  We have developed an inversion method for determination of the
characteristics of the acceleration mechanism directly and non-parametrically
from observations, in contrast to the usual forward fitting of parametric model
variables to observations. In two recent papers (Petrosian & Chen 2010, Chen &
Petrosian 2013), we demonstrate the efficacy of this inversion method by its
application to acceleration of electrons in solar flares based on stochastic
acceleration by turbulence. Here we explore its application for determining the
characteristics of shock acceleration in supernova remnants (SNRs) based on the
electron spectra deduced from the observed nonthermal radiation from SNRs and
the spectrum of the cosmic ray electrons observed near the Earth. These spectra
are related by the process of escape of the electrons from SNRs and energy loss
during their transport in the galaxy. Thus, these observations allow us to
determine spectral characteristics of the momentum and pitch angle diffusion
coefficients, which play crucial roles in both direct acceleration by
turbulence and in high Mach number shocks. Assuming that the average electron
spectrum deduced from a few well known SNRs is representative of those in the
solar neighborhood we find interesting discrepancies between our deduced forms
for these coefficients and those expected from well known wave-particle
interactions. This may indicate that the standard assumptions made in treatment
of shock acceleration need revision. In particular, the escape of particles
from SNRs may be more complex than generally assumed.
