Mathematicians will be key in identifying the potential of emerging and existing mathematical fields for, amongst other areas, the development of exascale and quantum computing, analytical and simulation tools for big data and for the modelling needed to meet the future environmental, societal and industrial challenges.
It is well known, and the consultation confirms that mathematics is a prerequisite for contemporary development in most fields of science. It is essential for both the exploitation of big data and the development of HPC towards exascale and quantum. At the same time, these developments are also enablers for new mathematics.
The consultation received 181 responses covering a large variety of mathematical disciplines. The consultation did not aim at covering all fields of mathematics, nor do the contributions do so. The consultation was a fully open, public consultation addressed to professionals who could contribute on a voluntary basis.
Several contributions to the discussion also addressed the challenges of the sizes of European Commission grants and the difficulties in matching them with the mathematical and computer science research needs. The concern is that the present format of European funding will not allow Europe to retain its mathematical talent.
Accrding to the report, the conclusion is clear: Mathematics is a vital part of the European research and innovation landscape. By playing a bigger role in the Horizon 2020 calls as a horizontal, cross cutting competence, mathematics would certainly increase the scalability and the quality of the projects.
Exascale computing is the expected next step in the long road of exponential performance increase. Today, HPC systems continue to scale up in compute node and processor core count. New mathematics, mathematical methods and tools are required to tackle new and more complex problems and crunch increasing amounts of data.
New mathematics will be needed to implement contemporary multicore processors, computers and HPC systems. The computational power of future exascale computers will be based on massive parallelism requiring new solutions to be developed. New methods can be developed to deal effectively with massive parallelism, combining ideas from numerical analysis, HPC, probability and inference, complementing the classical deterministic methods such as iterative methods for linear and non-linear systems.
According to the consultation, algorithms are needed to address the engineering and very large-scale matrix problems arising with exascale computing. Developing and analyzing the methods and algorithms will require substantial mathematical effort.
The landscape of parallel computers is dynamic and quickly changing, and mathematics needs to keep up with this. Different methods turn out to be optimal for different scales of HPC and deserve our continuous attention, research efforts and support. All in all, the mathematical development is crucial to fully harness the capacities of these computing powers.
Scalable mathematical methods and corresponding scientific algorithms for multi-petaflop/s and exaflop/s systems must be fault tolerant and fault resilient, since the probability of faults increases with scale. Resilience at the system software and at the algorithmic level is needed as a crosscutting and co-design effort. Additionally, employing novel mathematics and algorithms can lead to a substantial improvement in the performance of important applications. More mathematical effort is necessary.
According to the report, essential scientific and industrial applications require novel mathematics and mathematical software that address the scalability and resilience challenges of current and future-generation extreme-scale HPC systems. However, often there are limitations to scalability inherent to the numerical methods.
Collaboration between computer scientists and mathematicians is crucial to achieve the new era of exascale computing and the mathematical development that is a prerequisite for the exploitation of these future computers. Moreover, the role of statisticians will be important, to quantify uncertainty in new high-performance simulations, and thereby assess their accuracy in a reliable way.
Quantum technologies promise new ways to solve complex problems. Quantum research is at the crossroads of mathematics, theoretical physics and computer science. However, quantum technology is not sufficiently robust yet to deliver production quality computational power.
According to the report, real life quantum computer and related solutions will however also present a concrete risk to many contemporary security protocols, from military applications to block chain. Cryptographical solutions based on the impossibility to solve them within reasonable time frames may need rethinking or replacing with new quantum-proof algorithms.
Modelling, simulation and optimisation methods (MSO) have proven to be effective tools for solving many problems, e.g. energy production and transportation, risk evaluation and pricing, finance modelling, realistic prediction of wind fields, solar radiation, air pollution and forest fires, prediction of climate change, improving the filtration process for drinking water treatment and optimization methods for intensity-modulated radiation therapy.
The consultation notes that these methods are highly complex and are typically processed via the most modern tools of informatics including HPC and access to big data bases and usually need support of skilled experts. These experts are scarce, in particular in small and medium enterprises, or they leave Europe. Mathematical modelling, simulation and optimization (MSO) is a central cross-cutting scientific approach which today forms the third pillar of science besides experiment and theory (although in physics and chemistry sometimes this is part of theory).
In recent years mathematicians together with their partners in application fields and computing have made great efforts to improve the mathematical technologies involved in MSO. Examples are the great achievements in areas such as model reduction, adaptive solution of partial differential equations, compressed sensing, or image and signal processing.
Mathematical techniques have revolutionized the scientific development of some areas of science and technology, but as a transversal research field MSO is seldom seen in European funding schemes, says the report.
Apart from the report summarizing the consultation, also all contributions are available online.
See the EC announcement .