Calibration and machine learning techniques for building a Digital twin of the eye

The (https://premyom.com) PREMYOM project (Management and Slowing Down of the Myopia Epidemic through Medical Optics) aims to develop medical optics-based solutions to curb the global myopia epidemic. It aims to establish a therapeutic reference for personalized myopia treatment, leveraging unique expertise and a rigorous research, development, and innovation approach.

PREMYOM is a multidisciplinary consortium of renowned industry, healthcare, and research partners coordinated by EssilorLuxottica. It brings together an unprecedented blend of technical, clinical, and digital expertise, including the Hôpital Fondation Adolphe de Rothschild, Inria, InSimo, Institut Mines-Télécom, and the Institut de la Vision.

The French Prime Minister's General Secretariat for Investment (SGPI) and its operational agency, Bpifrance, co-financed the project under the France 2030 plan and the i-Demo-2 public funding program. This selection highlights the critical importance of children's visual health as a major public health issue and the fight against the myopia epidemic in Europe.

A numerical model of the eye is being developed to integrate various geometrical and optical parameters specific to each patient. The goal is to determine the optimal values of these parameters from laser measurements of retinal images reduced to observation vectors.
The current optimization approach to estimate the model parameters faces several challenges, including the lack of guaranteed optimum uniqueness, the existence of local minima, and poor conditioning of the problem. The project aims to develop advanced Bayesian methods for calibrating the eye model and integrating prior knowledge (based on population statistics), rigorous treatment of measurement noise and modeling errors. Developping efficient numerical strategies will give access to the parameters' full posterior distribution, enabling uncertainty and robustness analyses of the model predictions.

The (https://team.inria.fr/platon) Platon project-team focuses on developing innovative methods and algorithms for uncertainty mangament in numerical models, including advanced calibration strategies from data (observations, measurements, other model predictions) and uncertainty reduction.

This thesis will primarily develop and implement Bayesian inference methods to calibrate the parameters of the numerical eye model. A special attention will be given to the design of likelihood functions, including the representation of optical aberrations on polynomial bases, such as Zernike polynomials, to ease the comparison between the measurements and the model predictions. An essential aspect of this first part of the work will also concern the reduction of the computational burden of Bayesian methods, using low-cost surrogate models fitted to the calibration task. The PhD candidate will test the proposed methods using synthetic data generated using a model with known parameter values.The thesis will then progressively address model uncertainty by accounting for model errors in the calibration procedure and propose model selection procedures. Finally, the research will concentrate on creating a virtual twin of a patient's eye using laser images through machine learning techniques.

The work of the PhD candidate will be supervised by (http://www.pietrocongedo.altervista.org) P.M. Congedo, (https://edenimal-goy.github.io) E. Denimal Goy and (http://olemaitre.perso.math.cnrs.fr) Olivier Le Maitre, experts in uncertainty quantification methods.

The work will be conducted in the Platon team, a joint research group between Ecole Polytechnique and CNRS, hosted by the Center for Applied Mathematics (CMAP) of École Polytechnique.  

Inria is the only French public research body fully dedicated to computational sciences. It is a national operator in research in digital sciences and is a primary contact point for the French Government on digital matters. Under its founding decree as a public science and technology institution, jointly supervised by the French ministries for research and industry, Inria's missions are to produce outstanding research in the computing and mathematical fields of digital sciences and to ensure the impact of this research on the economy and society in particular. Inria covers the entire spectrum of research at the heart of these activity fields and works on digitally-related issues raised by other sciences and by actors in the economy and society at large. Beyond its structures, Inria's identity and strength are forged by its ability to develop a culture of scientific innovation, to stimulate creativity in digital research. Throughout its 8 research centres and its 180 project teams, Inria has a workforce of 3 400 scientists with an annual budget of 265 million euros, 29% of which coming from its own resources.

Candidates are required to have a Master's degree in engineering, applied mathematics or a related discipline, and a specialization in machine learning, uncertainty quantification, optimization or related fields. Preferable qualifications for candidates include proven research talent, an excellent command of English, and good academic writing and presentation skills. Applicants should submit a CV, a covering letter as a single document detailing the knowledge, skills and experience you think make you the right candidate for the job, a list of your MSc courses and grades, copy of your Master's thesis, a list of names of references and preferably a list of publications. For further details and applications, please contact Pietro Marco Congedo (\verb+pietro.congedo@inria.fr/+). All applications should be emailed to \verb+pietro.congedo@inria.fr/+.