  Visual inspections for identifying focusing points in inertial microfluidic
flows are prone to misinterpreting stable locations and focusing shifts in the
case of non-trivial focusing patterns. We develop and deploy an approach for
automating the calculation of focusing patterns for a general channel geometry,
and thereby reduce the dependence on empirical/visual procedures to confirm the
presence of stable locations. We utilize concepts from interpolation theory (to
represent continuous force-fields using discrete points), and stability theory
to identify "basins of attraction" and quantitatively identify stable
equilibrium points. Our computational experiments reveal that predicting
equilibrium points accurately requires upto $\times$10-20 times more refined
force-maps that conventionally used, which highlights the spatial resolution
required for an accurate representation of cross-sectional forces. These
focusing patterns are validated using experimental results for a rectangular
channel, and triangular channel with an apex angle of $90^\circ$. We then apply
the approach to predict and explain focusing patterns and shifts for a
$90^\circ$-isosceles triangular channel across a range of Reynolds numbers for
$\frac{a}{H} = 0.4$ (particle-to-channel size ratio). We observe that the
predicted focusing patterns match experiments well. The force-maps also reveal
certain "clouds" of localized stable points, which aid in explaining the onset
of bifurcation observed in experiments. The current algorithm is agnostic to
channel cross-sections and straight/curved channels, which could pave way to
generating a library of focusing patterns as a function of channel geometry,
and $Re$, to assist in design of novel devices for tailored particle-streams.
