SYNTOLOGY HomeExplorerAtlasCodeMethodologyAboutDevelopersFeedPricing
Paper · 2106.11927 · 2021

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

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 4 functions out of this paper's own repositories and ran 4 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
YuntianChen/SGA-PDE canonical 1 of 1
yingtaoluo/PDE-Discovery-with-Evolutionary-Tree-Search reimplementation 3 of 3
FunctionStatusWhere it lives
Diff Ran yingtaoluo/PDE-Discovery-with-Evolutionary-Tree-Search/PDE_find.py
pointer only (licence: NONE) · get_code("e40d4a2dcd4267d7")
FiniteDiff Ran yingtaoluo/PDE-Discovery-with-Evolutionary-Tree-Search/PDE_find.py
pointer only (licence: NONE) · get_code("41d34afc94b7b979")
Train Ran yingtaoluo/PDE-Discovery-with-Evolutionary-Tree-Search/PDE_find.py
pointer only (licence: NONE) · get_code("2d11d7f451e6ee66")
divide Ran YuntianChen/SGA-PDE/codes/configure.py
code served (permissive licence) · get_code("c6fbd09210e67c4a")

Repositories linked to this paper

Some links come from the archived Papers with Code dataset (CC BY-SA 4.0): attribution and licence.

Abstract

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.

For agents

The same record, over MCP at https://syntology.ai/mcp:

get_harvested_code_for_paper("2106.11927")
get_code_for_paper("2106.11927")
have("2106.11927")

Connect an agent — have() is free.