I am a Research Associate at the Oden Institute for Computational Engineering and Sciences at UT Austin. My research is in the field of computational stochastics, uncertainty quantification and computational and industrial mathematics, with a focus on multilevel (quasi-) Monte Carlo methods, PDEs with random coefficients, reduced- and mixed-precision numerical algorithms, and biomedical computing.

I am an extensive user of and occasional contributor to FEniCS, libsupermesh and Pragmatic.
BLUEST: Python package for single- and multi-output multilevel best linear unbiased estimation: here.
FEMLMC: FEniCS-based multilevel (quasi) Monte Carlo software for PDEs with random coefficients: here.
Basic multilevel Monte Carlo routines in Python: here.
C++ and Python low-precision emulator software: here.

Research Interests

Finite element method
Multilevel Monte Carlo methods
Reduced- and mixed-precision PDE solvers
Uncertainty Quantification
Biomedical Computing
Deflation for variational inequalities

Highlighted Publications

Learn more → M. Croci, K. E. Willcox, S. J. Wright Multi-output multilevel best linear unbiased estimators via semidefinite programming Computer Methods in Applied Mechanics and Engineering Article | Software
Learn more → M. Croci, and G. Rosilho de Souza Mixed-precision explicit stabilized Runge-Kutta methods for single- and multi-scale differential equations Journal of Computational Physics Article | Talk
Learn more → M. Croci, M. Fasi, N. J. Higham, T. Mary, M. Mikaitis Stochastic Rounding: Implementation, Error Analysis and Applications Royal Society Open Science Article
Learn more → M. Croci, and M. B. Giles Effects of round-to-nearest and stochastic rounding in the numerical solution of the heat equation in low precision IMA Journal of Numerical Analysis Article | Talk
Learn more → M. Kloewer, S. Hatfield, M. Croci, P. Dueben, T. Palmer Fluid simulations accelerated with 16 bit: Approaching 4x speedup on A64FX by squeezing ShallowWaters.jl into Float16 Journal of Advances in Modeling Earth Systems Article
Learn more → M. Croci, M. B. Giles, M. E. Rognes, and P. E. Farrell Multilevel quasi Monte Carlo methods for elliptic PDEs driven by spatial white noise SIAM Journal on Scientific Computing Article | Talk
Learn more → M. Croci and P. E. Farrell Complexity bounds on supermesh construction for quasi-uniform meshes Journal of Computational Physics Article
Learn more → M. Croci, V. Vinje, M. E. Rognes Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo International Journal for Numerical Methods in Biomedical Engineering Article
Learn more → M. Croci, V. Vinje, M. E. Rognes Uncertainty quantification of parenchymal tracer distribution using random diffusion and convective velocity fields Fluids and Barriers of the CNS Article

Learn more → M. Croci, M. B. Giles, M. E. Rognes, and P. E. Farrell Efficient white noise sampling and coupling for multilevel Monte Carlo with non-nested meshes SIAM/ASA Journal on Uncertainty Quantification Article | Talk
Learn more → P. E. Farrell, M. Croci, T. M. Surowiec Deflation for semismooth equations Optimization Methods and Software - Charles Broyden prize for best OMS paper in 2020 Article
Learn more → M. Croci, J. Munoz-Matute Exploiting Kronecker structure in exponential integrators: Fast approximation of the action of phi-functions of matrices via quadrature Journal of Computational Science Article | Preprint
Learn more → J. Enderlein, D. Sakhapov, I. Gregor, M. Croci, N. Karedla Modeling charge separation in charged nanochannels for single-molecule electrometry The Journal of Chemical Physics Article | Preprint