# Reconstruction of observed mechanical motions with Artificial Intelligence tools

arXiv: https://arxiv.org/abs/2202.11447 · HTML: https://mlsanity.com/paper/2202.11447/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 24 references that are in the map.
- First posted on arXiv 23 Feb 2022.

## Builds on (most cited first, 9 of 9)

- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [Learning effective physical laws for generating cosmological hydrodynamics with Lagrangian Deep Learning](https://mlsanity.com/paper/2010.02926/) (2020)
- [Time series analysis with dynamic law exploration](https://mlsanity.com/paper/2104.10970/) (2021)
- [Understanding understanding: a renormalization group inspired model of (artificial) intelligence](https://mlsanity.com/paper/2010.13482/) (2020)

## Built on by (most cited first, 7 of 7)

- [LLT: An R package for Linear Law-based Feature Space Transformation](https://mlsanity.com/paper/2304.14211/) (2023)
- [Predicting the Price Movement of Cryptocurrencies Using Linear Law-based Transformation](https://mlsanity.com/paper/2305.04884/) (2023)
- [Learning ECG Signal Features Without Backpropagation Using Linear Laws](https://mlsanity.com/paper/2307.01930/) (2023)
- [Training Hamiltonian neural networks without backpropagation](https://mlsanity.com/paper/2411.17511/) (2024)
- [Adaptive Law-Based Transformation (ALT): A Lightweight Feature Representation for Time Series Classification](https://mlsanity.com/paper/2501.09217/) (2025)
- [ALT: A Python Package for Lightweight Feature Representation in Time Series Classification](https://mlsanity.com/paper/2504.12841/) (2025)
- [Extrapolating the emergence of Hamiltonian chaos with random-feature Hamiltonian neural networks](https://mlsanity.com/paper/2607.28977/) (2026)

## Abstract (arXiv)

The goal of this paper is to determine the laws of observed trajectories assuming that there is a mechanical system in the background and using these laws to continue the observed motion in a plausible way. The laws are represented by neural networks with a limited number of parameters. The training of the networks follows the Extreme Learning Machine idea. We determine laws for different levels of embedding, thus we can represent not only the equation of motion but also the symmetries of different kinds. In the recursive numerical evolution of the system, we require the fulfillment of all the observed laws, within the determined numerical precision. In this way, we can successfully reconstruct both integrable and chaotic motions, as we demonstrate in the example of the gravity pendulum and the double pendulum.