Grupo de lectura: Deep Learning para Ecuaciones Diferenciales Parciales

Este grupo de lectura, organizado en conjunto con académicos e investigadores en Ecuaciones Diferenciales Parciales y Machine Learning de la Universidad de Chile, tiene el objetivo de aprender juntos sobre temas de investigación en Machine Learning para resolver ecuaciones.

Nos reunimos los jueves a las 12:00 viernes a las 15:00 por zoom.
 

2020-11-13
15:00hrs.
Javier Castro. Uchile (Dim)
Deep backward schemes for high-dimensional nonlinear PDEs
https://uchile.zoom.us/j/86346682467?pwd=NlJkdGc0TTQzQ2lqNVV3NmM0bjMyQT09
Abstract:
Se discutira el paper Deep backward schemes for high-dimensional nonlinear PDEs 
https://arxiv.org/abs/1902.01599
2020-11-06
15:00hrs.
Jocelyn Dunstan. Uchile
Physics-Informed Deep Learning
Zoom: https://uchile.zoom.us/j/86346682467?pwd=NlJkdGc0TTQzQ2lqNVV3NmM0bjMyQT09 Pass: pedir a M. Petrache
Abstract:
Se discutiran los articulos
2020-10-30
15:00hrs.
Gonzalo Mena. oxford University
Neural Ordinary Differential Equations
https://uchile.zoom.us/j/89083121892?pwd=cHovbUhRalBHelpqckpyU3NXZnQwQT09 (pedir pass a Mircea Petrache)
Abstract:
Se discuten los papers:

https://arxiv.org/abs/1806.07366
https://arxiv.org/abs/2002.08071
2020-10-23
15:00hrs.
Mircea Petrache. PUC
Deep Neural Networks Desde el Punto de Vista del Grupo de Renormalisacion
Zoom: https://uchile.zoom.us/j/86346682467?pwd=NlJkdGc0TTQzQ2lqNVV3NmM0bjMyQT09 Pass: pedir a M. Petrache
2020-10-16
15:00hrs.
Joaquin Fontbona. Uchile
Mean-Field Interpretation of Deep Learning Algorithms (1)
Zoom: https://uchile.zoom.us/j/86346682467?pwd=NlJkdGc0TTQzQ2lqNVV3NmM0bjMyQT09 Pass: pedir a M. Petrache
2020-10-01
12:00hrs.
Nicolas Valenzuela. Uchile
Sobre "Solving high-dimensional partial differential equations using deep learning", de Jiequn Han, Arnulf Jentzen, y Weinan E (parte 2)
https://uchile.zoom.us/j/89083121892?pwd=cHovbUhRalBHelpqckpyU3NXZnQwQT09 (pedir pass a Mircea Petrache)
Abstract:
"Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the “curse of dimensionality.” This paper introduces a deep learning-based approach that can handle general high-dimensional parabolic PDEs. To this end, the PDEs are reformulated using backward stochastic differential equations and the gradient of the unknown solution is approximated by neural networks, very much in the spirit of deep reinforcement learning with the gradient acting as the policy function. Numerical results on examples including the nonlinear Black–Scholes equation, the Hamilton–Jacobi–Bellman equation, and the Allen–Cahn equation suggest that the proposed algorithm is quite effective in high dimensions, in terms of both accuracy and cost. This opens up possibilities in economics, finance, operational research, and physics, by considering all participating agents, assets, resources, or particles together at the same time, instead of making ad hoc
assumptions on their interrelationships"
2020-09-24
12:30hrs.
Claudio Munoz. Uchile
Sobre "Solving High-Dimensional Partial Differential Equations Using Deep Learning", de Jiequn Han, Arnulf Jentzen, y Weinan e (Parte 1)
https://uchile.zoom.us/j/89083121892?pwd=cHovbUhRalBHelpqckpyU3NXZnQwQT09 (pedir pass a Mircea Petrache)
Abstract:
"Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the “curse of dimensionality.” This paper introduces a deep learning-based approach that can handle general high-dimensional parabolic PDEs. To this end, the PDEs are reformulated using backward stochastic differential equations and the gradient of the unknown solution is approximated by neural networks, very much in the spirit of deep reinforcement learning with the gradient acting as the policy function. Numerical results on examples including the nonlinear Black–Scholes equation, the Hamilton–Jacobi–Bellman equation, and the Allen–Cahn equation suggest that the proposed algorithm is quite effective in high dimensions, in terms of both accuracy and cost. This opens up possibilities in economics, finance, operational research, and physics, by considering all participating agents, assets, resources, or particles together at the same time, instead of making ad hoc
assumptions on their interrelationships."