Related papers: Parametric subordination in fractional diffusion p…
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…
The topic of these notes could be easily expanded into a full one-semester course. Nevertheless, we shall try to give some flavour along with theoretical bases of spectral and pseudo-spectral methods. The main focus is made on Fourier-type…
Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
The light damping hypothesis is usually assumed in structural dynamics since dissipative forces are in general weak with respect to inertial and elastic forces. In this paper a novel numerical method of time integration based on the…
Inference-time controllable generation is essential for real-world applications of unconditional diffusion models. However, most existing techniques focus on individual samples, struggling in applications that require the sample population…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…
Single-particle tracking allows to infer the motion of single molecules in living cells. When we observe a long trajectory (more than 100 points), it is possible that the particle switches mode of motion over time. Then, fitting a single…
The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-partial differential equation. In this paper we propose a…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
Targeting to understand the underlying explainable factors behind observations and modeling the conditional generation process on these factors, we connect disentangled representation learning to Diffusion Probabilistic Models (DPMs) to…
In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…
Time-changed stochastic processes have attracted great attention and wide interests due to their extensive applications, especially in financial time series, biology and physics. This paper pays attention to a special stochastic process,…
We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…
Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a transformation of the state of the process is observed with noise. The smoothing problem consists of recovering the path of the…
We present and analyze a parallel implementation of a parallel-in-time collocation method based on $\alpha$-circulant preconditioned Richardson iterations. While many papers explore this family of single-level, time-parallel "all-at-once"…
Diffusion-based motion planners are becoming popular due to their well-established performance improvements, stemming from sample diversity and the ease of incorporating new constraints directly during inference. However, a primary…
Diffusion models provide a principled framework for generative modeling via stochastic differential equations and time-reversed dynamics. Extending spectral diffusion approaches to spherical data, however, raises nontrivial geometric and…
In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the…