# Path sampling of recurrent neural networks by incorporating known physics

arXiv: https://arxiv.org/abs/2203.00597 · HTML: https://mlsanity.com/paper/2203.00597/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 72 references that are in the map.
- First posted on arXiv 1 Mar 2022.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Can recurrent neural networks warp time?](https://mlsanity.com/paper/1804.11188/) (2018)
- [Addressing the Rare Word Problem in Neural Machine Translation](https://mlsanity.com/paper/1410.8206/) (2014)
- [Theory of gating in recurrent neural networks](https://mlsanity.com/paper/2007.14823/) (2020)
- [Molecular Latent Space Simulators](https://mlsanity.com/paper/2007.00728/) (2020)
- [A Note on Learning Rare Events in Molecular Dynamics using LSTM and Transformer](https://mlsanity.com/paper/2107.06573/) (2021)

## Built on by (most cited first, 4 of 4)

- [Quantum Adaptive Self-Attention for Quantum Transformer Models](https://mlsanity.com/paper/2504.05336/) (2025)
- [Density Matrix Emulation of Quantum Recurrent Neural Networks for Multivariate Time Series Prediction](https://mlsanity.com/paper/2310.20671/) (2023)
- [Unraveling Quantum Environments: Transformer-Assisted Learning in Lindblad Dynamics](https://mlsanity.com/paper/2505.06928/) (2025)
- [Beyond Ensembles: Simulating All-Atom Protein Dynamics in a Learned Latent Space](https://mlsanity.com/paper/2509.02196/) (2025)

## Abstract (arXiv)

Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with prior knowledge or intuition about the system. While the recurrent nature of these networks allows them to model arbitrarily long memories in the time series used in training, it makes it harder to impose prior knowledge or intuition through generic constraints. In this work, we present a path sampling approach based on principle of Maximum Caliber that allows us to include generic thermodynamic or kinetic constraints into recurrent neural networks. We show the method here for a widely used type of recurrent neural network known as long short-term memory network in the context of supplementing time series collected from different application domains. These include classical Molecular Dynamics of a protein and Monte Carlo simulations of an open quantum system continuously losing photons to the environment and displaying Rabi oscillations. Our method can be easily generalized to other generative artificial intelligence models and to generic time series in different areas of physical and social sciences, where one wishes to supplement limited data with intuition or theory based corrections.