ZENO
A model combining neural operators with physics-informed loss that approximates the unnormalized posterior distribution in nonlinear filtering by embedding the Zakai equation as a physical constraint, and is embedded within an EM framework for parameter learning and state inference.
Timeline (last 90 days)
ZENO (Zakai Equation Neural Operator) is a model that approximates the exact unnormalized filtering distribution by combining neural operators with physics-informed loss.
ZENO trains the neural operator by minimizing the Zakai equation residual, and can learn the implicit filtering distribution without large amounts of labeled data and generalize to different initial conditions and parameter settings.
ZENO embeds the posterior distribution into an expectation-maximization (EM) framework, achieving parameter learning and state inference by alternating between the E step (estimating the posterior distribution using current parameters) and the M step (maximizing the complete-data log-likelihood to update parameters).
The researchers tested ZENO on three simulated stochastic dynamical systems: the double-well bistable system, the Van der Pol oscillator, and the Lorenz system.
Compared with existing latent SDE inference methods, ZENO shows advantages in both accurately recovering the posterior distribution and learning SDE parameters, and is more precise especially in distribution shape and parameter consistency.
ZENO was applied to the whole-brain imaging dataset of Caenorhabditis elegans (C. elegans), successfully recovering the limit cycles corresponding to the worm's forward and backward locomotion.
The computational cost of ZENO and its dependence on the physical equations remain factors to consider in practical deployment.
Extending ZENO to non-Gaussian noise or time-varying parameter systems is a direction worth exploring.
All Facts (8)
ZENO (Zakai Equation Neural Operator) is a model that approximates the exact unnormalized filtering distribution by combining neural operators with physics-informed loss.
50%UnverifiedZENO trains the neural operator by minimizing the Zakai equation residual, and can learn the implicit filtering distribution without large amounts of labeled data and generalize to different initial conditions and parameter settings.
50%UnverifiedZENO embeds the posterior distribution into an expectation-maximization (EM) framework, achieving parameter learning and state inference by alternating between the E step (estimating the posterior distribution using current parameters) and the M step (maximizing the complete-data log-likelihood to update parameters).
50%UnverifiedThe researchers tested ZENO on three simulated stochastic dynamical systems: the double-well bistable system, the Van der Pol oscillator, and the Lorenz system.
50%UnverifiedCompared with existing latent SDE inference methods, ZENO shows advantages in both accurately recovering the posterior distribution and learning SDE parameters, and is more precise especially in distribution shape and parameter consistency.
50%UnverifiedZENO was applied to the whole-brain imaging dataset of Caenorhabditis elegans (C. elegans), successfully recovering the limit cycles corresponding to the worm's forward and backward locomotion.
50%UnverifiedThe computational cost of ZENO and its dependence on the physical equations remain factors to consider in practical deployment.
50%UnverifiedExtending ZENO to non-Gaussian noise or time-varying parameter systems is a direction worth exploring.
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