It is one of the most challenging problems in applied mathematics to approximatively solve
high-dimensional partial differential equations (PDEs). Recently, several deep learning …

Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite
their high-quality generation performance, DPMs still suffer from their slow sampling as they …

Diffusion probabilistic models (DPMs) have demonstrated a very promising ability in high-
resolution image synthesis. However, sampling from a pre-trained DPM is time-consuming …

Diffusion probabilistic models (DPMs) have exhibited excellent performance for high-fidelity
image generation while suffering from inefficient sampling. Recent works accelerate the …

In this paper we consider the construction, analysis, implementation and application of
exponential integrators. The focus will be on two types of stiff problems. The first one is …

Recently, there has been a great deal of interest in the construction of exponential
integrators. These integrators, as their name suggests, use the exponential function (and …

The ubiquity of semilinear parabolic equations is clear from their numerous applications
ranging from physics and biology to materials and social sciences. In this paper, we …

Denoising Diffusion models have demonstrated their proficiency for generative sampling.
However, generating good samples often requires many iterations. Consequently …

The nonlocal Allen--Cahn equation, a generalization of the classic Allen--Cahn equation by
replacing the Laplacian with a parameterized nonlocal diffusion operator, satisfies the …

In this paper, we develop a general framework for constructing higher-order, unconditionally
energy-decreasing exponential time differencing Runge-Kutta (ETDRK) methods applicable …