Research Interests

Uncertainty Quantification, ​Stochastic Differential Equation, Numerical methods for SDEs and PDEs, Multilevel Monte Carlo, Particle systems, Crowd modelling, Mean-field theory, Sparse Grids, Combination techniques, Multi-index techniques, Inverse problems.

Recent Publications

  • N. Collier, A. Haji-Ali, F. Nobile, E. von Schwerin, R. Tempone, “A continuation multilevel Monte Carlo algorithm”, BIT Numerical Mathematics, 55(2), 399–432, 2014.
  • A. Haji-Ali, F. Nobile, E. von Schwerin, R. Tempone, “Optimization of mesh hierarchies in multilevel Monte Carlo samplers”, Stochastic Partial Differential Equations: Analysis and Computations, 4(1), 76–112, 2015.
  • A. Haji-Ali, F. Nobile, R. Tempone, “Multi-Index Monte Carlo: when sparsity meets sampling”, Numerische Mathematik, 132(4), 767–806, 2015.
  • A. Haji-Ali, F. Nobile, L. Tamellini, R. Tempone, “Multi-Index Stochastic Collocation for random PDEs”, Computer Methods in Applied Mechanics and Engineering, 306, 95–122, 2016.
  • A. Haji-Ali, H. Harbrecht, M. Peters, M. Siebenmorgen, “Novel results for the anisotropic sparse quadrature and their impact on random diffusion problems”, 2015. Submitted. Pre-print: https://arxiv.org/abs/1509.05521
  • A. Haji-Ali, F. Nobile, L. Tamellini, R. Tempone, “Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity”, Foundations of Computational Mathematics, 2016. doi:10.1007/s10208-016-9327-7