# Assumed Density Filtering and Smoothing with Neural Network Surrogate Models

arXiv: https://arxiv.org/abs/2511.09016 · HTML: https://mlsanity.com/paper/2511.09016/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 49 references that are in the map.
- First posted on arXiv 12 Nov 2025.

## Builds on (most cited first, 18 of 18)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks](https://mlsanity.com/paper/2303.02243/) (2023)
- [Multi-Step Prediction of Dynamic Systems with Recurrent Neural Networks](https://mlsanity.com/paper/1806.00526/) (2018)
- [Uncertainty Quantification via Stable Distribution Propagation](https://mlsanity.com/paper/2402.08324/) (2024)
- [ECLipsE: Efficient Compositional Lipschitz Constant Estimation for Deep Neural Networks](https://mlsanity.com/paper/2404.04375/) (2024)
- [Kalman Bayesian Neural Networks for Closed-form Online Learning](https://mlsanity.com/paper/2110.00944/) (2021)
- [Uncertainty Propagation in Deep Neural Networks Using Extended Kalman Filtering](https://mlsanity.com/paper/1809.06009/) (2018)
- [Bayesian Perceptron: Towards fully Bayesian Neural Networks](https://mlsanity.com/paper/2009.01730/) (2020)
- [Synthesizing Neural Network Controllers with Closed-Loop Dissipativity Guarantees](https://mlsanity.com/paper/2404.07373/) (2024)
- [Kalman-Bucy-Informed Neural Network for System Identification](https://mlsanity.com/paper/2210.03424/) (2022)
- [Risk-Aware Control of Discrete-Time Stochastic Systems: Integrating Kalman Filter and Worst-case CVaR in Control Barrier Functions](https://mlsanity.com/paper/2312.15638/) (2023)
- [Deterministic Uncertainty Propagation for Improved Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2406.04088/) (2024)
- [Mitigating Overconfidence in Nonlinear Kalman Filters via Covariance Recalibration](https://mlsanity.com/paper/2407.05717/) (2024)
- [A Novel Neural Filter to Improve Accuracy of Neural Network Models of Dynamic Systems](https://mlsanity.com/paper/2409.13654/) (2024)
- [RCUKF: Data-Driven Modeling Meets Bayesian Estimation](https://mlsanity.com/paper/2508.04985/) (2025)

## Built on by (most cited first, 1 of 1)

- [Uncertainty propagation in auto-regressive random neural network models](https://mlsanity.com/paper/2608.20483/) (2026)

## Abstract (arXiv)

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.