Analytical Hamiltonian Nullspace Shuttles

This small collection of educational codes is intended to illustrate the basic concept of the Hamiltonian Nullspace Shuttle using 1D examples that are easy to visualise.

DownloadNullspace Shuttle - 1D Analytic (IPYNB, 324 KB) is a Python Jupyter Notebook that applies the Hamiltonian Nullspace Shuttle to a 1D misfit (potential energy) function that can be defined by the user.

DownloadNullspace Shuttle - Harmonic Oscillator (IPYNB, 564 KB) is a slightly more complicated example where the misfit is defined based on observations of the noise-contaminated amplitude of a harmonic oscillator. The Nullspace Shuttle searchers for circular frequencies of the oscillator that all explain the observations to within a (probabilistically defined) misfit tolerance. The Jupyter Notebook requires an Downloadinput file (YML, 479 Bytes) and some Downloadhelper functions (PY, 3 KB). The Downloadharmonic oscillator (IPYNB, 294 KB) itself is described in a separate Jupyter Notebook.

Relevant literature:

Fichtner, A., Zunino, A., 2019. Hamiltonian Nullspace Shuttles. Geophysical Research Letters 46. external pagehttps://doi.org/10.1029/2018GL080931

Fichtner, A., Gebraad, L., Zunino, A., Boehm, C., 2021. Autotuning Hamiltonian Monte Carlo for efficient generalised nullspace exploration. Geophysical Journal International, submitted.