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Since its conception, in late 2020 - early 2021, the group has followed the most recent and relevant works in the area and started to develop new results and improvements in the research directions mentioned in Research Lines. Below you can see our most recent works.
Since its conception, in late 2020 - early 2021, the group has followed the most recent and relevant works in the area and started to develop new results and improvements in the research directions mentioned in Research Lines. Below you can see our most recent works.
Papers and Preprints
2026
Christopher Maulén, Claudio Muñoz and Alfredo Padilla
Error bounds for Physics-Informed Neural Networks for the Good and Bad Boussinesq models (under preparation).
Álvaro Márquez, Paula Jofré, Claudio Muñoz and Álvaro Rojas
Generating stellar atmosphere models using PINNs (under preparation).
Ricardo Freire, Claudio Muñoz and Nicolás Valenzuela
Neural Discovery of Strichartz Estimates (preprint).
https://doi.org/10.13140/RG.2.2.17167.34728
Claudio Muñoz and Alonso Rojas
Quantification of error bounds and related estimates for Neural Inverse Operators (under preparation).
2025
Julio Vivanco, Nicolás Valenzuela and Claudio Muñoz
Applications of Artificial Intelligence in economic diameter estimation for high-pressure water long-distance pipelines
Proc. 22nd International Conference on Hydrotransport
https://www.iha-hydrotransport-conference.com/2025-conference-proceedings/
Ricardo Freire, Claudio Muñoz and Nicolás Valenzuela
Error bounds for Physics Informed Neural Networks in generalized KdV equations placed on unbounded domains
2024
Javier Castro, Claudio Muñoz and Nicolás Valenzuela
The Calderón's problem via DeepONets
Vietnam J. Math
https://doi.org/10.1007/s10013-023-00674-8
Claudio Muñoz and Nicolás Valenzuela
Bounds on the approximation error for deep neural networks applied to dispersive models: Nonlinear waves
https://arxiv.org/abs/2405.13566
To appear in Partial Differential Equations and Applications.
Miguel A. Alejo, Lucrezia Cossetti, Luca Fanelli, Claudio Muñoz and Nicolás Valenzuela
Error bounds for Physics Informed Neural Networks in Nonlinear Schrödinger equations placed on unbounded domains
2023
Javier Castro
The Kolmogorov Infinite Dimensional Equation in a Hilbert space Via Deep Learning Methods
Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2023.127413
Nicolás Valenzuela
A new approach for the fractional Laplacian via deep neural networks
https://arxiv.org/abs/2205.05229
Nicolás Valenzuela
A Numerical Approach for the Fractional Laplacian via Deep Neural Networks
Proceedings of the 2024 Computing Conference, Volume 2
2022
Javier Castro
Deep Learning Schemes For Parabolic Nonlocal Integro-Differential Equations
Partial Differential Equations and Applications
Talks
2026
Discovery and absence of Strichartz extremizers using Physics Informed Neural Networks
Nicolás Valenzuela
Seminar Math-AI CMM
April 2026
Discovery and absence of Strichartz extremizers using Physics Informed Neural Networks
Nicolás Valenzuela
Second WAFFLE Meeting
https://sites.google.com/view/mathamsud-waffle/second-waffle-meeting?authuser=0
March 2026
Bounds on the approximation error for deep neural networks applied to dispersive models: Nonlinear waves
Nicolás Valenzuela
Recent Progress in Asymptotic Stability of Solitons and Related Problems
January 2026
https://eventos.cmm.uchile.cl/asympstab2026/
Error estimates of neural operators for inverse problems
Alonso Rojas
Inverse Problems in the Physical Sciences
Summer Schoool IPPhys2026,
January 2026
2025
Error bounds for Physics Informed Neural Networks in Nonlinear Schrödinger equations placed on unbounded domains
Claudio Muñoz
PDE Seminar DIM-CMM
January 2025
Resolution of chemical equilibrium through the use of PINNs.
Álvaro Márquez
Workshop on Applied Math PUC
March 6-7 2025
https://appliedmathuc.github.io/workshop-applied-math-2025/
Error bounds for Physics Informed Neural Networks in Nonlinear Schrödinger equations placed on unbounded domains
Claudio Muñoz
Workshop on Applied Math PUC
March 6-7 2025
https://appliedmathuc.github.io/workshop-applied-math-2025/
An Introduction to Physics Informed Neural Networks Applied to the Nonlinear Schrödinger Equation
Nicolás Valenzuela
INRIA Lille
June 2025
https://team.inria.fr/panda/workshop-panda-in-lille-2025/
Error Bounds for PINNS in gKdV equations placed on unbounded domains
Ricardo Freire
INRIA Lille
June 2025
https://team.inria.fr/panda/workshop-panda-in-lille-2025/
An Introduction to Physics Informed Neural Networks and Their Application to Nonlinear Dispersive Equations
Nicolás Valenzuela
Universidad de Miami
July 21-25
Mathematical Congress of the Americas (MCA)
Construction of stellar atmospheres models through the use of PINNs
Álvaro Márquez
Conference on Mathematics of Machine Learning 2025, Universidad de Hamburgo
September 2025
Generación de Modelos de Atmósferas Estelares Mediante PINNS
Álvaro Márquez
III Simposio de Postgrado en Ingeniería, Ciencias e Innovación, U. Chile
August 2025
Bounds on the approximation error for deep neural networks applied to dispersive models: Nonlinear waves
Nicolás Valenzuela
Conference on Mathematics of Machine Learning 2025, Universidad de Hamburgo
September 2025
Applications of Artificial Intelligence in economic diameter estimation for high-pressure water long-distance pipelines
Nicolás Valenzuela
Czech Technical University in Prague
May 2025
https://www.iha-hydrotransport-conference.com
2024
A numerical approach for fractional Laplacian via deep neural networks.
Nicolás Valenzuela
12th Computing Conference, London, United Kingdom.
July 2024
Aplicación de PINN’s en atmósferas estelares
Álvaro Márquez
Seminario de Magister Departamento de Ingeniería Matemática, U. Chile
July 2024
Bounds on the approximation error for deep neural networks applied to dispersive models: Nonlinear waves
Nicolás Valenzuela
II Postgraduate Symposium of Engineering, Science and Innovation. Santiago, Chile
August 2024
Bounds on the approximation error for deep neural networks applied to dispersive models: Nonlinear waves
Nicolás Valenzuela
PDE Seminar. University of Chile. Santiago, Chile.
August 2024
Bounds on the approximation error for deep neural networks applied to dispersive models: Nonlinear waves
Nicolás Valenzuela
First Research Workshop: Universidad de O'Higgins and Universidad de Chile. Rancagua, Chile.
September 2024
Bounds on the approximation error for deep neural networks applied to dispersive models: Nonlinear waves
Claudio Muñoz
Workshop in Nonlinear PDE, Brasil
August 19-23 2024
https://impa-dev.kindle.com.br/arquivo_base/eventos-do-impa/2024-2/workshop-in-nonlinear-pde/
Bounds on the approximation error for deep neural networks applied to dispersive models: Nonlinear waves
Claudio Muñoz
Brasil
August 26-30 2024
https://mat.ufpb.br/clam/index.php/atividades/sessoes-tematicas#sessoes-15-21
Tres lineas de trabajo recientes en ecuaciones dispersivas
Claudio Muñoz
Primera Jornada de Investigación: Universidad de O'Higgins y Universidad de Chile
September 24 2024
https://eventos.cmm.uchile.cl/pde-uoh-2024/
Aplicación de PINNs en atmósferas estelares
Álvaro Márquez
ENIM Encuentro Nacional de Ingeniería Matemática 2024
December 2024
2023
Una nueva visión para el Laplaciano fraccionario vía redes neuronales profundas.
Nicolás Valenzuela
Analysis and Geometry Seminar. Universidad Católica
June 2023
https://www.mat.uc.cl/seminarios/seminario-de-analisis-y-geometria.html?page=2
Una breve introducción a la teoría de redes neuronales profundas y su relación con EDPs
Nicolás Valenzuela
PhD seminar of the Department of Mathematical Engineering, Universidad de Chile
Octuber 2023
A numerical approach for fractional Laplacian via deep neural networks.
Nicolás Valenzuela
XCI Annual Meeting of the Mathematical Society of Chile
December 2023
https://sites.google.com/uchile.cl/somachi2023/inicio?authuser=0
Approximation of solutions of the wave equation via deep neural networks.
Nicolás Valenzuela
XCI Annual Meeting of the Mathematical Society of Chile
December 2023
https://sites.google.com/uchile.cl/somachi2023/inicio?authuser=0
A numerical approach for fractional Laplacian via deep neural networks.
Nicolás Valenzuela
Summer School on Computing Intelligence EVIC. Santiago, Chile
December 2023
2022
Una nueva visión para el Laplaciano fraccionario vía redes neuronales profundas.
Nicolás Valenzuela
XXXIV Southern Zone Mathematics Conference. Chile.
April 2022
Una nueva visión para el Laplaciano fraccionario vía redes neuronales profundas.
Nicolás Valenzuela
PhD seminar of the Department of Mathematical Engineering, Universidad de Chile
September 2022
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