Nonlinear Reduced Models for Parametric/Random PDEs

Explore a comprehensive lecture on nonlinear reduced models for parametric and random partial differential equations. Delve into the motivational example, linear reduced models, and performance analysis of reduced models. Examine the model problem, diffusion coefficient, and global error estimate. Learn about the construction of a library, including general ideas and types of partitions. Investigate local error estimates and upper bounds on library size. Study specific sequences with polynomial growth. Analyze numerical examples, including thermal block, multi-cells, state estimation, and single-cell scenarios. Gain insights from Diane Guignard of the University of Ottawa in this 41-minute presentation from the Fields Institute's Workshop on Controlling Error and Efficiency of Numerical Models.

Intro
Motivational example
Introduction
Outline
Linear reduced models
Performance of a reduced model
Model problem
Diffusion coefficient
Global error estimate
Construction of a library general idea
Type of partitions
Local error estimate
Upper bound on the size of the library
Specific sequence: polynomial growth
Numerical example: thermal block
Numerical example l: multi cells
Numerical example II: state estimation
Numerical example II: one cell