SIRD: Symbolic Integration Rules Dataset

Advancements in neural networks and computer hardware lead to new use cases for deep learning in the natural sciences every day. Even though symbolic mathematics tasks have been explored, symbolic integration only has a few studies using black box models and currently lacks explainability. Symbolic integration is a challenging search problem and we obtain the final result by applying different integration rules such as integration by parts or u-substitution. We address this by proposing a novel and interpretable approach to perform symbolic integration using deep learning through integral rule prediction. To our knowledge, we contribute the first Symbolic Integration Rules Dataset (SIRD), comprising 2 million distinct functions and integration rule pairs. For complex rules such as u-substitution and integration by parts, our dataset also includes the expression to be substituted or used in the rule application. We also train a transformer model on our proposed dataset and incorporate it into Sympy's integral_steps function, resulting in 6 times fewer branches explored by allowing our model to guide the depth-first-search procedure.