Log In Sign Up

Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)

by   Yuntian Chen, et al.

Partial differential equations (PDEs) are concise and understandable representations of domain knowledge, which are essential for deepening our understanding of physical processes and predicting future responses. However, the PDEs of many real-world problems are uncertain, which calls for PDE discovery. We propose the symbolic genetic algorithm (SGA-PDE) to discover open-form PDEs directly from data without prior knowledge about the equation structure. SGA-PDE focuses on the representation and optimization of PDE. Firstly, SGA-PDE uses symbolic mathematics to realize the flexible representation of any given PDE, transforms a PDE into a forest, and converts each function term into a binary tree. Secondly, SGA-PDE adopts a specially designed genetic algorithm to efficiently optimize the binary trees by iteratively updating the tree topology and node attributes. The SGA-PDE is gradient-free, which is a desirable characteristic in PDE discovery since it is difficult to obtain the gradient between the PDE loss and the PDE structure. In the experiment, SGA-PDE not only successfully discovered nonlinear Burgers' equation, Korteweg-de Vries (KdV) equation, and Chafee-Infante equation, but also handled PDEs with fractional structure and compound functions that cannot be solved by conventional PDE discovery methods.


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

Data-driven methods have recently been developed to discover underlying ...

DISCOVER: Deep identification of symbolic open-form PDEs via enhanced reinforcement-learning

The working mechanisms of complex natural systems tend to abide by conci...

Discovering Governing Equations by Machine Learning implemented with Invariance

The partial differential equation (PDE) plays a significantly important ...

Deep Learning Models for Global Coordinate Transformations that Linearize PDEs

We develop a deep autoencoder architecture that can be used to find a co...

PDE-READ: Human-readable Partial Differential Equation Discovery using Deep Learning

PDE discovery shows promise for uncovering predictive models for complex...

Anomaly detection and classification for streaming data using PDEs

Nondominated sorting, also called Pareto Depth Analysis (PDA), is widely...

Multi-objective discovery of PDE systems using evolutionary approach

Usually, the systems of partial differential equations (PDEs) are discov...

Code Repositories


De novo Discovery of Partial Derivative Equations with Neural Evolutionary Tree Search.

view repo