# DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm

arXiv: https://arxiv.org/abs/2001.07305 · HTML: https://mlsanity.com/paper/2001.07305/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2020.

## Built on by (most cited first, 30 of 46)

- [Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)](https://mlsanity.com/paper/2106.11927/) (2021)
- [Robust discovery of partial differential equations in complex situations](https://mlsanity.com/paper/2106.00008/) (2021)
- [PDE-LEARN: Using Deep Learning to Discover Partial Differential Equations from Noisy, Limited Data](https://mlsanity.com/paper/2212.04971/) (2022)
- [DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization](https://mlsanity.com/paper/2108.00069/) (2021)
- [WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimming](https://mlsanity.com/paper/2211.03134/) (2022)
- [Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion](https://mlsanity.com/paper/2208.03322/) (2022)
- [Weak-PDE-LEARN: A Weak Form Based Approach to Discovering PDEs From Noisy, Limited Data](https://mlsanity.com/paper/2309.04699/) (2023)
- [Noise-aware Physics-informed Machine Learning for Robust PDE Discovery](https://mlsanity.com/paper/2206.12901/) (2022)
- [Integration of knowledge and data in machine learning](https://mlsanity.com/paper/2202.10337/) (2022)
- [Generative Discovery of Partial Differential Equations by Learning from Math Handbooks](https://mlsanity.com/paper/2505.05869/) (2025)
- [Deep-OSG: Deep Learning of Operators in Semigroup](https://mlsanity.com/paper/2302.03358/) (2023)
- [Symbolic Recovery of Differential Equations: The Identifiability Problem](https://mlsanity.com/paper/2210.08342/) (2022)
- [Physics-constrained robust learning of open-form partial differential equations from limited and noisy data](https://mlsanity.com/paper/2309.07672/) (2023)
- [DUE: A Deep Learning Framework and Library for Modeling Unknown Equations](https://mlsanity.com/paper/2504.10373/) (2025)
- [D-CIPHER: Discovery of Closed-form Partial Differential Equations](https://mlsanity.com/paper/2206.10586/) (2022)
- [Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis](https://mlsanity.com/paper/2503.01036/) (2025)
- [Physics-Guided Discovery of Highly Nonlinear Parametric Partial Differential Equations](https://mlsanity.com/paper/2106.01078/) (2021)
- [Adaptive Uncertainty-Guided Model Selection for Data-Driven PDE Discovery](https://mlsanity.com/paper/2308.10283/) (2023)
- [Physics-informed Temporal Alignment for Auto-regressive PDE Foundation Models](https://mlsanity.com/paper/2505.10930/) (2025)
- [Deep-Learning Discovers Macroscopic Governing Equations for Viscous Gravity Currents from Microscopic Simulation Data](https://mlsanity.com/paper/2106.00009/) (2021)
- [Parsimony-Enhanced Sparse Bayesian Learning for Robust Discovery of Partial Differential Equations](https://mlsanity.com/paper/2107.07040/) (2021)
- [DISCOVER: Deep identification of symbolically concise open-form PDEs via enhanced reinforcement-learning](https://mlsanity.com/paper/2210.02181/) (2022)
- [An invariance constrained deep learning network for PDE discovery](https://mlsanity.com/paper/2402.03747/) (2024)
- [Robust identifiability for symbolic recovery of differential equations](https://mlsanity.com/paper/2410.09938/) (2024)
- [A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems](https://mlsanity.com/paper/2412.03970/) (2024)
- [Data-driven discovery of governing differential equations across physical systems](https://mlsanity.com/paper/2606.09638/) (2026)
- [Interpretable AI-Driven Discovery of Terrain-Precipitation Relationships for Enhanced Climate Insights](https://mlsanity.com/paper/2309.15400/) (2023)
- [A Deep-Genetic Algorithm (Deep-GA) Approach for High-Dimensional Nonlinear Parabolic Partial Differential Equations](https://mlsanity.com/paper/2311.11558/) (2023)
- [Discovering an interpretable mathematical expression for a full wind-turbine wake with artificial intelligence enhanced symbolic regression](https://mlsanity.com/paper/2406.00695/) (2024)
- [Evaluating PDE discovery methods for multiscale modeling of biological signals](https://mlsanity.com/paper/2506.20694/) (2025)

## Abstract (arXiv)

Data-driven methods have recently been developed to discover underlying partial differential equations (PDEs) of physical problems. However, for these methods, a complete candidate library of potential terms in a PDE are usually required. To overcome this limitation, we propose a novel framework combining deep learning and genetic algorithm, called DLGA-PDE, for discovering PDEs. In the proposed framework, a deep neural network that is trained with available data of a physical problem is utilized to generate meta-data and calculate derivatives, and the genetic algorithm is then employed to discover the underlying PDE. Owing to the merits of the genetic algorithm, such as mutation and crossover, DLGA-PDE can work with an incomplete candidate library. The proposed DLGA-PDE is tested for discovery of the Korteweg-de Vries (KdV) equation, the Burgers equation, the wave equation, and the Chaffee-Infante equation, respectively, for proof-of-concept. Satisfactory results are obtained without the need for a complete candidate library, even in the presence of noisy and limited data.