  Modifications of the matter power spectrum due to baryonic physics are one of
the major theoretical uncertainties in cosmological weak lensing measurements.
Developing robust mitigation schemes for this source of systematic uncertainty
increases the robustness of cosmological constraints, and may increase their
precision if they enable the use of information from smaller scales. Here we
explore the performance of two mitigation schemes for baryonic effects in weak
lensing cosmic shear: the PCA method and the halo-model approach in
\textsc{HMcode}. We construct mock tomographic shear power spectra from four
hydrodynamical simulations, and run simulated likelihood analyses with
\textsc{CosmoLike} assuming LSST-like survey statistics. With an angular scale
cut of $\ell_{\rm max}<2000$, both methods successfully remove the biases in
cosmological parameters due to the various baryonic physics scenarios, with the
PCA method causing less degradation in the parameter constraints than
\textsc{HMcode}. For a more aggressive $\ell_{\rm max}=$5000, the PCA method
performs well for all but one baryonic physics scenario, requiring additional
training simulations to account for the extreme baryonic physics scenario of
Illustris; \textsc{HMcode} exhibits tensions in the 2D posterior distributions
of cosmological parameters due to lack of freedom in describing the power
spectrum for $k > 10\ h^{-1}\mathrm{Mpc}$. We investigate variants of the PCA
method and improve the bias mitigation through PCA by accounting for the noise
properties in the data via Cholesky decomposition of the covariance matrix. Our
improved PCA method allows us to retain more statistical constraining power
while effectively mitigating baryonic uncertainties even for a broad range of
baryonic physics scenarios.
