Deep-Picard iteration uses supervised neural networks trained on Monte Carlo labels from beta-stable subordinators and alpha-stable Levy walks to approximate solutions of high-dimensional fractional PDEs up to dimension 100.
Deep picard iteration for high-dimensional nonlinear PDEs
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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.
A convergent deep splitting scheme approximates the nonlinear filtering density via Fokker-Planck prediction and exact Bayesian update, with sampling to address high dimensions.
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Deep-Picard Iteration for Space-time Fractional Diffusion PDEs
Deep-Picard iteration uses supervised neural networks trained on Monte Carlo labels from beta-stable subordinators and alpha-stable Levy walks to approximate solutions of high-dimensional fractional PDEs up to dimension 100.
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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.
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A convergent scheme for the Bayesian filtering problem based on the Fokker--Planck equation and deep splitting
A convergent deep splitting scheme approximates the nonlinear filtering density via Fokker-Planck prediction and exact Bayesian update, with sampling to address high dimensions.