Symbolic Regression via Neural Networks

• URL: http://arxiv.org/abs/2605.04337v1
• Date: Tue, 05 May 2026 22:43:35 GMT
• Title: Symbolic Regression via Neural Networks
• Abstract summary: We present a novel approach that combines the flexibility and accuracy of deep learning approaches with the utility of symbolic solutions.<n>We first describe the architecture for our model, then show the accuracy of our algorithm across a range of classical dynamical systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their capabilities in approximating dynamics from data, but a shortcoming of traditional deep learning is that there is little insight into the underlying mapping beyond its numerical output for a given input. This limits their utility in analysis beyond simple prediction. Simultaneously, a number of strategies exist which identify models based on a fixed dictionary of basis functions, but most either require some intuition or insight about the system, or are susceptible to overfitting or a lack of parsimony. Here we present a novel approach that combines the flexibility and accuracy of deep learning approaches with the utility of symbolic solutions: a deep neural network that generates a symbolic expression for the governing equations. We first describe the architecture for our model, then show the accuracy of our algorithm across a range of classical dynamical systems.

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