# Neural Integro-Differential Equations

@article{Zappal2022NeuralIE, title={Neural Integro-Differential Equations}, author={Emanuele Zappal{\`a} and Antonio Henrique de Oliveira Fonseca and Andrew Henry Moberly and Michael J. Higley and Chadi G. Abdallah and Jessica A. Cardin and David van Dijk}, journal={ArXiv}, year={2022}, volume={abs/2206.14282} }

. Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that present an integral over time. As such, these systems are modeled with Integro-Diﬀerential Equations (IDEs); generalizations of diﬀerential equations that comprise both an integral and a diﬀerential component. For example, brain dynamics are not accurately modeled by diﬀerential equations since their behavior is…

## One Citation

### Neural Integral Equations

- Computer Science, MathematicsArXiv
- 2022

An attentional version of NIE is introduced, called Attentional Neural Integral Equations (ANIE), where the integral is replaced by self-attention, which improves scalability and provides interpretability and it is shown that learning dynamics via integral equations is faster than doing so via other continuous methods, such as Neural ODEs.

### Numerical analysis of finite difference schemes arising from time-memory partial integro-differential equations

- MathematicsFrontiers in Applied Mathematics and Statistics
- 2022

This paper investigates the partial integro-differential equation of memory type numerically. The differential operator is discretized based on θ-finite difference schemes, while the integral…

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