# Hybrid Neural Network Augmented Physics-based Models for Nonlinear Filtering

arXiv: https://arxiv.org/abs/2204.06471 · HTML: https://mlsanity.com/paper/2204.06471/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 30 references that are in the map.
- First posted on arXiv 13 Apr 2022.

## Builds on (most cited first, 6 of 6)

- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Kalman Filtering and Expectation Maximization for Multitemporal Spectral Unmixing](https://mlsanity.com/paper/2001.00425/) (2020)
- [Model-Based Deep Autoencoder Networks for Nonlinear Hyperspectral Unmixing](https://mlsanity.com/paper/2104.08409/) (2021)
- [Nonparametric Detection of Nonlinearly Mixed Pixels and Endmember Estimation in Hyperspectral Images](https://mlsanity.com/paper/1503.05521/) (2015)
- [Cubature Kalman Filter Based Training of Hybrid Differential Equation Recurrent Neural Network Physiological Dynamic Models](https://mlsanity.com/paper/2110.06089/) (2021)

## Built on by (most cited first, 5 of 5)

- [Dynamical Hyperspectral Unmixing with Variational Recurrent Neural Networks](https://mlsanity.com/paper/2303.10566/) (2023)
- [AI-Aided Kalman Filters](https://mlsanity.com/paper/2410.12289/) (2024)
- [On the Impact of Sampling on Deep Sequential State Estimation](https://mlsanity.com/paper/2311.17006/) (2023)
- [Recursive Deep Inverse Reinforcement Learning](https://mlsanity.com/paper/2504.13241/) (2025)
- [RTS Smoother-Guided Learning of Physics-Based Neural Differential Models](https://mlsanity.com/paper/2607.15180/) (2026)

## Abstract (arXiv)

In this paper we present a hybrid neural network augmented physics-based modeling (APBM) framework for Bayesian nonlinear latent space estimation. The proposed APBM strategy allows for model adaptation when new operation conditions come into play or the physics-based model is insufficient (or incomplete) to properly describe the latent phenomenon. One advantage of the APBMs and our estimation procedure is the capability of maintaining the physical interpretability of estimated states. Furthermore, we propose a constraint filtering approach to control the neural network contributions to the overall model. We also exploit assumed density filtering techniques and cubature integration rules to present a flexible estimation strategy that can easily deal with nonlinear models and high-dimensional latent spaces. Finally, we demonstrate the efficacy of our methodology by leveraging a target tracking scenario with nonlinear and incomplete measurement and acceleration models, respectively.