From e52f937ccd5e356b9e3bbd9bafa7993c37b2baf1 Mon Sep 17 00:00:00 2001 From: Feda Curic Date: Wed, 7 Aug 2024 09:26:55 +0200 Subject: [PATCH] Add introduction to 2d heat eq problem --- notebooks/ES_2D_Heat_Equation.py | 12 +++++++++++- 1 file changed, 11 insertions(+), 1 deletion(-) diff --git a/notebooks/ES_2D_Heat_Equation.py b/notebooks/ES_2D_Heat_Equation.py index 21f5f39..5328502 100644 --- a/notebooks/ES_2D_Heat_Equation.py +++ b/notebooks/ES_2D_Heat_Equation.py @@ -14,7 +14,17 @@ # --- # %% [markdown] -# # Parameter estimation using ES and the 2D Heat Equation +# # Estimating Spatially Varying Heat Transfer Coefficients Using Ensemble Smoothers +# +# Imagine you're an archaeologist who has discovered a large, ancient metal plate buried in your garden.\ +# You're intrigued by its thermal properties, particularly how well it transfers heat, as this could provide clues about its composition and origin.\ +# Using a metal detector you've established the size and have concluded that it is too large to excavate without risking damage.\ +# Instead, you drill a few small holes at specific locations and measure the heat transfer coefficient at these points.\ +# The sparse measurements show that the plates' heat transfer coefficient varies in space, but you need to know it everywhere.\ +# To gather more information, you decide to introduce a heat source by drilling a hole and lowering a heat element to warm up the plate at that point.\ +# After removing the heat source, the plate will cool down according to the heat equation from physics.\ +# Using the sparse measurements and the observed cooling behavior, your goal is to estimate the heat transfer coefficient everywhere on the plate. +# # %% import numpy as np