  We present a framework to take new measurements in nematic systems that
contain active elements such as molecular motors. Spatio-temporal fields of
stress, velocity, pressure, and forces are obtained jointly from microscopy
images. Our inverse-problem approach ensures that they comply with physical
laws and are accurate near system boundaries. Our measurements in active
biological materials provide new insight for the design of boundary-aware
nematic systems. The shear stress unveils a correlation with the nucleation of
topological defects. The velocity and pressure fields characterize how boundary
effects drive the dynamics of the system in terms of attractors. And the force
relates the underlying fluid with the nematic tensor to reveal the activity
scales of the system. More broadly, our work establishes a generalizable
approach to study experimental systems that are inaccessible to measuring
probes.
