# Discovering an interpretable mathematical expression for a full wind-turbine wake with artificial intelligence enhanced symbolic regression

arXiv: https://arxiv.org/abs/2406.00695 · HTML: https://mlsanity.com/paper/2406.00695/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 70 references that are in the map.
- First posted on arXiv 2 Jun 2024.

## Builds on (most cited first, 23 of 23)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [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)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl](https://mlsanity.com/paper/2305.01582/) (2023)
- [DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm](https://mlsanity.com/paper/2001.07305/) (2020)
- [Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)](https://mlsanity.com/paper/2106.11927/) (2021)
- [DL-PDE: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data](https://mlsanity.com/paper/1908.04463/) (2019)
- [Robust discovery of partial differential equations in complex situations](https://mlsanity.com/paper/2106.00008/) (2021)
- [Controllable Neural Symbolic Regression](https://mlsanity.com/paper/2304.10336/) (2023)
- [Integration of knowledge and data in machine learning](https://mlsanity.com/paper/2202.10337/) (2022)
- [Physics-constrained robust learning of open-form partial differential equations from limited and noisy data](https://mlsanity.com/paper/2309.07672/) (2023)
- [Interpretable Symbolic Regression for Data Science: Analysis of the 2022 Competition](https://mlsanity.com/paper/2304.01117/) (2023)
- [Active Learning in Symbolic Regression with Physical Constraints](https://mlsanity.com/paper/2305.10379/) (2023)
- [Physics-constrained indirect supervised learning](https://mlsanity.com/paper/2004.14293/) (2020)
- [Physical Constraint Embedded Neural Networks for inference and noise regulation](https://mlsanity.com/paper/2105.09146/) (2021)
- [Empowering Machines to Think Like Chemists: Unveiling Molecular Structure-Polarity Relationships with Hierarchical Symbolic Regression](https://mlsanity.com/paper/2401.13904/) (2024)

## Built on by (most cited first, 2 of 2)

- [On the definition and importance of interpretability in scientific machine learning](https://mlsanity.com/paper/2505.13510/) (2025)
- [An Empirical Wall-Pressure Spectrum Model for Aeroacoustic Predictions Based on Symbolic Regression](https://mlsanity.com/paper/2501.08134/) (2025)

## Abstract (arXiv)

The rapid expansion of wind power worldwide underscores the critical significance of engineering-focused analytical wake models in both the design and operation of wind farms. These theoretically-derived ana lytical wake models have limited predictive capabilities, particularly in the near-wake region close to the turbine rotor, due to assumptions that do not hold. Knowledge discovery methods can bridge these gaps by extracting insights, adjusting for theoretical assumptions, and developing accurate models for physical processes. In this study, we introduce a genetic symbolic regression (SR) algorithm to discover an interpretable mathematical expression for the mean velocity deficit throughout the wake, a previously unavailable insight. By incorporating a double Gaussian distribution into the SR algorithm as domain knowledge and designing a hierarchical equation structure, the search space is reduced, thus efficiently finding a concise, physically informed, and robust wake model. The proposed mathematical expression (equation) can predict the wake velocity deficit at any location in the full-wake region with high precision and stability. The model's effectiveness and practicality are validated through experimental data and high-fidelity numerical simulations.