ZENO learns nonlinear filters with Zakai equation neural operators
Original title: ZENO: Nonlinear filtering with Zakai Equation Neural Operators
The operator is trained with a physics-informed Zakai loss and used inside EM for state inference and SDE parameter learning.
ZENO approximates the unnormalized filtering distribution of latent stochastic dynamical systems by optimizing a neural operator against a physics-informed loss from the Zakai equation. The inferred posterior is used in expectation-maximization for parameter learning and state inference. The authors test a double-well bistable system, a Van der Pol oscillator, and the Lorenz system, and compare with established latent SDE methods. On whole-brain imaging of immobilized C. elegans, ZENO recovers previously observed limit cycles linked to forward and backward locomotion.
- The Zakai equation combines the Fokker-Planck operator with likelihood updates.
- Simulated tests cover double-well, Van der Pol, and Lorenz systems.
- The nematode result uses an existing whole-brain imaging dataset.
- ZENO targets high-dimensional SPDEs that are intractable to solve directly.
From the original article
1 min read at arxiv.orgState inference and parameter learning for nonlinear filters is a core computation for scientific machine learning with varied applications in engineering and neuroscience. The unnormalized filtering distribution is governed by the Zakai equation, a stochastic partial differential equation (SPDE) that combines the forward Kolmogorov operator (known as the Fokker-Planck equation) with observed likelihood updates.
By Aaditya Prasad · arxiv.org
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