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.
Nonlinear filtering based on density approximation and deep BSDE prediction
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abstract
A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using the well-known deep BSDE method and neural networks. The method is trained offline, which means that it can be applied online with new observations. A hybrid a priori-a posteriori error bound is proved under a parabolic H\"ormander condition. The theoretical convergence rate is confirmed in two numerical examples.
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math.NA 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
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High-dimensional Bayesian filtering through deep density approximation
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.