CORDIS - Forschungsergebnisse der EU

TIME parallelisation: for eXascale computing and beyond

Periodic Reporting for period 1 - TIME-X (TIME parallelisation: for eXascale computing and beyond)

Berichtszeitraum: 2021-04-01 bis 2022-09-30

Recent successes have established the potential of parallel-in-time integration as a powerful algorithmic paradigm to unlock the performance of Exascale systems. However, these successes have mainly been achieved in a rather academic setting, without an overarching understanding. TIME-X will take the next leap in the development and deployment of this promising new approach for massively parallel HPC simulation, enabling efficient parallel-in-time integration for real-life applications. We will:
1. Provide software for parallel-in-time integration on current and future Exascale HPC architectures, delivering substantial improvements in parallel scaling;
2. Develop novel algorithmic concepts for parallel-in-time integration, deepening our mathematical understanding of their convergence behaviour and including advances in multi-scale methodology;
3. Demonstrate the impact of parallel-in-time integration, showcasing the potential on problems that, to date, cannot be tackled with full parallel efficiency in three diverse and challenging application fields with high societal impact: weather and climate, medicine and fusion.
To realize these ambitious, yet achievable goals, the inherently inter-disciplinary TIME-X Consortium unites top researchers from numerical analysis and applied mathematics, computer science and the selected application domains. Europe is leading research in parallel-in-time integration. TIME-X unites all relevant actors at the European level for the first time in a joint strategic research effort. The project will enable taking the necessary next step: advancing parallel-in-time integration from an academic/mathematical methodology into a widely available technology with a convincing proof of concept, maintaining European leadership in this rapidly advancing field and paving the way for industrial adoption.
- We developed a unified performance model for the various PinT algorithms and presented it at the PinT Workshop in Marseilles. A paper describing it is currently under review. Improvements regarding the load balancing strategies have been identified based on this model and more systematic studies are currently underway.
- We made significant progress towards establishing MPI extensions supporting dynamic resource utilisation in an efficient way based on MPI Sessions. Time-X is currently the main driver behind this progress in the MPI Session working group, targeting the genericity of these interfaces also beyond Time-X. This already resulted in two publications.
- We started to implement time-adaptive spectral deferred correction methods within the pySDC framework. First steps have been taken to extend this to time-parallel methods on small- and larger-scales. Furthermore, we published a theoretical analysis of the impact of reduced coarse level resolution on convergence of Parareal.
- We developed two new PinT methods for solving optimal control problems or more generally time dependent PDE constraint optimization problems, called ParaOpt1 and ParaOpt2, which use the structure of the coupled forward and backward problems directly. We obtained a complete converge analysis of the new ParaOpt1 algorithm, which appeared in a joint paper. Time-X enabled an additional contribution, unforeseen at the time of writing the proposal, that complements the above work, involving a collaboration with application experts in turbulent flow simulations. We also have a complete convergence analysis of ParaOpt2.
- We formulated general iterative PinT algorithms together with other project partners using the technique of block iterations, which led to a general framework of analysis using generating functions for Parareal, MGRIT, PFASST and STMG. A manuscript is currently in revision.
- We investigated how the model error of the approximate model influences the convergence of the micro-macro Parareal algorithms, both from a theory side as using numerical experiments. We performed numerical experiments for various (nonlinear) stochastic differential equations. We are developing methods that aim at speeding up the simulation of stochastic differential equations by using moment models. Several publications are in preparation. The upscaling for differential algebraic equations similar to the micro/macro Parareal was investigated and the results are published. A publication describing the application of the developed approach is in preparation.
- We designed an adaptive variant of the Parareal algorithm, specifically tailored to molecular dynamics simulations. A significant gain in efficiency is obtained in comparison to the standard Parareal algorithm. We then implemented this algorithm in LAMMPS (a very well distributed software in the material science community), that will open the way to the simulation of realistic physical systems. A manuscript collecting the results is currently in preparation and should be submitted soon.
- We accomplished the design of a PinT multirate explicit stabilised method with applications to cardiac electrophysiology. Preliminary results are promising. A conference proceeding has appeared and a paper is in preparation.
- We worked on space/time multigrid preconditioners for fractional diffusion equations (FDEs). We started by considering a FDE with non-smooth solutions and built tailored multigrid preconditioners. Then we considered the case of tempered FDEs. We provided a spectral study and exploited it to build tailored multigrid solvers. Finally, we dealt with a new method for solving time-dependent n-dimensional PDEs through a particular approach. Each of the first two topics led to a publication, while the paper related to the third one is in preparation.
The innovation process that leads to the development and deployment of PinT methods for simulation in a wide range of disciplines leads to an “innovation chain” with three distinct (and interacting) phases. TIME-X will provide significant advances to the state of the art at all steps in this innovation chain:
- In the algorithm development phase, TIME-X will propose significant algorithmic enhancements to PinT methodology, including advances in multi-scale methodology and enabling PinT methods to be incorporated in UQ, optimisation and control computation;
- In the software implementation phase, TIME-X will provide a software implementation for PinT methods on current and future Exascale HPC architectures, delivering substantial improvements in parallel scaling and load balancing;
- For adoption in simulation practice, TIME-X will showcase its potential in four diverse and challenging applications with high societal relevance: medicine, electromagnetics, drug design and weather/climate.

The desired impact of the scientific advances made by TIME-X will only be achieved by a concerted inter-disciplinary research effort at European scale. Consequently, TIME-X will address the following impact challenges:
- Unify the European community working on PinT methods; foster a strategic research approach exploiting synergies between complementary expertises of the Partners; cement European leadership in this field, thus contributing to the ETP4HPC Strategic Research Agenda.
- Educate stakeholders about PinT methods and facilitate widespread adoption by domain scientists, based on methodological advances and application-specific results.
- Boost research in four challenging domains with high societal impact​: medicine, electromagnetics, drug design and climate/weather
The left parallelization does not converge, even after many iteration. The modified algorithm works.