# Physical Symbolic Optimization

arXiv: https://arxiv.org/abs/2312.03612 · HTML: https://mlsanity.com/paper/2312.03612/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 16 references that are in the map.
- First posted on arXiv 6 Dec 2023.

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

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [Analytical Modelling of Exoplanet Transit Specroscopy with Dimensional Analysis and Symbolic Regression](https://mlsanity.com/paper/2112.11600/) (2021)
- [Improving exploration in policy gradient search: Application to symbolic optimization](https://mlsanity.com/paper/2107.09158/) (2021)

## Built on by (most cited first, 1 of 1)

- [Generalizing the SINDy approach with nested neural networks](https://mlsanity.com/paper/2404.15742/) (2024)

## Abstract (arXiv)

We present a framework for constraining the automatic sequential generation of equations to obey the rules of dimensional analysis by construction. Combining this approach with reinforcement learning, we built Phi-SO, a Physical Symbolic Optimization method for recovering analytical functions from physical data leveraging units constraints. Our symbolic regression algorithm achieves state-of-the-art results in contexts in which variables and constants have known physical units, outperforming all other methods on SRBench's Feynman benchmark in the presence of noise (exceeding 0.1%) and showing resilience even in the presence of significant (10%) levels of noise.