Projects

Hana Krakovská

Project selection:

International projects

STOCHASTICA – Stochastic Differential Equations: Computation, Inference, Applications
Stochastické diferenciálne rovnice: výpočty, inferencia, aplikácie
Program: COST
Duration: 26.9.2025 – 25.9.2029
Project leader: MSc. Krakovská Hana
Annotation: Stochastic differential equations (SDEs) are used to model phenomena under the influence of random noise and uncertainty and are useful in an extraordinary range of applications. In health, SDE models of tumour growth can help medical practitioners design interventions. In clean energy, they can model airflow around wind turbine blades, and enable multiscale modelling of entire wind farms and energy grids by representing small scale effects as noise. In computing, SDEs can be used to develop training algorithms for deep learning algorithms.The development and effective deployment of stochastic models requires input from a broad range of specialist experts: applied modellers, theoretical mathematicians, numerical analysts, and statisticians, all guided by the needs of stakeholders in academia and industry. However, in the current European research landscape, there is no large scale framework enabling these communities to interact, and opportunities for goal-driven research progress that is informed by all relevant expertise are being lost.Under the umbrella of computational stochastics, STOCHASTICA will bring together members of all of these communities to create a network of researchers with common goals informed by academic and industry partners. The work of the Action will generate a computational toolbox including a database of test problems, implementation guidance, and accessible descriptions of mathematical quality that empower non-specialist experts to make appropriate and routine use of stochastic models in applications such as natural resource management, renewable energy transmission, medical and public health applications including epidemiology and models of tumour growth.
Project website: https://www.ucc.ie/en/stochastica/

National projects

CAUSMET – Methods and algorithms for causal analysis and quantification of measurement uncertainty
Názov projektu Metódy a algoritmy kauzálnej analýzy a kvantifikácie neistôt meraní
Program: SRDA
Duration: 1.9.2026 – 31.12.2029
Project leader: Doc. RNDr. Witkovský Viktor, CSc.
Annotation: The project develops advanced methods and algorithms for causal analysis of stochastic and deterministic processes and for quantifying measurement uncertainties. It addresses methodological challenges in the analysis of time series and dynamical data, where correlation alone is insufficient to reveal the mechanisms governing system behavior. Manyapplications, therefore, require identifying causal relations between variables while reliably characterizing uncertainties arising from measurement processes, noise, and incomplete observations.The project will develop classical and modern approaches to causal analysis of time series based on probabilistic and statistical modeling, and integrate them with algorithms enabling statistical inference and prediction in the presence of randomness, measurement errors, and uncertainty.Modern applications in physical, biomedical, economic, environmental, and linguistic measurements, as well as in the social sciences (education, psychology), generate large and complex datasets with intricate dependence structures and temporal dynamics. A significant project component is hence the study of stochastic dynamical models, including diffusion processes, as a natural framework for modeling random dynamics observed via measurement time series. When modeling complex temporal or spatio-temporal data using kriging, causal structure will serve as a key starting point.The project also advances uncertainty methods for quantifying measurement uncertainties in line with modern metrology and aims to establish a unified methodological framework combining causal analysis, dynamical modeling, and statistical inference and forecasting. Interdisciplinary collaboration among the Institute of Measurement Science of the SAS, theMathematical Institute of the SAS, and the Faculty of Science of P. J. Šafárik University creates favorable conditions for the development of new theoretical results, efficient algorithms, and their applications.