Related papers: Efficient Sampling of Stochastic Differential Equa…
We introduce and test methods for the calibration of the diffusion term in Stochastic Partial Differential Equations (SPDEs) describing fluids. We take two approaches, one uses ideas from the singular value decomposition and the Biot-Savart…
Accurate prediction of rarefied gas flows is important for space vehicle design, particularly in rarefied regimes where the Navier-Stokes equations are no more valid. While the direct simulation Monte Carlo (DSMC) method acts as a numerical…
SDE's must be solved in the "anti-Ito" sense when their coefficients are independent. While the "noise-induced drift" matters for the sample paths, it is absent in the Fokker-Planck equation, which takes a particularly simple form and is…
We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function $f$, we want to recover $f$ up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on…
Solving time-dependent partial differential equations (PDEs) that exhibit sharp gradients or local singularities is computationally demanding, as traditional physics-informed neural networks (PINNs) often suffer from inefficient point…
This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…
Stochastic gradients have been widely integrated into Langevin-based methods to improve their scalability and efficiency in solving large-scale sampling problems. However, the proximal sampler, which exhibits much faster convergence than…
We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally…
Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…
Determinantal Point Processes (DPPs) are elegant probabilistic models of repulsion and diversity over discrete sets of items. But their applicability to large sets is hindered by expensive cubic-complexity matrix operations for basic tasks…
Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling, due to their state-of-the art performance in many generation tasks while relying on mathematical foundations such as stochastic…
The paper investigates existence and uniqueness for a stochastic differential equation (SDE) with distributional drift depending on the law density of the solution. Those equations are known as McKean SDEs. The McKean SDE is interpreted in…
Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…
Reinforcement learning (RL) has become an effective way to improve prompt alignment and perceptual quality in diffusion and flow-matching generators. A critical step for applying online RL to flow matching is turning the deterministic…
Consider an $n \times p$ data matrix $X$ whose rows are independently sampled from a population with covariance $\Sigma$. When $n,p$ are both large, the eigenvalues of the sample covariance matrix are substantially different from those of…
Diffusion bridge models have demonstrated promising performance in conditional image generation tasks, such as image restoration and translation, by initializing the generative process from corrupted images instead of pure Gaussian noise.…
Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function…
This paper outlines an approach to the approximation of probability density functions by quadratic forms of weighted orthonormal basis functions with positive semi-definite Hermitian matrices of unit trace. Such matrices are called…
This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures.…
This paper studies the nonlinear stochastic partial differential equation of fractional orders both in space and time variables: \[ \left(\partial^\beta+\frac{\nu}{2}(-\Delta)^{\alpha/2}\right)u(t,x) =…