# Joint Parameter Discovery and Generative Modeling of Dynamic Systems

arXiv: https://arxiv.org/abs/2103.10905 · HTML: https://mlsanity.com/paper/2103.10905/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 19 Mar 2021.

## Builds on (most cited first, 8 of 8)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [AllenNLP: A Deep Semantic Natural Language Processing Platform](https://mlsanity.com/paper/1803.07640/) (2018)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Physical Symmetries Embedded in Neural Networks](https://mlsanity.com/paper/1904.08991/) (2019)

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

- [Disentangled Generative Models for Robust Prediction of System Dynamics](https://mlsanity.com/paper/2108.11684/) (2021)
- [Physical Constraint Embedded Neural Networks for inference and noise regulation](https://mlsanity.com/paper/2105.09146/) (2021)

## Abstract (arXiv)

Given an unknown dynamic system such as a coupled harmonic oscillator with n springs and point masses. We are often interested in gaining insights into its physical parameters, i.e. stiffnesses and masses, by observing trajectories of motion. How do we achieve this from video frames or time-series data and without the knowledge of the dynamics model? We present a neural framework for estimating physical parameters in a manner consistent with the underlying physics. The neural framework uses a deep latent variable model to disentangle the system physical parameters from canonical coordinate observations. It then returns a Hamiltonian parameterization that generalizes well with respect to the discovered physical parameters. We tested our framework with simple harmonic oscillators, n=1, and noisy observations and show that it discovers the underlying system parameters and generalizes well with respect to these discovered parameters. Our model also extrapolates the dynamics of the system beyond the training interval and outperforms a non-physically constrained baseline model. Our source code and datasets can be found at this URL: https://github.com/gbarber94/ConSciNet.