Scientific machine learning
Neural networks, topological descriptors and statistical learning for elastic properties, porous media, quantum materials and molecular simulations.
Academic researcher · Scientific ML engineer
Rafał Topolnicki
I combine academic research in topological data analysis, mathematical statistics and computational physics with senior ML/AI engineering and research practice in industry. My work focuses on physics-informed and data-driven methods for materials, molecular systems and high-dimensional scientific data.
2×PhD: Mathematics and Physics
25+research papers
Physcomputational physics and materials
Mathstatistics and modelling
ML/AIsenior engineer/researcher in industry
Profile
My academic path started in solid-state physics and mathematical statistics. I now use machine learning, topological data analysis and statistical modelling to solve problems motivated by physical systems: porous materials, high-entropy alloys, superconductors, molecular junctions and quantum/molecular simulations.
Topological data analysis
Topology-driven statistical testing and feature construction for high-dimensional data, with applications in statistics and materials science.
Mathematical statistics
ROC curve estimation, inequality measures, semiparametric methods, rare-event simulation and uncertainty reduction.
Molecular modelling & electronics
DFT, molecular dynamics and quantum-chemical modelling of surfaces, adsorbates, molecular junctions and finite-temperature electronic transport.
Two complementary tracks
The site intentionally separates my academic identity from my applied ML/AI engineering and research work in industry. The common thread is scientific problem solving: translating mathematical ideas into robust algorithms and working software.
Research and teaching
I work on applied topology, mathematical statistics and computational physics, with active links to materials science and molecular modelling. My academic roles include the Mathematical Institute of the Polish Academy of Sciences and the Faculty of Physics and Astronomy at the University of Wrocław.
- Topological data analysis for statistics and materials
- Computational physics, DFT and molecular modelling
- Teaching: programming, mechanics, physics, statistics and modelling
Senior ML engineer / researcher
In industry-oriented ML/AI work, I build practical methods and production-minded workflows for real-life data analysis, modelling and algorithm development. This includes Python-based machine learning, problem decomposition and applied research in collaboration with technical teams.
- Python, ML/AI, algorithm development and data analysis
- Scientific modelling translated into applied software
- Experience bridging researchers, engineers and domain experts
Applications in physics and materials
A central part of my research is the use of statistics, topology and machine learning in physical systems. I highlight this explicitly because it connects my two PhDs, postdoctoral work and recent publications in computational materials science.
Porous materials
Direction-aware topological descriptors and neural-network models for Young’s modulus and elastic-property prediction in porous media and nanoporous metals.
Quantum and magnetic materials
Interpretable ML for magnetic anisotropy, high-entropy superconductors and composition-property relationships in complex alloy systems.
Molecular and surface systems
DFT, molecular dynamics and machine-learning approaches for adsorbates, molecular junctions, fluxional molecules and quantum delocalization effects.
Publications
Featured publications are ordered to emphasize recent work and high-visibility journals first. The full list below is chronological, newest first, so the page remains useful both as a researcher profile and as a complete publication record.
Featured journal papers
Transferable 3D convolutional neural networks for elastic constants prediction in nanoporous metalsMaterials & Design, 2025. DOI: 10.1016/j.matdes.2025.114896.
Interpretable machine learning for atomic scale magnetic anisotropy in quantum materialsnpj Computational Materials, 2025.
New type of Ti-rich HEA superconductors with high upper critical fieldActa Materialia, 2025.
Violation of Matthias rule: Elemental composition as the key determinant of critical temperature in bcc high-entropy superconductorsPhysical Review B, 2025.
Topology-driven goodness-of-fit tests in arbitrary dimensionsStatistics and Computing, 2024.
Deciphering High-Order Structural Correlations within Fluxional Molecules from Classical and Quantum Configurational EntropyJournal of Chemical Theory and Computation, 2020.
Combining multiscale MD simulations and machine learning methods to study electronic transport in molecular junctions at finite temperaturesThe Journal of Physical Chemistry C, 2021.
Selected arXiv and preprints
Physics-informed convolutional neural networks for fluid flow through porous mediaarXiv:2605.20890, 2026. Physics-informed ML / fluid flow / porous media. DOI: 10.48550/ARXIV.2605.20890.
Direction-aware topological descriptors for Young’s modulus prediction in porous materialsarXiv:2604.08105, 2026. Computational physics / TDA / porous materials.
Reducing Estimation Uncertainty Using Normalizing Flows and StratificationarXiv:2602.10706, 2026. Machine learning / uncertainty reduction / Monte Carlo estimation.
Estimation of conditional inequality curves and measures via estimating the conditional quantile functionarXiv:2412.20228, 2024–2025. Mathematical statistics / conditional inequality measures.
Topology-Driven Goodness-of-Fit Tests in Arbitrary DimensionsarXiv:2210.14965, 2022–2023. Topological data analysis / statistical testing.
Deciphering High-order Structural Correlations within Fluxional Molecules from Classical and Quantum Configurational EntropyarXiv:2006.13624, 2020. Molecular dynamics / quantum chemistry / fluxional molecules.
Full publication list
- Transferable 3D convolutional neural networks for elastic constants prediction in nanoporous metals. Materials & Design 260, 114896, 2025. DOI: 10.1016/j.matdes.2025.114896.
- Violation of Matthias rule: Elemental composition as the key determinant of critical temperature in bcc high-entropy superconductors. Physical Review B 112, 014513, 2025.
- Interpretable machine learning for atomic scale magnetic anisotropy in quantum materials. npj Computational Materials 11, 138, 2025.
- New type of Ti-rich HEA superconductors with high upper critical field. Acta Materialia 285, 120666, 2025.
- Superconductivity in a New High-Entropy Alloy (NbTi)0.67(MoHfV)0.33. Metallurgical and Materials Transactions A 55, 3789–3898, 2024.
- Topology-driven goodness-of-fit tests in arbitrary dimensions. Statistics and Computing 34, 34, 2024.
- Superconductivity in high-entropy alloy system containing Th. Scientific Reports 13, 16317, 2023.
- Enhanced Superconducting Critical Parameters in a New High-Entropy Alloy Nb0.34Ti0.33Zr0.14Ta0.11Hf0.08. Materials 16(17), 5814, 2023.
- Deciphering the Impact of Helium Tagging on Flexible Molecules: Probing Microsolvation Effects of Protonated Acetylene by Quantum Configurational Entropy. Journal of Physical Chemistry A 127(11), 2023.
- Superconductivity in the high-entropy alloy (NbTa)0.67(MoHfW)0.33. Physical Review B 106, 184512, 2022.
- Minimum distance estimation of the Lehmann ROC curve. Statistics 55, 618–634, 2021.
- Combining multiscale MD simulations and machine learning methods to study electronic transport in molecular junctions at finite temperatures. The Journal of Physical Chemistry C 125(36), 19961, 2021.
- Temperature driven interchange of the effective size of proton with deuterium. Chemical Physics Letters 778, 138775, 2021.
- Deciphering High-Order Structural Correlations within Fluxional Molecules from Classical and Quantum Configurational Entropy. Journal of Chemical Theory and Computation 16(11), 6785–6794, 2020.
- Estimation of the ROC curve from the Lehmann family. Computational Statistics & Data Analysis 142, 106820, 2020.
- Characterization of (In,Pb)/Si(111): Tuning normal and lateral atom distributions in mixed metal systems. Journal of Alloys and Compounds 819, 153030, 2020.
- Minimum distance estimation of the binormal ROC curve. Statistical Papers 60, 2161–2183, 2019.
- Early stages of growth of Pb, Sn and Ge on Ru(0001): A comparative density functional theory study. Thin Solid Films 665, 123–130, 2018.
- Estimation of the Ratio of the Geometric Process. Applicationes Mathematicae 44, 105–121, 2017.
- Tuning the conductance of benzene-based single-molecule junctions. Organic Electronics 34, 254–261, 2016.
- On the formation of two-dimensional alloys of Sn and Pb co-adsorbed on Ru(0001). Journal of Alloys and Compounds 672, 317–323, 2016.
- Structural and electronic properties of submonolayer-thick Sn films on Ru(0001). Applied Surface Science 329, 376–383, 2015.
- Structural properties of ultrathin Pb layers on Ru(0001) revealed by LEED, AES and DFT. Applied Surface Science 311, 426–434, 2014.
- Electronic properties of experimentally observed Pb/Ru(0001) adsorbate structures: A DFT study. Applied Surface Science 304, 115–121, 2014.
- Phase diagram for a zero-temperature Glauber dynamics under partially synchronous updates. Physical Review E 86, 051113, 2012.
Experience
Academic research, teaching, postdoctoral work and applied machine-learning/software-engineering roles.
2021 — present
Visiting Assistant Professor
Mathematical Institute, Polish Academy of Sciences — Dioscuri Centre in Topological Data Analysis. Research in applied topology, statistics, materials science and machine learning.
2017 — present
Assistant Professor
University of Wrocław, Faculty of Physics and Astronomy — solid-state physics, computational physics and chemistry, DFT, molecular electronics and teaching.
2020 — present
Senior ML Engineer / Data Scientist
Applied ML/AI in Python, algorithm development, data analysis and engineering-oriented implementation of modelling workflows.
2019 — 2020
Postdoctoral Research Associate
Ruhr-Universität Bochum — neural-network potentials, molecular dynamics and quantum-chemical simulations of fluxional molecules in superfluid helium environments.
Education
A dual academic background in mathematics and physics, followed by postdoctoral research in molecular modelling and scientific machine learning.
Postdoctoral Research in Theoretical Chemistry
Ruhr-Universität Bochum, 2019–2020. Work on neural-network approaches for quantum chemistry, molecular dynamics, fluxional molecules and superfluid helium environments.
PhD in Mathematics
Wrocław University of Science and Technology, 2020. PhD in statistics, focused on semiparametric estimation and ROC curve methodology.
PhD in Physics
University of Wrocław, 2017, with distinction. PhD in solid-state physics, focused on computational modelling of surfaces and adsorbate systems.
MSc in Mathematics
Wrocław University of Science and Technology, 2014. Specialization: mathematical statistics.
MSc in Physics
University of Wrocław, 2012, with distinction. Specialization: physics of new materials.
Contact
For research collaboration, scientific machine-learning projects, consulting, talks or academic inquiries, please get in touch.