# Time series analysis with dynamic law exploration

arXiv: https://arxiv.org/abs/2104.10970 · HTML: https://mlsanity.com/paper/2104.10970/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 10 references that are in the map.
- First posted on arXiv 22 Apr 2021.

## Builds on (most cited first, 5 of 5)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Model-free, Model-based, and General Intelligence](https://mlsanity.com/paper/1806.02308/) (2018)
- [Understanding understanding: a renormalization group inspired model of (artificial) intelligence](https://mlsanity.com/paper/2010.13482/) (2020)

## Built on by (most cited first, 6 of 6)

- [Reconstruction of observed mechanical motions with Artificial Intelligence tools](https://mlsanity.com/paper/2202.11447/) (2022)
- [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)
- [Linear Laws of Markov Chains with an Application for Anomaly Detection in Bitcoin Prices](https://mlsanity.com/paper/2201.09790/) (2022)
- [ALT: A Python Package for Lightweight Feature Representation in Time Series Classification](https://mlsanity.com/paper/2504.12841/) (2025)

## Abstract (arXiv)

In this paper we examine, how the dynamic laws governing the time evolution of a time series can be identified. We give a finite difference equation as well as a differential equation representation for that. We also study, how the required symmetries, like time reversal can be imposed on the laws. We study the compression performance of linear laws on sound data.