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Abstract:
Uncertainties in the parameters which define differential equations give rise to distributions of solutions, hence distributions of functionals of the solutions. Quantities of interest can be represented as expectations of such functionals. The resulting high-dimensional integrals, involving expensive function evaluations, has lead to a wealth of new Mathematics. Further complexity is introduced if data is available. The Bayesian framework gives rise to a probabilistic interpretation of inverse problems. Monte Carlo methods comprise a robust and versatile class of methods for solving both forward and statistical inference problems. These methods are expected to become only more prevalent as the emerging architecture of modern and future supercomputers becomes progressively more parallel. This special session aims to bring together researchers interested in all aspects of Monte Carlo methods, to share ideas and discuss these interesting problems and the interplay between them.
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