Technical solutions: from fundamental research, through modelling and design, to prototypes. The application of mathematical, information technology, and electronics tools to macro-, micro-, and nanoscale problems (PRA 4)

The goal of PRA 4 is to develop a broad spectrum of mathematical and IT techniques to facilitate the description, modelling, understanding, and control of processes that occur in the real world. The aim is to develop and apply various theoretical techniques and approaches, those based on actual data, as well as heuristic approaches supported by artificial intelligence methods in particular. These approaches require scientists to develop a multidirectional and multidimensional scientific repertoire. The additional necessity is to possess theoretical knowledge of the applied tools and the latest research results in the field, as well as expert and practical knowledge in the field of engineering sciences where the developed tools are to find application. The key role in such endeavours falls to mathematicians who have the possibilities to modify the available theoretical tools to adjust them to specific practical applications. Yet another indispensable thing is the cooperation with industry, without which there would be no chance of acquiring properly broad data collections coming from real-life processes or performing the necessary validation of laboratory results in practical conditions. The gap between mathematical solutions and the final application in industry is filled by numerical solutions and complex IT systems. Research in the field includes the following:

  • Deterministic systems related to industrial processes based on differential equations (ordinary, partial, and with time delay)
  • Stochastic modelling used to better describe and predict actual data (predictive models, statistical models of process evolution, models based on stochastic differential equations, Monte Carlo methods)
  • Statistical data analysis, development of new quality standards, construction of new statistical tools for problems originating in engineering sciences, and predictions aiding decision processes
  • Uncertainty analysis – developing randomized algorithms for data analysis to facilitate the determination of probability distribution of data collected from measurements, as well as the determination of industrial equipment and measuring devices reliability
  • Development of new numerical algorithms, including efficiency analysis of parallel computing (especially computations on graphics processing units and hybrid architectures), computational complexity analysis, software design flaw analysis, and possible algorithm optimality so that the computation is mathematically sound and numerically effective
  • Methods and services for effective management of large-scale data and computing (AI+HPC) in HPC systems and in heterogeneous clouds for the needs of intelligent systems, including machine learning training models
  • Development of paradigms for artificial intelligence applications that use continuous and autonomous learning processes
  • Innovative process modelling with the use of simulation methods and computational intelligence synergy for the needs of efficient and flexible studying of phenomena and processes using highly autonomous selection of algorithms and implementation of simulations based on intelligent monitoring data aggregation
  • Implementation of comprehensive hybrid systems combining machine learning and artificial intelligence solutions to form surrogate models and advanced numerical methods with high computational cost
  • Solving difficult inverse problems related to issues of complex parameter identification, multiscale computational models using dedicated hybrid optimisation methods and sensitivity analysis
  • Development of augmented intelligence in industry, where various methods are in use together with people rather than in separation, which, in turn, is a typical application of artificial intelligence
  • Construction and building of intelligent decision support systems
  • Development of decision-making methods and algorithms; the use of uncertain data to make decisions; data quality assessment for improved decision-making and ways to measure it
  • Data aggregation collected from various sources; preference modelling; development of algebraic and hybrid models used in preference modelling and processing
  • Design and implementation of intelligent decision-making systems for industry
  • Computational intelligence, artificial intelligence, machine learning in system modelling and simulation, as well as intelligent system creation
  • Use of computational intelligence in industry