2022-04982 - PhD Position F/M Scaling the solving of Ordinary Differential Equation for Computational Biology (and Deep Learning)

Contract type : Fixed-term contract

Level of qualifications required : Graduate degree or equivalent

Fonction : PhD Position

About the research centre or Inria department

The Inria research centre in Lyon (previously the Lyon branch of the Inria centre in Grenoble) is the 9th Inria research centre, formally created in December 2021.  It brings together approximately 270 people (including 110 Inria employees) in 15 research teams and research support services.

Its staff are distributed at this stage on 2 campuses: in Villeurbanne La Doua (Centre / INSA Lyon / UCBL) on the one hand, and Lyon Gerland  (ENS de Lyon) on the other. A third site should be opened in the course of 2022. The teams are mainly hosted with our partners.  The centre's teams work closely with research and higher education institutions (ENS de Lyon, UCBL, INSA Lyon, etc.), their laboratories, and other research organisations in Lyon (CNRS, INRAE, competitiveness clusters, etc.), but also with Lyon and regional economic players. Many international collaborations are also underway.

The Lyon centre is active in the fields of software, distributed and high-performance computing, embedded systems, quantum computing and privacy in the digital world, but also in digital health and computational biology.


In biology, the vast majority of systems can be modeled as ordinary differential equations (ODEs). Modeling more finely biological objects leads to increase the number of equations. Simulating ever larger systems also leads to increasing the number of equations. Therefore, we observe a large increase in the size of the ODE systems to be solved. A major lock is the limitation of ODE numerical resolution software (ODE solver) to a few thousand equations due to prohibitive calculation time. The AEx ExODE tackles this lock via 1) the introduction of new numerical methods that will take advantage of the mixed precision that mixes several floating number precisions within numerical methods, 2) the adaptation of these new methods for next generation highly hierarchical and heterogeneous computers composed of a large number of CPUs and GPUs. For the past year, a new approach to Deep Learning has been proposed to replace the Recurrent Neural Network (RNN) with ODE systems. The numerical and parallel methods of ExODE will be evaluated and adapted in this framework in order to improve the performance and accuracy of these new approaches.

Description of the thesis



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[2] Dominik Göddeke, Robert Strzodka, and Stefan Turek. Performance and accuracy of hardware-oriented native-, Emulated-and mixed-precision solvers in fem simulations. International Journal of Parallel, Emergent and Distributed  Systems, 22(4) :221-256, 2007.
[3] Will Grathwohl, Ricky TQ Chen, Jesse Betterncourt, Ilya Sutskever, and David Duvenaud. Ffjord : Free-form  Continuous dynamics for scalable reversible generative models. arXiv preprint arXiv :1810.01367, 2018.
[4] Azzam Haidar, Stanimire Tomov, Jack Dongarra, and Nicholas J. Higham. Harnessing gpu tensor cores for fast fp16 arithmetic to speed up mixed-precision iterative refinement solvers. In Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis, SC '18, pages 47 :1-47 :11, Piscataway, NJ, USA, 2018. IEEE Press.
[5] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2016.
[6] Alan C Hindmarsh. Serial fortran solvers for ode initial value problems. URL:  https://computation.llnl.gov/casc/odepack/ [cited June 6, 2019], 2002.
[7] P.J. Van Der Houwen and B.P. Sommeijer. Parallel iteration of high-order runge-kutta methods with stepsize control. Journal of Computational and Applied Mathematics, 29(1) :111 - 127, 1990.
[8] Natalia Kalinnik, Matthias Korch, and Thomas Rauber. An efficient time-step-based self-adaptive algorithm for predictor-corrector methods of runge-kutta type. Journal of Computational and Applied Mathematics, 236(3) :394 - 410, 2011. Aspects of Numerical Algorithms, Parallelization and Applications.
[9] Natalia Kalinnik, Matthias Korch, and Thomas Rauber. Online auto-tuning for the time-step-based parallel solution of odes on shared-memory systems. Journal of Parallel and Distributed Computing, 74(8) :2722 - 2744, 2014.
[10] Matthias Korch and Tim Werner. Accelerating explicit ode methods on gpus by kernel fusion. Concurrency and Computation : Practice and Experience, 30(18) :e4470, 2018. e4470 cpe.4470.
[11] Tomonori Kouya. Practical implementation of high-order multiple precision fully implicit runge-kutta methods with step size control using embedded formula. arXiv preprint arXiv :1306.2392, 2013.
[12] Xiaoye S. Li, James W. Demmel, David H. Bailey, Greg Henry, Yozo Hida, Jimmy Iskandar, William Kahan, Suh Y. Kang, Anil Kapur, Michael C. Martin, Brandon J. Thompson, Teresa Tung, and Daniel J. Yoo. Design,  Implementation and testing of extended and mixed precision blas. ACM Trans. Math. Softw., 28(2) :152-205, June 2002.
[13] L. Murray. Gpu acceleration of runge-kutta integrators. IEEE Transactions on Parallel and Distributed Systems, 23(1) :94-101, Jan 2012.
[14] T. Rauber and G. Rünger. How do loop transformations affect the energy consumption of multi-threaded runge-kutta methods ? In 2018 26th Euromicro International Conference on Parallel, Distributed and Network-based Processing (PDP), pages 499-507, March 2018.
[15] Thomas Rauber and Gudula Rünger. Parallel execution of embedded and iterated rungekutta methods. Concurrency : Practice and Experience, 11(7) :367-385, 1999.


The PhD student will contribute to the research activities of the exploratory action ExODE (Scaling the Resolution of Ordinary Differential Equation for Computational Biology) on the following subjects: numerical and parallel methods for the resolution of ordinary differential equation (ODE), ODE resolution scheme in mixed precision, numerical method adaptation for the ODE resolution applied to computational biology (and deep learning) and more generally to participate in all the scientific activities of the exploratory action ExODE.

Main activities


  • Analyze requirements
  • Propose and analyze solutions
  • Design experimental platforms
  • Write articles
  • Write the reports
  • Present the work


Technical skills and level required :

Research master, Applied mathemathics (and/or), Computational sciences (and/or), high performance computing


Languages : English

Benefits package

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage


1st and 2nd year: 1 982 euros gross salary /month
3rd year: 2 085 euros gross salary / month