4 papers
Multi-index importance sampling for McKean--Vlasov stochastic differential equations
Nadhir Ben Rached, Abdul-Lateef Haji-Ali, Shyam Mohan Subbiah Pillai +1
This work addresses the estimation of rare-event quantities expressed as expectations of smooth observables of solutions to a broad class of McKean--Vlasov stochastic differential…
An Adaptive Sampling Algorithm for Level-set Approximation
Matteo Croci, Abdul-Lateef Haji-Ali, Ian C. J. Powell
We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive…
Bayesian computation with generative diffusion models by Multilevel Monte Carlo
Abdul-Lateef Haji-Ali, Marcelo Pereyra, Luke Shaw +1
Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a…
The multi-index Monte Carlo method for semilinear stochastic partial differential equations
Abdul-Lateef Haji-Ali, HÃ¥kon Hoel, Andreas Petersson
Stochastic partial differential equations (SPDEs) are often difficult to solve numerically due to their low regularity and high dimensionality. These challenges limit the practical…