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Darcy flow in random porous medium
AMCS 301 Numerical methods for random partial differential equations: hierarchical approximation and machine learning approaches
Bayesian Inversion, Bayesian optimal experimental design, hierarchical and sparse approximation, Hierarchical regression, Low-rank approximation, Monte carlo methods, Multi-index, Multilevel Monte Carlo, Quasi-Monte Carlo, Random PDEs, stochastic algorithms, Stochastic collocation, Teaching
Species count mRNA, proteins, dimers - jump processes
AMCS 308 Stochastic Numerics with Application in Simulation and Data Science
data assimilation, Filtering theory, Importance sampling, Monte carlo methods, stochastic algorithms, Stochastic Methods, Stochastic Modeling, Stochastic Optimal Control, Stochastic processes, Variance Reduction, Teaching
Illustration weak approximation SDE
AMCS 336 Numerical Methods for Stochastic Differential Equations with connections to Machine Learning
Fokker-Planck equations, Hamilton-Jabobi-Bellman, Importance sampling, Ito integral, Kolmogorov Backward Equation, Monte Carlo, Multilevel Monte Carlo, stochastic differential equations, Stochastic Optimal Control, Variance Reduction, Teaching

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