Software

GeoCS (by H. Schoeller)
Coherent sets are time-dependent regions in the physical space of nonautonomous flows that exhibit little mixing with
their neighborhoods, robustly under small random perturbations of the flow. This Python package calculates coherent
sets from geophysical trajectory data.

H. Schoeller, R. Chemnitz, P. Koltai, M. Engel, and S. Pfahl. Assessing Lagrangian coherence in atmospheric blocking. Nonlinear Processes in Geophysics 32, 51–73, 2025. DOI: 10.5194/npg-32-51-2025

MatherCoherent (by R. Chemnitz)
Coherent sets are time-dependent regions in the physical space of nonautonomous flows that exhibit little mixing with
their neighborhoods, robustly under small random perturbations of the flow. This package implements a Fourier-Galerkin discretization of the so-called Mather-semigroup to compute coherent sets of quasiperiodically driven flows on the torus
in a trajectory-free manner.

R. Chemnitz, M. Engel, P. Koltai. Extracting coherent sets in aperiodically driven flows from generators of Mather semigroups. Discrete and Continuous Dynamical Systems - Series B 30(6): 1952–1995. 2025. DOI: 10.3934/dcdsb.2024149

DynamicPLaplacian (by A. de Diego)
The dynamic p-Laplacian provides solutions (for p approaching 1 from above) to the dynamic isoperimetric problem,
which in turn characterizes coherent sets in fluid flows. This package is a loose collection of methods to produce the figures of the work:

A. de Diego Unanue, G. Froyland, O. Junge, P. Koltai. A dynamic p-Laplacian. Preprint, to appear in SIAM J Math. Anal. arxiv:2308.05947. 2023.

SPoNet (by M. Lücke)
The package provides an efficient implementation of popular discrete-state spreading processes on networks of
interacting agents. It can be used to describe the time-evolution of certain opinions in a population, or the spreading of infectious diseases.

M. Lücke, S. Winkelmann, J. Heitzig, N. Molkenthin, P. Koltai. Learning interpretable collective variables for spreading processes on networks. Physical Review E 109, L022301, 2024. DOI: 10.1103/PhysRevE.109.L022301

PyTMRC (by A. Bittracher and M. Mollenhauer)
The Python Transition Manifold Reaction Coordinate package for computing reaction coordinates of high-dimensional stochastic systems is based on the transition manifold data analysis framework. Based on: 

A. Bittracher, P. Koltai, S. Klus, R. Banisch, M. Dellnitz, Ch. Schütte. Transition Manifolds of Complex Metastable Systems. Journal of Nonlinear Science 28(2): 471–512, 2018. DOI: 10.1007/s00332-017-9415-0.

A. Bittracher, S. Klus, B. Hamzi, P. Koltai, Ch. Schütte. Dimensionality Reduction of Complex Metastable Systems via
Kernel Embeddings of Transition Manifolds. Journal of Nonlinear Science 31, 3. 2021. DOI: 10.1007/s00332-020-09668-z.

PyTPT (by L. Helfmann and E. Ribera Borrell)
Python package for the Transition Path Theory (TPT) analysis of stationary Markov chains, periodically driven Markov chains, and for time-inhomogeneous Markov chains over finite time intervals. Based on:

L. Helfmann, E. Ribera Borrell, Ch. Schütte, P. Koltai. Extending Transition Path Theory: Periodically-Driven and Finite-Time Dynamics. Journal of Nonlinear Science 30, 3321-3366, 2020. DOI: 10.1007/s00332-020-09652-7.

SINAR (by N. Wulkow)
Matlab code for learning sparse nonlinear autoregressive models from trajectory data; in particular with an application in opinion dynamics. Based on: 

N. Wulkow, P. Koltai, Ch. Schütte. Memory-based reduced modelling and data-based estimation of opinion spreading. Journal of Nonlinear Science 31, 19, 2021. DOI: 10.1007/s00332-020-09673-2.

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:

​R. Banisch, Z. Trstanova, A. Bittracher, S. Klus, P. Koltai. Diffusion maps tailored to arbitrary non-degenerate Itô processes. Applied and Computational Harmonic Analysis 48(1), 242-265, 2020. DOI: 10.1016/j.acha.