Related papers: Exact simulation of diffusions
Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion approximation and it is accurate for optically thin, thick, and intermediate…
For rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and…
In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…
Diffusion models (DMs) have established themselves as the state-of-the-art generative modeling approach in the visual domain and beyond. A crucial drawback of DMs is their slow sampling speed, relying on many sequential function evaluations…
We present an ``equation-free'' multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast…
We address the multiclass classification problem for stochastic diffusion paths, assuming that the classes are distinguished by their drift functions, while the diffusion coefficient remains common across all classes. In this setting, we…
Although diffusion models can generate remarkably high-quality samples, they are intrinsically bottlenecked by their expensive iterative sampling procedure. Consistency models (CMs) have recently emerged as a promising diffusion model…
We study the problem of training neural stochastic differential equations, or diffusion models, to sample from a Boltzmann distribution without access to target samples. Existing methods for training such models enforce time-reversal of the…
In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large…
We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase space density and are suitable for…
Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…
We introduce a simple method for nearly simultaneous computation of all moments needed for quasi maximum likelihood estimation of parameters in discretely observed stochastic differential equations commonly seen in finance. The method…
We present a new and straightforward algorithm that simulates exact sample paths for a generalized stress-release process. The computation of the exact law of the joint interarrival times is detailed and used to derive this algorithm.…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
We present a perfect simulation of the hard disks model via the partial rejection sampling method. Provided the density of disks is not too high, the method produces exact samples in $O(\log n)$ rounds, and total time $O(n)$, where $n$ is…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
3D data simulation aims to bridge the gap between simulated and real-captured 3D data, which is a fundamental problem for real-world 3D visual tasks. Most 3D data simulation methods inject predefined physical priors but struggle to capture…
The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…