A differentiable Kalman filter that learns the state-transition operator by field inversion and a neural closure model is demonstrated on rocket and Allen-Cahn models, with reported 90% error reductions over a fixed-model Kalman filter.
Differentiable Particle Filtering via Entropy-Regularized Optimal Transport
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abstract
Particle Filtering (PF) methods are an established class of procedures for performing inference in non-linear state-space models. Resampling is a key ingredient of PF, necessary to obtain low variance likelihood and states estimates. However, traditional resampling methods result in PF-based loss functions being non-differentiable with respect to model and PF parameters. In a variational inference context, resampling also yields high variance gradient estimates of the PF-based evidence lower bound. By leveraging optimal transport ideas, we introduce a principled differentiable particle filter and provide convergence results. We demonstrate this novel method on a variety of applications.
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DKFNet: Differentiable Kalman Filter for Field Inversion and Machine Learning
A differentiable Kalman filter that learns the state-transition operator by field inversion and a neural closure model is demonstrated on rocket and Allen-Cahn models, with reported 90% error reductions over a fixed-model Kalman filter.