Investigation reveals deep learning efficiently addresses integral equations in complex differential systems, suggesting improved computational methods.
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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Lemaire et al. (2026) studied this question.
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