KrylovDESwitch language: Deutsch

Background

Since 2023 I have been a researcher at Fraunhofer IISB, in the AI-Augmented Research group, working mostly on physics-informed neural operators: models that do not just find patterns in data, but build the underlying physics in directly.

In practice that means stress and strain in steel, the growth environment of crystal wafers, libraries for training and fine-tuning foundation models. And locally deployed agents that take work off the hands of engineers and researchers. That last one is the direct predecessor of Krylov: the same systems, built for companies rather than a research institute.

Before that I reconstructed electron densities at the Wendelstein 7-X fusion reactor at the Max Planck Institute for Plasma Physics, and worked on computer vision for metallurgy at Primetals. My training is in computational mathematics and physics.

Two habits stayed with me. A method is not finished when it produces one good result, but when you know when it fails. And the interesting part is rarely the model itself, it is everything beside it: data quality, boundary conditions, interfaces, operations.

Both are missing from a lot of projects. A convincing demo gets built, it fails on edge cases in daily use, and afterwards nobody can explain why. I prefer to work the other way round: a small start, real data, a measurable result, and a clear account of what the system cannot do.

Working locally came out of practice too. Anyone handling production data from industry, or measurement data from research, cannot simply send it to somebody else’s API. That very capable open models now run on modest hardware of your own turns that restriction into a solvable engineering problem. It stays the default rather than a doctrine, though: where a workload’s data allows, the same system can run in your own cloud or call a hosted model API instead — and I measure the difference on your data, so moving a step off your own hardware is an informed decision, not a leap of faith.

Publications

Some of it is published.

  • L. Armbruster et al., jNO: A JAX library for neural operator and foundation model training. arXiv, 2026
  • V. Medvedev, L. Armbruster et al., Physics-informed fine-tuning of foundation models for partial differential equations. ICLR 2026
  • L. Armbruster et al., Physics-Informed PointNets for Modeling Electromagnetic Scattering from All-Dielectric Metasurfaces with Inclined Nanopillars. arXiv
  • Nature of barriers determines first passage times in heterogeneous media. Soft Matter (RSC)

On the name

Why Krylov?

Krylov subspace methods solve systems of equations too large to write down in full. They need to know only how the system acts on a single vector, and approach the answer step by step. That is how I work too: start small, check each step, stop once it is accurate enough.

Outlook

What I still want to work on

In the longer run I want to bring both strands together and work in simulation and engineering software as well, where numerical methods and machine learning meet. I do not offer it as a service today, but it shapes how I approach problems.

Contact

Let us talk about your process

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