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This paper introduces a generalised 3rd-order Spectral Representation Method for the simulation of multi-dimensional stochastic fields with asymmetric non-linearities. The simulated random fields satisfy a prescribed Power Spectrum and…
We study the convergence to equilibrium in high dimensions, focusing on explicit bounds on mixing times and the emergence of the cutoff phenomenon for Dyson-Laguerre processes. These are interacting particle systems with non-constant…
We derive a numerically stable method to compute an image representation of an unknown linear system only from data, leveraging a continuous-time version of Willems et al.'s fundamental lemma. To this end, we use derivatives approximated by…
We consider a fully-discrete approximations of 1-D heat equation with dynamic boundary conditions for which we provide a controllability result. The proof of this result is based on a relaxed observability inequality for the corresponding…
We propose a Deep-Picard iteration framework for high-dimensional nonlinear space-time fractional diffusion equations.The method is based on a nonlinear fractional Feynman--Kac fixed-point formulation, which replaces direct discretization…
This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…
The dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements and…
We introduce a novel, training-free method for sampling differentiable representations (diffreps) using pretrained diffusion models. Rather than merely mode-seeking, our method achieves sampling by "pulling back" the dynamics of the…
In this study, an implicit-explicit local differential transform method (IELDTM) based on Taylor series representations is produced for solving 2D and 3D advection-diffusion equations. The parabolic advection-diffusion equations are reduced…
Implicit particle filters for data assimilation generate high-probability samples by representing each particle location as a separate function of a common reference variable. This representation requires that a certain underdetermined…
In this thesis we propose a novel method to compute higher-order corrections to physical cross sections, bypassing more traditional approaches. This technique, the Four-Dimensional Unsubtraction (FDU), is based on the Loop-Tree Duality…
Diffusion models (DMs) have achieved state-of-the-art results for image synthesis tasks as well as density estimation. Applied in the latent space of a powerful pretrained autoencoder (LDM), their immense computational requirements can be…
We describe spatio-temporal random processes using linear mixed models. We show how many commonly used models can be viewed as special cases of this general framework and pay close attention to models with separable or product-sum…
We present an efficient separation of variables algorithm for the evaluation of imaginary time Feynman diagrams appearing in the bold pseudo-particle strong coupling expansion of the Anderson impurity model. The algorithm uses a fitting…
One of the main obstacles for the signal extraction of the three point correlation function using photometric surveys, such as the Rubin Observatory Legacy Survey of Space and Time (LSST), will be the prohibitive computation time required…
The purpose of this manuscript is to derive two distinct integral representations of the generalized polylogarithm using two different techniques. The first approach involves the Dirichlet series and its Laplace representation, which leads…
In this paper approximation methods for infinite-dimensional Levy processes, also called (time-dependent) Levy fields, are introduced. For square integrable fields beyond the Gaussian case, it is no longer given that the one-dimensional…
The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the…
Implicit Neural Representations (INRs) provide a powerful continuous framework for modeling complex visual and geometric signals, but spectral bias remains a fundamental challenge, limiting their ability to capture high-frequency details.…
The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation…