora of different phases…

We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…

In this paper, we investigate the data-driven identification of asymmetric interaction kernels in the Motsch-Tadmor model based on observed trajectory data. The model under consideration is governed by a class of semilinear evolution…

Kernels are key in machine learning for modeling interactions. Unfortunately, brute-force computation of the related kernel sums scales quadratically with the number of samples. Recent Fourier-slicing methods lead to an improved linear…

We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…

Quasiparticle interference (QPI) imaging is a powerful tool for probing electronic structures in quantum materials, but extracting the single-scatterer QPI pattern (i.e., the kernel) from a multi-scatterer image remains a fundamentally…

This paper deals with the problem of inferring the signals and parameters that cause neural activity to occur. The ultimate challenge being to unveil brain's connectivity, here we focus on a microscopic vision of the problem, where single…

While the density functional theory with integral equations techniques are very efficient tools in numerical analysis of complex fluids, an analytical insight into the phenomenon of effective interactions is still limited. In this paper we…