A multilevel Monte Carlo virtual element method is developed and analyzed for uncertainty quantification of stochastic elliptic PDEs, using mesh agglomeration to cut the number of fine-level samples needed for target accuracy.
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A deep BSDE neural network method approximates unnormalized filtering densities for nonlinear Bayesian filtering, trained offline and applied online, with a hybrid a priori-a posteriori error bound proved under the parabolic Hörmander condition.
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A Multilevel Monte Carlo Virtual Element Method for Uncertainty Quantification of Elliptic Partial Differential Equations
A multilevel Monte Carlo virtual element method is developed and analyzed for uncertainty quantification of stochastic elliptic PDEs, using mesh agglomeration to cut the number of fine-level samples needed for target accuracy.
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Nonlinear filtering based on density approximation and deep BSDE prediction
A deep BSDE neural network method approximates unnormalized filtering densities for nonlinear Bayesian filtering, trained offline and applied online, with a hybrid a priori-a posteriori error bound proved under the parabolic Hörmander condition.