2019-01677 - PhD Position F/M - From measures to model : inferring causal states and their relations

Contract type : Public service fixed-term contract

Level of qualifications required : Graduate degree or equivalent

Fonction : PhD Position

About the research centre or Inria department

The GeoStat project makes fundamental and applied research on new non linear methods for the analysis of complex signals and systems, using paradigms and tools coming from statistical physics.


This PhD is supervised by Nicolas Brodu (Geostat team, Inria Bordeaux). Short stays are planned at the University of California, Davis, for collaboration with the team of James P. Crutchfield (Complexity Sciences Center). Attending multidisciplinary summer schools will be encouraged


Scientific context

The context of this PhD is modeling physical systems, starting from measured data and accounting for their dynamics [1]. The idea is to statistically describe the evolution of a system in terms of causally-equivalent states; states that lead to the same predictions [2]. Transitions between these states can be reconstructed from data, leading to a theoretically-optimal predictive model [3]. In practice, however, no algorithm is currently able to reconstruct these models from data in a reasonable time and without substantial discrete approximations. Recent progress now allows a continuous formulation of predictive causal models. Within this framework, more efficient algorithms may be found. The broadened class of predictive models promises a new perspective on structural complexity in many applications.

PhD objectives

The goal is to explore this new class of continuous models. These can be formulated as stochastic differential equations, but in the functional space of causal states. In addition, observed data are often acquired at their own sampling rate, which may differ greatly from the characteristic scale of the original physical processes. A second goal is to ensure consistency between renormalized versions of the model at different scales. A last objective is to validate the new models on real data. This part will be done in collaboration with disciplinary specialists.

[1] James P. Crutchfield, “Between order and chaos”. Nature Physics vol 8, p17-24, 2012.
[2] Nicolas Brodu, “Reconstruction of epsilon-machines in predictive frameworks and decisional states”. Advances in Complex Systems 14(5), p761-794, 2011.
[3] Cosma R. Shalizi, Kristina L. Klinkner, Robert Haslinger. “Quantifying self-organization with optimal predictors”. Physical Review Letters, 93:118701, 2004.

Main activities

Depending on her/his skills, own interests and ideas, the candidate shall participate on some or all the aspects of this project:
– Theory : the properties of stochastic processes describing the evolution of causal states ;
– Algorithmic : how to best estimate the model from data ;
– Applications : validating the model on real data, in collaboration with disciplinary experts on these data.

In any case, it is expected that the candidate is highly motivated by the general context of this PhD proposal.


Prior experience in physics, scientific data analysis or modeling will be strongly appreciated. Being autonomous with scientific programming is required.
It is necessary to be fluent in English. Learning French is not required for working at Inria, but greatly facilitates daily life outside the institute.

Benefits package

  • Subsidized meals (restaurant on site)
  • Discount on public transportation
  • Possibility of teleworking (after 6 months of employment) and organisation of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc).
  • Social, cultural and sports events and activities (Inria Social Work Management Association)
  • Access to vocational training
  • Social Security


  • 1982€ / month (before taxes) during the first 2 years
  • 2085€ / month (before taxes) during the third year

Note : Taxes are based on your personal and family situation.