Hamiltonian Nullspace Shuttles

Andreas Fichtner; Andrea Zunino

doi:10.1029/2018GL080931

Hamiltonian Nullspace Shuttles

Andreas Fichtner^*, Andrea Zunino

^*Corresponding author af dette arbejde

Klima- og Geofysik / Climate and Geophysics

11 Citationer (Scopus)

Abstract

We present a method to explore the effective nullspace of nonlinear inverse problems without Monte Carlo sampling. This is based on the construction of an artificial Hamiltonian system where a model is treated as a high-dimensional particle. Depending on its initial momentum and mass matrix, the particle evolves along a trajectory that traverses the effective nullspace, thereby producing a series of alternative models that are consistent with observations and their uncertainties. Variants of the nullspace shuttle enable hypothesis testing, for example, by adding features or by producing smoother or rougher models. Furthermore, the Hamiltonian nullspace shuttle can serve as a tunable hybrid between deterministic and probabilistic inversion methods: Choosing random initial momenta, it resembles Hamiltonian Monte Carlo; requiring misfits to decrease along a trajectory, it transforms into gradient descent. We illustrate the concept with a low-dimensional toy example and with high-dimensional nonlinear inversions of seismic traveltimes and magnetic data, respectively.

Originalsprog	Engelsk
Tidsskrift	Geophysical Research Letters
Vol/bind	46
Udgave nummer	2
Sider (fra-til)	644-651
Antal sider	8
ISSN	0094-8276
DOI	https://doi.org/10.1029/2018GL080931
Status	Udgivet - 28 jan. 2019

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10.1029/2018GL080931

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AB - We present a method to explore the effective nullspace of nonlinear inverse problems without Monte Carlo sampling. This is based on the construction of an artificial Hamiltonian system where a model is treated as a high-dimensional particle. Depending on its initial momentum and mass matrix, the particle evolves along a trajectory that traverses the effective nullspace, thereby producing a series of alternative models that are consistent with observations and their uncertainties. Variants of the nullspace shuttle enable hypothesis testing, for example, by adding features or by producing smoother or rougher models. Furthermore, the Hamiltonian nullspace shuttle can serve as a tunable hybrid between deterministic and probabilistic inversion methods: Choosing random initial momenta, it resembles Hamiltonian Monte Carlo; requiring misfits to decrease along a trajectory, it transforms into gradient descent. We illustrate the concept with a low-dimensional toy example and with high-dimensional nonlinear inversions of seismic traveltimes and magnetic data, respectively.

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Hamiltonian Nullspace Shuttles

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