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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

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Hamiltonian Nullspace Shuttles.

Andreas Fichtner¹, Andrea Zunino²

¹Department of Earth Sciences ETH Zurich Zurich Switzerland.

Geophysical Research Letters

|April 23, 2019

Summary

This summary is machine-generated.

We developed a new Hamiltonian nullspace shuttle method to explore nonlinear inverse problems without Monte Carlo sampling. This approach generates alternative models consistent with data, aiding hypothesis testing and inversion flexibility.

Keywords:

Hamiltonian dynamics inverse theory nullspace theoretical seismology

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Area of Science:

Geophysics
Computational Science
Applied Mathematics

Background:

Nonlinear inverse problems are common in scientific fields like geophysics.
Exploring the nullspace of these problems is crucial for understanding model uncertainties and generating alternative solutions.
Current methods often rely on computationally expensive Monte Carlo sampling.

Purpose of the Study:

To present a novel, efficient method for exploring the effective nullspace of nonlinear inverse problems.
To offer a technique that avoids computationally intensive Monte Carlo sampling.
To provide a flexible tool for hypothesis testing and generating diverse, data-consistent models.

Main Methods:

Construction of an artificial Hamiltonian system treating the model as a high-dimensional particle.
Utilizing particle trajectories, guided by initial momentum and mass matrix, to traverse the effective nullspace.
Development of the 'nullspace shuttle' for exploring alternative model solutions and enabling hypothesis testing.

Main Results:

Demonstrated the method's efficacy on a low-dimensional toy example.
Successfully applied the Hamiltonian nullspace shuttle to high-dimensional nonlinear inversions of seismic traveltime and magnetic data.
Showcased the method's ability to generate alternative models consistent with observations and uncertainties.

Conclusions:

The Hamiltonian nullspace shuttle provides an effective, sampling-free approach to explore nonlinear inverse problem nullspaces.
The method offers flexibility for hypothesis testing and generating models with specific characteristics (e.g., smoothness).
This technique serves as a tunable hybrid between deterministic and probabilistic inversion, bridging gradient descent and Hamiltonian Monte Carlo.