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#The solution of inverse problems...

##... using Gradient Descent Techniques implemented in Python and built from scratch

###by Tomás Gómez Álvarez-Arenas

###Institute of Physical and Information Technologies (CSIC)


Inverse problems (IP) are commonly found in physics, engineering, biology, ... but also in economy and social sciences.

The concept of Inverse Problem is a powerful way to approach the problem we encounter when we want to convert DATA into KNOWLEDGE.

In particular, given a data set and a model that it is expected to describe the data set, by solving the IP we are able to determine the model parameters.

The talk introduces the inverse problem, its main elements and applications. Introduces the main algorithms used, and the implementations already available in Python.

Then the Gradient Descent Algorithm (systematic and stochastic) is explained in detail and applied to several examples, from a very simple linear regression to a complex high dimensional problem found in ultrasound analysis.

A simple implementation of the Gradient Descent algorithm and the examples shown in the talk is also available, both the python code and the ipython notebook.