UE Inverse problem and data assimilation: variational and Bayesian approaches

Degrees incorporating this pedagocial element :


This course is about inverse problem and data assimilation.

Inverse methods allow to combine optimally all sources of information available about a given (physical, biological, chemical, …) system: - mathematical equations (physical laws or the biological processes, …); - observations (measures of real experiments); - error statistics (observation errors, model errors, …). These sources of information are usually heterogeneous: different nature, varying quality and quantity. In geosciences, inverse methods are often called data assimilation. Historically, the idea was to estimate the initial state of the atmosphere, in order to produce weather forecasts. Today, it has many applications, not only initial state estimation (parameter estimation, physical law parameterisation, numerical parameter estimation, unknown forcing sources estimation…). It is also used in many application domains, not only weather forecasting (oceanography, oil drill, seismology, energy, medicine, biology, glaciology, agronomy, construction industry, …).

The purpose of this course is to give an overview of the existing methods, from variational approaches - which describes the problem in terms of function optimisation - to Bayesian techniques - that relie on sampling theory. Labs are also part of the course.


parameter estimation, uncertainty quantification and reduction, numerical modeling, optimisation, Monte Carlo filter