  The resolution and contrast of microscope imaging is often affected by
aberrations introduced by imperfect optical systems and inhomogeneous
refractive structures in specimens. Adaptive optics (AO) compensates these
aberrations and restores diffraction limited performance. A wide range of AO
solutions have been introduced, often tailored to a specific microscope type or
application. Until now, a universal AO solution -- one that can be readily
transferred between microscope modalities -- has not been deployed. We propose
versatile and fast aberration correction using a physics-based machine learning
(ML) assisted wavefront-sensorless AO control method. Unlike previous ML
methods, we used a bespoke neural network (NN) architecture, designed using
physical understanding of image formation, that was embedded in the control
loop of the microscope. The approach means that not only is the resulting NN
orders of magnitude simpler than previous NN methods, but the concept is
translatable across microscope modalities. We demonstrated the method on a
two-photon, a three-photon and a widefield three-dimensional (3D) structured
illumination microscope. Results showed that the method outperformed
commonly-used modal-based sensorless AO methods. We also showed that our
ML-based method was robust in a range of challenging imaging conditions, such
as extended 3D sample structures, specimen motion, low signal to noise ratio
and activity-induced fluorescence fluctuations. Moreover, as the bespoke
architecture encapsulated physical understanding of the imaging process, the
internal NN configuration was no-longer a ``black box'', but provided physical
insights on internal workings, which could influence future designs.
