Dr. Robert Gruhlke

Research

I am a postdoc working at the Freie Universität Berlin working with Claudia Schillings funded by the Berlin Mathematics Research Center MATH+. My research interests include Bayesian inverse problems, uncertainty quantification, low-rank tensor formats, numerical analysis, non-linear optimization and machine learning with special interest in the high-dimensional settings. My project within the MATH+ cluster of excellence is titled Wasserstein Gradient Flows for Generalised Transport in Bayesian Inversion. I completed my PhD on "Uncertainty quantification of material imperfections: surrogates, upscaling and inference" in 2023 at TU Berlin and WIAS Berlin supervised by Martin Eigel and Dietmar Hömberg.

Research Interests

My research interests refine as follows:

📊 Bayesian inverse problems: Sampling, interacting particle systems, optimal transport maps.
🌪️ Uncertainty quantification: Random PDEs and SDEs.
🧩 Low-rank tensor formats: Low-rank techniques for function approximations in high-dimensional PDEs and Fokker-Planck equations.
🔧 Numerical analysis: Adaptive finite element methods, domain decomposition methods.
📐 Non-linear optimization: Manifold learning with a special focus on optimal sampling techniques.
🤖 Machine learning: Focus on generative modeling.

Publications

Preprints

Gradient-Free Sequential Bayesian Experimental Design via Interacting Particle Systems

Gruhlke, R., Hanu, M., Schillings, C., & Wacker, P.

arXiv preprint, arXiv:2504.13320 (2025)

📄 Paper

Generative modeling with low-rank Wasserstein polynomial chaos expansions

Gruhlke, R., & Eigel, M.

arXiv preprint, arXiv:2203.09358v2 (2024)

📄 Paper

Generative Modelling with Tensor Train approximations of Hamilton–Jacobi–Bellman equations

Sommer, D., Gruhlke, R., Kirstein, M., Eigel, M., & Schillings, C.

arXiv preprint, arXiv:2402.15285 (2024) — In revision at SISC

📄 Paper

Optimal sampling for stochastic and natural gradient descent

Gruhlke, R., Nouy, A., & Trunschke, P.

arXiv preprint, arXiv:2402.03113 (2024) — In revision at JOTA

📄 Paper

Upcoming Preprints

The following preprints will be available soon, reflecting current research directions:

"Automatic Differentiation within Hierarchical Tensor Formats"
with D. Moser
"Quasi-Monte Carlo Meets Kernel Cubature through Optimal Sampling"
with V. Kaarnioja & C. Schillings
"Pathwise Tensor Train Approximation of Hamilton–Jacobi–Bellman Equations: A BSDE Perspective"
with J. Berner, L. Richter & D. Sommer
"Conditional Rectified Flows for Homogenization of Materials with Non-Periodic Stochastic Structures"
with M. Eigel, H. Martin, H. Gu & B. Sprungk
"High-Accuracy Physics-Informed Machine Learning with Optimal Sampling and Tensor Networks"
with P. Trunschke

Journal/Conference Papers

Importance Corrected Neural JKO Sampling

Hertrich, J. & Gruhlke, R. (to appear)

International Conference on Machine Learning (ICML), Accepted (2025)

📄 Paper 💻 Code

Multiplicative score-based generative models for fluid dynamics

Talla, M., Resseguier, V., Gruhlke, R., Heitz, D., & Mémin, E.

SIAM Computational Science and Engineering (CSE25) (2025)

📄 Paper

Less Interaction with Forward Models in Langevin Dynamics: Enrichment and Homotopy

Eigel, M., Gruhlke, R. & Sommer, D.

SIAM Journal on Applied Dynamical Systems, 23(3): 1870–1908 (2024)

📄 Paper

Numerical upscaling of parametric microstructures in a possibilistic uncertainty framework with tensor trains

Eigel, M., Gruhlke, R., Moser, D., & Grasedyck, L.

Computational Mechanics, 71(4): 615–636 (2023)

📄 Paper

Local surrogate responses in the Schwarz alternating method for elastic problems on random voided domains

Drieschner, M., Gruhlke, R., Petryna, Y., Eigel, M., & Hömberg, D.

Computer Methods in Applied Mechanics and Engineering, 405: 115858 (2023)

📄 Paper

Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion

Eigel, M., Gruhlke, R., & Marschall, M.

Statistics and Computing, 32(2): 27 (2022)

📄 Paper

A local hybrid surrogate‐based finite element tearing interconnecting dual‐primal method for nonsmooth random partial differential equations

Eigel, M. & Gruhlke, R.

International Journal for Numerical Methods in Engineering, 122(4): 1001–1030 (2021)

📄 Paper

Comparison of various uncertainty models with experimental investigations regarding the failure of plates with holes

Drieschner, M., Eigel, M., Gruhlke, R., Hömberg, D. & Petryna, Y.

Reliability Engineering & System Safety, 203: 107106 (2020)

📄 Paper

Challenges of order reduction techniques for problems involving polymorphic uncertainty

Pivovarov, D., et al.

GAMM‐Mitteilungen, 42(2): e201900011 (2019)

📄 Paper

Assessment and design of an engineering structure with polymorphic uncertainty quantification

Papaioannou, I., et al.

GAMM‐Mitteilungen, 42(2): e201900009 (2019)

📄 Paper

Dr. Robert Gruhlke

Research

Research Interests

Publications

Preprints

Gradient-Free Sequential Bayesian Experimental Design via Interacting Particle Systems

Generative modeling with low-rank Wasserstein polynomial chaos expansions

Generative Modelling with Tensor Train approximations of Hamilton–Jacobi–Bellman equations

Optimal sampling for stochastic and natural gradient descent

Upcoming Preprints

Journal/Conference Papers

Importance Corrected Neural JKO Sampling

Multiplicative score-based generative models for fluid dynamics

Less Interaction with Forward Models in Langevin Dynamics: Enrichment and Homotopy

Numerical upscaling of parametric microstructures in a possibilistic uncertainty framework with tensor trains

Local surrogate responses in the Schwarz alternating method for elastic problems on random voided domains

Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion

A local hybrid surrogate‐based finite element tearing interconnecting dual‐primal method for nonsmooth random partial differential equations

Comparison of various uncertainty models with experimental investigations regarding the failure of plates with holes

Challenges of order reduction techniques for problems involving polymorphic uncertainty

Assessment and design of an engineering structure with polymorphic uncertainty quantification

Teaching

Code & Software