SGD dynamics in Hilbert spaces are approximated by an SDE with cylindrical noise, with the weak error between discrete and continuous versions shown to be second order in the step size.
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Lipschitz stability holds for low-rank unknowns in the fully nonlinear inverse medium scattering problem, with an ensemble Kalman filter proposed for iterative reconstruction whose dimension is set by the wave number.
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Stochastic Modified Equations for Stochastic Gradient Descent in Infinite-Dimensional Hilbert Spaces
SGD dynamics in Hilbert spaces are approximated by an SDE with cylindrical noise, with the weak error between discrete and continuous versions shown to be second order in the step size.
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Low-rank-assisted inverse medium scattering: Lipschiz stability and ensemble Kalman filter
Lipschitz stability holds for low-rank unknowns in the fully nonlinear inverse medium scattering problem, with an ensemble Kalman filter proposed for iterative reconstruction whose dimension is set by the wave number.