# Unifying Model-Based and Neural Network Feedforward: Physics-Guided Neural Networks with Linear Autoregressive Dynamics

arXiv: https://arxiv.org/abs/2209.12489 · HTML: https://mlsanity.com/paper/2209.12489/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 34 references that are in the map.
- First posted on arXiv 26 Sep 2022.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [Nonlinear System Identification: A User-Oriented Roadmap](https://mlsanity.com/paper/1902.00683/) (2019)
- [Physics-Guided Neural Networks for Inversion-based Feedforward Control applied to Linear Motors](https://mlsanity.com/paper/2103.06092/) (2021)
- [Physics-Guided Neural Networks for Feedforward Control: An Orthogonal Projection-Based Approach](https://mlsanity.com/paper/2201.03308/) (2022)

## Built on by (most cited first, 2 of 2)

- [Deep Grey-Box Modeling With Adaptive Data-Driven Models Toward Trustworthy Estimation of Theory-Driven Models](https://mlsanity.com/paper/2210.13103/) (2022)
- [Hybrid Generative Modeling for Incomplete Physics: Deep Grey-Box Meets Optimal Transport](https://mlsanity.com/paper/2506.22204/) (2025)

## Abstract (arXiv)

Unknown nonlinear dynamics often limit the tracking performance of feedforward control. The aim of this paper is to develop a feedforward control framework that can compensate these unknown nonlinear dynamics using universal function approximators. The feedforward controller is parametrized as a parallel combination of a physics-based model and a neural network, where both share the same linear autoregressive (AR) dynamics. This parametrization allows for efficient output-error optimization through Sanathanan-Koerner (SK) iterations. Within each SK-iteration, the output of the neural network is penalized in the subspace of the physics-based model through orthogonal projection-based regularization, such that the neural network captures only the unmodelled dynamics, resulting in interpretable models.