[Paper] A Data-Free Symbolic Regression Approach for Solving Equations
Source: arXiv - 2606.07152v1
Overview
Many equations arising in science currently cannot be solved by available analytical techniques and are therefore solved numerically, without yielding explicit symbolic expressions. Existing symbolic regression approaches can recover symbolic expressions, but require training data obtained from the underlying process, rather than the governing equation alone. We propose the Symbolic Equation Solver (SES), a framework that formulates equation solving as an optimization problem over differentiable symbolic models. SES constructs its objective from the equation together with initial or boundary conditions, eliminating the need for paired input-output data. The learned model is expressed in explicit symbolic form, enabling further analysis. We evaluate SES on representative algebraic and differential equations, including a system of algebraic equations, an equation with transcendental terms, an ordinary differential equation, and partial differential equations with different initial or boundary conditions. Across these settings, SES recovers compact symbolic expressions that match the corresponding analytical solutions.
Key Contributions
This paper presents research in the following areas:
- cs.NE
- cs.SC
Methodology
Please refer to the full paper for detailed methodology.
Practical Implications
This research contributes to the advancement of cs.NE.
Authors
- Sergei Garmaev
- Vinay Sharma
- Olga Fink
Paper Information
- arXiv ID: 2606.07152v1
- Categories: cs.NE, cs.SC
- Published: June 5, 2026
- PDF: Download PDF