Pré-Publication, Document De Travail Année : 2026

Deep Learning for Integro-Differential Elimination

Résumé

We investigate the use of deep learning techniques for computing integral equations from systems of nonlinear differential equations. The class of integral equations we consider are very general and difficult to manipulate with purely symbolic computations. In order to rapidly explore and experiment with such complicated expressions, we have trained deep learning models to get valuable insight on the type of expressions that can be expected to be calculated using symbolic methods. The first contribution is a novel algorithm for converting an integral equation into a differential equation. The second is the discovery and resolution, via our trained models, of systems which are currently beyond the reach of classical computer algebra.

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Dates et versions

hal-05230281 , version 1 (29-08-2025)
hal-05230281 , version 2 (16-03-2026)
hal-05230281 , version 3 (30-03-2026)

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  • HAL Id : hal-05230281 , version 2

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François Lemaire, Louis Roussel. Deep Learning for Integro-Differential Elimination. 2026. ⟨hal-05230281v2⟩
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