Nicolás Valenzuela's Homepage

PhD candidate at the Departament of Mathematical Engineering (DIM) of the University of Chile, under the advice of Prof. Claudio Muñoz .

Previously, Claudio Muñoz was my master thesis advisor at the DIM of the University of Chile.

Contact Information: nvalenzuela (at) dim (dot) uchile (dot) cl

My research interest:

I am interested in Deep Neural Networks (DNNs) theory applied to Partial Differential Equations (PDEs). In particular, I like to work with Physics Informed Neural Networks (PINNs), Operator Learning, such as DeepONets, Fourier Neural Operators (FNOs), among others. I am also interested in the universal approximation of solutions of some PDEs via ReLU DNNs overcoming the curse of dimensionality (CoD).

Prediction of mKdV 2-Soliton via DNNs

Publications

Prediction of cubic Schrödinger Soliton via DNNs

A new approach for the fractional Laplacian via deep neural networks arXiv preprint.
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.
The Calderón's problem via DeepOnets (with J.Castro and C. Muñoz) published in Vietnam J. Math. (2024)
Bounds on the approximation error for deep neural networks applied to dispersive models: Nonlinear waves (with C. Muñoz) arXiv preprint.
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.

Talks

XXXIV Southern Zone Mathematics Conference. Chile. April 2022.
Analysis and Geometry Seminar. Universidad Católica. Santiago, Chile. June 2023.
PhD seminar of the Department of Mathematical Engineering, Universidad de Chile. Santiago, Chile. October 2023.
XCI Annual Meeting of the Mathematical Society of Chile. Santiago, Chile. December 2023.
Summer School on Computing Intelligence EVIC. Santiago, Chile. December 2023.
12th Computing Conference, London, United Kingdom. July 2024.
II Postgraduate Symposium of Engineering, Science and Innovation. Santiago, Chile. August 2024.
PDE Seminar. University of Chile. Santiago, Chile. August 2024.
First Research Workshop: Universidad de O'Higgins and Universidad de Chile. Rancagua, Chile. September 2024.

Klein-Gordon Solution approximation via DNNs and Branching Processes

Teaching experience

As an assistant professor at University of Chile (times)

In the courses: Introduction to Algebra (3), Linear Algebra (2), Ordinary Differential Equations (1), Multivariable Calculus (5), Probability and Statistics (2), Partial Differential Equations (1).

Research stays

Basque Center of Applied Mathematics (BCAM), Spain, with Professor Luca Fanelli. January-March 2024.
Inria Scool team, France, with Professor Phillip Preux. February-March 2025.

Fellowships

ANID-Subdirección de Capital Humano/Doctorado Nacional/2023-21231021.
Latin America Google PhD Fellowship (2023). Under the mentoring of Pablo Samuel Castro.

Page updated

Google Sites

Report abuse