Publications

Prediction of cubic Schrödinger Soliton via DNNs

1. Error bounds for Physics Informed Neural Networks in Generalized KdV Equations placed on unbounded domains (with R. Freire and C. Muñoz) arXiv preprint (2026)

2. Error bounds for Physics Informed Neural Networks in Nonlinear Schrödinger equations placed on unbounded domains (with M.A. Alejo, L. Cossetti, L. Fanelli and C. Muñoz) arXiv preprint. (2025)

3. Applications of artificial intelligence in economic diameter estimation for high-pressure water long-distance pipelines (with J. Vivanco and C. Muñoz) published in 22nd International Conference on Hydrotransport (2025).

4. Bounds on the approximation error for deep neural networks applied to dispersive models: Nonlinear waves (with C. Muñoz) accepted in SN Partial Differential Equations and Applications (2024).

5. The Calderón's problem via DeepOnets (with J.Castro and C. Muñoz) published in Vietnam J. Math. (2024)

6. A numerical approach for the fractional Laplacian via deep neural networks. In: Arai, K. (eds) Intelligent Computing. SAI 2024. Lecture Notes in Networks and Systems, vol 1017. Springer, Cham. 

7. A new approach for the fractional Laplacian via deep neural networks arXiv preprint.