Derives computable a posteriori error bounds for decoupled neural approximations of fully coupled FBSDEs that depend on terminal defect, pathwise residual, and control mismatch, backed by continuous-time stability estimates and numerical tests.
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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.
The logarithmic deep backward SDE filter succeeds in a 100-dimensional Lorenz-96 model where particle and ensemble Kalman filters fail, while cutting inference time by two to five orders of magnitude.
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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.