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Uncertainty Quantification
The Machine Learning and Uncertainty Quantification Group at the Faculty of Civil Engineering, Czech Technical University in Prague, is a hub of innovation in computational engineering. Our work centers around surrogate modeling for efficient system representation, model calibration for accurate predictions, and machine learning for extracting valuable insights from data. With a combination of fundamental and applied research, we seek to address the challenges posed by uncertainty in engineering systems, leading the way for smarter and more resilient infrastructure.
Uncertainty Quantification and Probabilistic Modeling
Our research has focused extensively on uncertainty quantification and probabilistic modeling, particularly in the context of thermal tomography and material behavior of heterogeneous materials. We have developed several polynomial chaos expansions-based surrogate models to address uncertainties in thermal and mechanical processes, which are crucial for accurate modeling and prediction. Our work involves creating efficient/accelerated inverse solvers and dimensionality reduction techniques, which enhance the precision, reliability, and robustness of proposed computational frameworks.
Model Data-driven Applications in Material Science and Engineering
A key aspect of our research is the application of deep learning techniques to model and simulate complex physical phenomena, particularly in material science and engineering. This emphasis is reflected in studies on AI-based approaches for modeling and simulating heat conduction, as well as reconstructing concrete morphology. These efforts highlight our focus on using modern computer methods to gain a better understanding and make accurate predictions about materials.
People
People
Eliška Kočková, PhD student. Her doctoral thesis focuses on Bayesian statistics, surrogate modeling, and polynomial chaos to advance the field of non-linear material modeling.
Kaustav Das, PhD student. As part of his studies, he creates data-driven models for materials with random microstructures, focusing on image reconstruction and the development of digital twins.
David Šilhánek, PhD student. In his doctoral research, he is concentrating on surrogate modeling of nuclear power plant containment to accelerate the calibration of material models using real-time experimental data.
Michal Zdražil, PhD student. His research is focused on algorithms for efficient Monte Carlo methods in inverse problems with bounded parameter spaces.
prof. Daniela Jarušková, CSc. Expert in mathematical statistics, specifically focusing on changepoint analysis and its applications in environmental and engineering sciences.
Alumni
Jan Havelka, former PhD student. His doctoral thesis -- Application of Boundary Inverse Methods in Civil Engineering -- aims to enhance thermal tomography methods for non-invasively determining heterogeneous thermal properties through boundary measurements. The research concentrates on creating efficient inverse solvers for dynamic boundary conditions, utilizing a transient heat model defined by volumetric capacity and thermal conductivity. The deterministic algorithms, grounded in a regularized Gauss-Newton method, are thoroughly validated through numerical simulations. The study emphasizes the importance of the effusivity field in reducing objective function error, addressing ambiguities in the inverse problem for particular measurement scenarios.
Adéla Hlobilová, former PhD student. Her doctoral thesis -- Reliability-Based Desing Optimization using Approximation Techniques -- addresses Reliability-Based Design Optimization (RBDO) by redefining the trade-off between cost and safety through multi-objective Pareto fronts. The proposed method utilizes an evolutionary double-loop approach enhanced by adaptive meta-modeling, significantly reducing the computational burden of expensive simulations. A key innovation lies in the repetitive optimization of the Design of Experiments (DoE), which leverages advanced Monte Carlo sampling to better capture highly non-linear limit states. The research demonstrates that Local Meta-Models (LMM) outperform global approaches in vast design spaces, offering superior accuracy for complex engineering problems. Ultimately, the framework achieves results two orders of magnitude more efficiently than standard FORM-based methods, providing a robust tool for engineering under uncertainty.
Ondřej Šperl, former Masters's student. His Master's thesis -- Deep Learning-Based Modeling and Simulation of Heat Conduction -- focuses on implementing deep neural networks to simulate and model heat conduction, addressing the challenge of limited training data by introducing Physics-Informed Neural Networks. The effectiveness of these models is evaluated against traditional methods, such as the finite element method and polynomial chaos, using various heat conduction scenarios.
Notable projects
Notable projects
2025 - 2028 Innovative methods of materials diagnostics and monitoring of engineering infrastructure to increase its durability and service life (INODIN), project No. CZ.02.01.01/00/23 020/0008487), European Regional Development Fund, Amount granted 100,000,000 CZK (≈ 4,000,000 EUR)
2023 - 2025 Synergy of multiscale Modelling and machine Learning: Strategy for biomedical sciences and battle against cancer, Ministry of Education, Youth and Sports of the Czech Republic, Mobility Project No. MEB 101105 solved jointly with the UT Compiegne, France, Amount granted 250,000 CZK (≈10,000 EUR)
2021 - 2024 Deep-Learning-Enabled On-Demand Design of Composite Microstructure: Application to Mechanical Metamaterials– DeeMa funded by the Technology Agency of the Czech Republic and National Research Fund (Luxembourg) within M-ERA.NET 2 call 2020, TH75020002
2018 - 2023 Theory- Optimization Methods, Reliability of Complicated Systems. Center of Advanced Applied Sciences (project No. CZ.02.1.01/0.0/0.0/16 019/0000778), European Regional Development Fund
2018 - 2020 Probabilistic identification of material transport parameters based on non-invasive experimental measurements, Czech Science Foundation, Project No. 18-04262S, Amount granted 5,208,000 CZK (≈ 192,000 EUR)
2016 - 2018 Identification of Aleatory Uncertainty in Parameters of Heterogenous Materials, Czech Science Foundation, Project No. 16-11473Y, Amount granted 5,590,000 CZK (≈ 207,000 EUR)
2014 - 2015 Thrust Chamber Life Prediction based on Survival Analysis (ThaLeS), European Space Agency; part of the Future Launcher Preparatory Programme
2014 - 2015 Reliability Analysis and Life Prediction with Probabilistic Methods (RALP), European Space Agency, part of the Future Launcher Preparatory Programme
2012 - 2013 Advanced Nozzle Extension Design Methodology, European Space Agency; part of the Future Launcher Preparatory Programme
Selected publications
Selected publications
A. Kučerová, J. Sýkora, P. Havlásek, D. Jarušková and M. Jirásek: Efficient probabilistic multi-fidelity calibration of a damage-plastic model for confined concrete. Computer Methods in Applied Mechanics and Engineering, Volume 412, 1 July 2023, 116099, https://doi.org/10.1016/j.cma.2023.116099
J. Havelka, A. Kučerová and J. Sýkora: Efficient inverse solvers for thermal tomography. Computers & Mathematics with Applications, 97, 314-328, https://doi.org/10.1016/j.camwa.2021.06.005, 2021.
E. Janouchová, A. Kučerová, J. Sýkora, J. Vorel and R. Wan-Wendner: Robust probabilistic calibration of a stochastic lattice discrete particle model for concrete. Engineering Structures. Engineering Structures, 236, 11200, https://doi.org/10.1016/j.engstruct.2021.112000, 2021.
J. Havelka, A. Kučerová and J. Sýkora: Dimensionality reduction in thermal tomography. Computers & Mathematics with Applications, 78(9), 3077-3089, https://doi.org/10.1016/j.camwa.2019.04.019, 2019.
E. Janouchová, J. Sýkora and A. Kučerová: Polynomial chaos in evaluating failure probability: A comparative study. Applications of Mathematics, 63 (6), 713-737, 2018.
J. Havelka, A. Kučerová and J. Sýkora: Compression and reconstruction of random microstructures using accelerated lineal path function. Computational Materials Science, 122, 102-117, 2016. arXiv.org
International collaboration
International collaboration
Industrial partners
Industrial partners
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