Learning Approximate Symbolic Solutions to Burgers' Equation using Symbolic Regression.

Benjamin G Cohen, Burcu Beykal, George M Bollas

Abstract read

In one paragraph

Article in IFAC-PapersOnLine, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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4 · The record

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5 · Who and what money

Authors and funding

3 authors.

Benjamin G CohenDepartment of Chemical and Biomolecular Engineering, University of Connecticut, Storrs, CT 60629 USA.

Burcu BeykalDepartment of Chemical and Biomolecular Engineering, University of Connecticut, Storrs, CT 60629 USA.

George M BollasDepartment of Chemical and Biomolecular Engineering, University of Connecticut, Storrs, CT 60629 USA.

Funding

Single cell, multi-parametric high throughput platform to classify endocrine disruptor potential of mixturesP42ES027704 · NIEHS · TEXAS A&M UNIVERSITY · PI Weihsueh A Chiu · 2017 to 2026

$21.2M

NIEHS NIH HHS P42 ES027704

6 · The paper itself

Abstract

This work explores the application of symbolic regression to learn symbolic solutions to Burgers' equation without data. We demonstrate a stepwise symbolic regression strategy that explores models that provide tractable logic from coordinates to state estimates. The first step is to learn a model representing part of the system's physics. This partial model is then used to help discover a model capturing the entire physics of the system. The method was able to learn a model of the solution of the diffusion equation with an R-squared value of 0.99 and produced models for Burgers' equation with different values of the convection coefficient, all with R-squared values greater than 0.98. These solutions to Burgers' equation, represented as transformations of the solution to the diffusion equation, demonstrate the potential of leveraging domain knowledge to simplify the symbol space and build useful primitives for symbolic regression. This work highlights how domain knowledge, expert intuition, and symbolic regression can complement each other to create more interpretable solutions to dynamical system models.

Indexed as

Artificial intelligenceEvolutionary algorithms in control and identificationIterative modeling and control designMan-in-the-loop systemsProcess modeling and identification

Identifiers

PMID40951715

DOI10.1016/j.ifacol.2025.07.162

PMCPMC12425487

What OpenQuestion holds

Textmetadata

LicenceCC BY-NC-ND

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.