Related papers: An exact kernel framework for spatio-temporal dyna…
Multiscale modeling of complex systems is crucial for understanding their intricacies. Data-driven multiscale modeling has emerged as a promising approach to tackle challenges associated with complex systems. On the other hand,…
This work considers the subdiffusion problem with non-positive memory, which not only arises from physical laws with memory, but could be transformed from sophisticated models such as subdiffusion or subdiffusive Fokker-Planck equation with…
Spatiotemporal forecasting is critical for real-world applications like traffic management, yet capturing reliable interactions remains challenging under noisy and non-stationary conditions. Existing methods primarily rely on historical…
Estimating environmental exposures from multi-source data is central to public health research and policy. Integrating data from satellite products and ground monitors are increasingly used to produce exposure surfaces. However,…
Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…
We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…
We present a framework for constructing physics and causally constrained neural models of turbulent dynamical systems from data. We first formulate a finite-time flow map with strict energy-preserving nonlinearities for stable modeling of…
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…
In this paper, we show empirical evidence on how to construct the optimal feature selection or input representation used by the input layer of a feedforward neural network for the propose of forecasting spatial-temporal signals. The…
Particle- and agent-based systems are a ubiquitous modeling tool in many disciplines. We consider the fundamental problem of inferring interaction kernels from observations of agent-based dynamical systems given observations of…
We revisit a simple toy model of two scalar fields in de Sitter space, playing the roles of "system" and "environment" degrees of freedom, which interact with each other. We show that there are secular divergences in physically relevant…
We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semi-parametric approach and represent the interaction kernel in terms of a…
We discuss the so-called Schr{\"o}dinger problem of deducing the microscopic (basically stochastic) evolution that is consistent with given positive boundary probability densities for a process covering a finite fixed time interval. The…
As in an earlier paper we start from the hypothesis that physics on the Planck scale should be described by means of concepts taken from ``discrete mathematics''. This goal is realized by developing a scheme being based on the dynamical…
The Fokker-Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines but it requires specification of the coefficients for each case, which can be functions of space-time and…
In data science, individual observations are often assumed to come independently from an underlying probability space. Kernel matrices formed from large sets of such observations arise frequently, for example during classification tasks. It…
Diffusion Maps framework is a kernel based method for manifold learning and data analysis that defines diffusion similarities by imposing a Markovian process on the given dataset. Analysis by this process uncovers the intrinsic geometric…
Statistical modeling of experimental physical laws is based on the probability density function of measured variables. It is expressed by experimental data via a kernel estimator. The kernel is determined objectively by the scattering of…
Three theoretically plausible techniques to developing a fractional scalar field cosmological model are pointed in this paper; the time-dependent kernel weighted action being then selected. Upon this choice, we proceed to establish (i) a…
We discuss the approach to equilibrium of systems governed by the Fokker-Planck equation. In particular, we focus on problems involving barrier penetration and the associated Kramers' time. We also describe the connection between stochastic…