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math.NA2025
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…
math.NA2025
The multi-index Monte Carlo method for semilinear stochastic partial differential equations
Abdul-Lateef Haji-Ali, Håkon 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…