Andreas Bittracher, Ph.D.

Hi! I am a Mathematician, Data Scientist and Postdoctoral Researcher at Free University of Berlin. I am developing Machine Learning methods for the analysis of complex dynamical systems.

Research Interests

  • Complex Dynamics analysis of high-dimensional, multi-scale, stochastic and chaotic dynamical systems
  • Machine Learning unsupervised feature discovery from numerical simulation data
  • Deep Learning with a focus on representation and learning theory
  • Molecular Dynamics biomolecular complexes such as proteins with thousands of degrees of freedom
  • Operator Methods data-driven approximation of transport operators and infinitesimal generators
  • Numerical Analysis efficient algorithms in scientific computing

Associations

I am currently associated with the following academic institutions.

Free University of Berlin

Research Scientist

SFB 1114

Senior Project Member

Biocomputing Berlin

Group Member

MATH+ Research Center

Project Advisor

Latest Research

A New Variational Principle for Optimal Reaction Coordinates

Bittracher, A., Mollenhauer, M., Koltai, P., Schütte, C.
Optimal Reaction Coordinates: Variational Characterization and Sparse Computation.
Submitted to SIAM Multiscale Modelling and Simulation (2021).

Reaction Coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that govern the long-term behavior of high-dimensional stochastic processes. We present a novel and general variational characterization of optimal RCs and provide conditions for their existence. Optimal RCs are minimizers of a certain loss function and reduced models based on them guarantee very good approximation of the long-term dynamics of the original high-dimensional process. We show that, for slow-fast systems, metastable systems, and other systems with known good RCs, the novel theory reproduces previous insight. Remarkably, the numerical effort required to evaluate the loss function scales only with the complexity of the underlying, low-dimensional mechanism, and not with that of the full system. The theory provided lays the foundation for an efficient and data-sparse computation of RCs via modern machine learning techniques.

Application of Transition Manifold Analysis to Amyloid Fibrillation

Bittracher, A., Moschner, J., Koksch, B., Netz, R., Schütte, C.
Exploring the Locking Stage of NFGAILS Amyloid Fibrillation via Transition Manifold Analysis.
Submitted to The European Physical Journal B (2021).

We demonstrate the application of the transition manifold framework to the late-stage fibrillation process of the NFGAILS peptide, a amyloidogenic fragment of the human islet amyloid polypeptide (hIAPP). This framework formulates machine learning methods for the analysis of multiscale stochastic systems from short, massively-parallel molecular dynamical simulations. We identify key intermediate states and dominant pathways of the process. Furthermore, we identify the optimally timescale-preserving reaction coordinate for the dock-lock process to a fixed pre-formed fibril and show that it exhibits strong correlation with the mean native hydrogen bond distance. These results pave the way for a comprehensive model reduction and multi-scale analysis of amyloid fibrillation processes.

Discovering latent mechanisms in Markov chains from sparse data

Bittracher, A., Schütte, C.
A probabilistic algorithm for aggregating vastly undersampled large Markov chains.
Physica D: Nonlinear Phenomena (2021). https://doi.org/10.1016/j.physd.2020.132799

Model reduction of large Markov chains is an essential step in a wide array of techniques for understanding complex systems and for efficiently learning structures from high-dimensional data. We present a novel aggregation algorithm for compressing such chains that exploits a specific low- rank structure in the transition matrix which, e.g., is present in metastable systems, among others. It enables the recovery of the aggregates from a vastly undersampled transition matrix which in practical applications may gain a speedup of several orders of magnitude over methods that require the full transition matrix. Moreover, we show that the new technique is robust under perturbation of the transition matrix. The practical applicability of the new method is demonstrated by identifying a reduced model for the large-scale traffic flow patterns from real-world taxi trip data.

Bibliography

A list of all my publications to date.

Resume

Education

Ph.D. Mathematics

2011 - 2016

Technical University of Munich, Munich, Germany

Development of a simulation-free model reduction method for non-Markovian dynamical systems. Discovery of new operator-theoretical relationships between the Langevin and Smoluchowski dynamics.

Diploma Mathematics

2005 - 2011

Technical University of Munich, Munich, Germany

Thesis: Quantitative comparison of various numerical methods for the metastability analysis of molecular dynamic systems.

Professional Experience

Research Scientist

2016 - Present

Free University of Berlin, Berlin, Germany

  • Development and implementation of machine learning methods for complex dynamic systems.
  • Data-based analysis of molecular dynamics processes on massively-parallel HLRN supercomputers.
  • Lecturer in the Master's program "Data Science" and the Bachelor's program "Mathematics".
  • Co-supervision of graduate and undergraduate students.

Academic CV

Contact me for a full academic CV.

Scientific Software

PyTMRC

by A. Bittracher, M. Mollenhauer

The Python Transition Manifold Reaction Coordinate package for computing reaction coordinates of high-dimensional stochastic systems. It is based on the transition manifold data analysis framework, proposed in:

Bittracher, A., Koltai, P., Klus, S., Banisch, R., Dellnitz, M., Schütte, C.
Transition Manifolds of Complex Metastable Systems.
Journal of Nonlinear Science (2017). https://doi.org/10.1007/s00332-017-9415-0

pyDiffMap

by R. Banisch, E. H. Thiede, Z. Trstanova

An open-source project to develop a robust and accessible diffusion map code for public use. Includes implementations of target measure diffusion maps and local kernel diffusion maps, based on:

Banisch, R., Trstanova, Z., Bittracher, A., Klus, S., Koltai, P.
Diffusion maps tailored to arbitrary non-degenerate Itô processes.
Applied and Computational Harmonic Analysis (2020). https://doi.org/10.1016/j.acha.2018.05.001

Contact

Location:

Freie Universität Berlin
Arnimallee 9, 12203 Berlin, Germany

Call:

+49 30 838 61433


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