Mathematics / Computation / Research

Learning,
optimization,
and dynamics.

I study how complex systems
adapt and remain stable.

I'm Thomas Richner, a research scientist at Mayo Clinic. I combine mathematical analysis with numerical experiments to investigate learning, adaptation, and recurrent systems.

Abstract illustration inspired by dynamical trajectories, not research dataExploring the structure of change.
Selected work

Questions into
computational methods.

Mathematical models. Numerical experiments.
Systems built to test ideas.

Publication graphic illustrating learning & stability
01 / Learning & stability

The dynamics of adaptation.

I investigate how adaptation shapes effective connectivity and stability in recurrent networks. My current research asks how networks can learn through local rules while maintaining stable dynamics.

Stability analysis · Recurrent networks
Read the paper ↗ Explore the code ↗
Publication graphic illustrating bayesian optimization
02 / Bayesian optimization

Better experiments, guided by uncertainty.

Using Gaussian process models and Bayesian optimization to guide the search for effective stimulation parameters in a closed-loop seizure-control system.

Gaussian processes · Sequential experiments
Read the paper ↗
Publication graphic illustrating neural interfaces
03 / Neural interfaces

Engineering a window into neural systems.

Developing transparent micro-electrocorticography arrays and integrating electrical recordings with optogenetics and advanced photonics.

Micro-ECoG · Optogenetics · Photonics
Read the paper ↗
Looking ahead

How do intelligent
systems keep learning?

My broader research interests concern how intelligent systems learn and adapt—particularly continual learning, local learning, and efficient recurrent architectures.

01

Learning over time

Continual and federated learning. Preserving useful behavior as systems adapt.

02

Local rules, global behavior

Stability in recurrent networks with local learning. The relationship between optimization and dynamics.

03

Structure and uncertainty

Compositional architectures, Bayesian methods, and efficient ways to explore difficult problems.

Background

From mathematical ideas
to working systems.

My background spans mathematics, computational modeling, and engineering. Across research in optimization, neural dynamics, and neural interfaces, I move between theory, numerical methods, and experiments.

At Mayo Clinic, I investigate network stability and use electrical brain stimulation for system identification. My broader interests connect this work to foundational questions in AI.