AI and the World's Hard Problems · Mathematics · arXiv · 2026-10-26
ZENO: Nonlinear filtering with Zakai Equation Neural Operators
State inference and parameter learning for nonlinear filters are core tasks in scientific machine learning, but the Zakai equation governing them is hard to solve. The authors propose ZENO, a neural operator trained with a Zakai-equation-based physics-informed loss to approximate the unnormalized filtering distribution. Using ZENO's posterior within an expectation-maximization framework, they accurately inferred posteriors and SDE parameters in three simulated systems and recovered limit cycles of forward and backward locomotion from whole-brain imaging of C. elegans.