{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# Solving PDE-based BIP using core CUQIpy\n", "\n", "\n", "Here we build a Bayesian problem in which the forward model is a partial differential equation (PDE) model, the 1D heat problem in particular.\n", "\n", "**Try to at least run through part 1 to 3 before working on the optional exercises.**\n", "\n", "## Learning objectives of this notebook:\n", "- Solve PDE-based Bayesian problem using CUQIpy.\n", "- Use different parametrizations of the Bayesian parameters (e.g. KL expansion, non-linear maps).\n", "\n", "## Table of contents: \n", "* [1. Loading the PDE test problem](#PDE_model)\n", "* [2. Building and solving the Bayesian inverse problem](#inverse_problem)\n", "* [3. Parametrizing the unknown parameters via step function expansion](#step_function)\n", "* [4. ★ Observe on part of the domain](#Partial_Observation) \n", "* [5. ★ Parametrizing the unknown parameters via KL expansion](#KL_expansion)\n", "\n", "★ Indicates optional section." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
cuqi.experimental.mcmc
module, which are expected to become the default soon. Check out the documentation for more details.\n",
"\n",
"\n",
"