PETAL: Physics Emulation Through Averaged Linearizations for Solving
  Inverse Problems
Jihui Jin Etienne Ollivier Richard Touret Matthew McKinley Karim G. Sabra Justin K. Romberg
Inverse problems describe the task of recovering an underlying signal of
interest given observables. Typically, the observables are related via some
non-linear forward model applied to the underlying unknown signal. Inverting
the non-linear forward model can be computationally expensive, as it often
involves computing and inverting a linearization at a series of estimates.
Rather than inverting the physics-based model, we instead train a surrogate
forward model (emulator) and leverage modern auto-grad libraries to solve for
the input within a classical optimization framework. Current methods to train
emulators are done in a black box supervised machine learning fashion and fail
to take advantage of any existing knowledge of the forward model. In this
article, we propose a simple learned weighted average model that embeds
linearizations of the forward model around various reference points into the
model itself, explicitly incorporating known physics. Grounding the learned
model with physics based linearizations improves the forward modeling accuracy
and provides richer physics based gradient information during the inversion
process leading to more accurate signal recovery. We demonstrate the efficacy
on an ocean acoustic tomography (OAT) example that aims to recover ocean sound
speed profile (SSP) variations from acoustic observations (e.g. eigenray
arrival times) within simulation of ocean dynamics in the Gulf of Mexico.