# Alpha Zero for Physics: Application of Symbolic Regression with Alpha Zero to find the analytical methods in physics

arXiv: https://arxiv.org/abs/2311.12713 · HTML: https://mlsanity.com/paper/2311.12713/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 37 references that are in the map.
- First posted on arXiv 21 Nov 2023.

## Builds on (most cited first, 12 of 12)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [Machine-learning-enhanced quantum sensors for accurate magnetic field imaging](https://mlsanity.com/paper/2202.00380/) (2022)

## Built on by (most cited first, 3 of 3)

- [Class Symbolic Regression: Gotta Fit 'Em All](https://mlsanity.com/paper/2312.01816/) (2023)
- [Generalizing the SINDy approach with nested neural networks](https://mlsanity.com/paper/2404.15742/) (2024)
- [Symbolic Regression for Shared Expressions: Introducing Partial Parameter Sharing](https://mlsanity.com/paper/2601.04051/) (2026)

## Abstract (arXiv)

Machine learning with neural networks is now becoming a more and more powerful tool for various tasks, such as natural language processing, image recognition, winning the game, and even for the issues of physics. Although there are many studies on the application of machine learning to numerical calculation and assistance of experiments, the methods of applying machine learning to find the analytical method are poorly studied. In this paper, we propose the frameworks of developing analytical methods in physics by using the symbolic regression with the Alpha Zero algorithm, that is Alpha Zero for physics (AZfP). As a demonstration, we show that AZfP can derive the high-frequency expansion in the Floquet systems. AZfP may have the possibility of developing a new theoretical framework in physics.