Polynomial equations are a cornerstone of modern science, providing a mathematical basis for celestial mechanics, computer graphics, market growth predictions and much more. But although most high ...

Image Restoration with Mean-Reverting Stochastic Differential Equations, ICML 2023. Winning solution of the NTIRE 2023 Image Shadow Removal Challenge.

Abstract: We present a method for learning latent stochastic differential equations (SDEs) from high dimensional time series data. Given a high-dimensional time series generated from a lower ...

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...

ABSTRACT: Stochastic differential equation (SDE) is an ordinary differential equation with a stochastic process that can model the unpredictable real-life behavior of any continuous systems. It is the ...

1 Departamento de Estadística, Análisis Matemático y Optimización, Universidade de Santiago de Compostela, Santiago de Compostela, Spain 2 Instituto de Matemáticas, Universidade de Santiago de ...

We introduce a doubly stochastic method for performing material failure theory based forecasts of volcanic eruptions. The method enhances the well known Failure Forecast Method equation, introducing a ...

ABSTRACT: In this paper, we discuss the dynamics of a stochastic SIRC epidemic model with infection rate affected by white noise. We prove that this stochastic model has a unique nonnegative solution ...

Partial differential equations (PDEs) are among the most ubiquitous tools used in modeling problems in nature. However, solving high-dimensional PDEs has been notoriously difficult due to the “curse ...

Abstract: Numerical schemes based on the simulation of suitable Markov jump processes such as the stochastic direct simulation method and its improved variants have shown to be a good alternative to ...