Assumed Density Filtering and Smoothing with Neural Network Surrogate Models

TL;DR

This paper introduces a method for uncertainty propagation in neural network models for nonlinear systems, improving state estimation and control performance.

Contribution

It applies a recent analytic formula for neural network moments to enhance Kalman filtering and smoothing with neural surrogates.

Findings

Superiority of the method demonstrated on Lorenz and Wiener systems.

Enables more optimal linear quadratic regulation with neural network-based estimates.

Cross entropy is shown to be a better performance metric than RMSE.

Abstract

The Kalman filter and Rauch-Tung-Striebel (RTS) smoother are optimal for state estimation in linear dynamic systems. With nonlinear systems, the challenge consists in how to propagate uncertainty through the state transitions and output function. For the case of a neural network model, we enable accurate uncertainty propagation using a recent state-of-the-art analytic formula for computing the mean and covariance of a deep neural network with Gaussian input. We argue that cross entropy is a more appropriate performance metric than RMSE for evaluating the accuracy of filters and smoothers. We demonstrate the superiority of our method for state estimation on a stochastic Lorenz system and a Wiener system, and find that our method enables more optimal linear quadratic regulation when the state estimate is used for feedback. Code available at https: //github.com/simontheflutist/analytic-moments.