The abundance of compact objects ranging from stellar to intermediate masses ($\sim 1 - 10^{5}M_{\odot}$) remains poorly constrained, particularly for populations such as primordial black holes and dark matter subhalos that emit little or no electromagnetic radiation. Gravitational-wave (GW) microlensing provides a complementary way to probe these populations through wave-optics effects imprinted on the GW signals, with implications for astrophysical and cosmological inference. We develop a hierarchical Bayesian framework to infer the population properties of microlenses from an ensemble of microlensed GW events, constraining the slope of the power-law lens mass function ($α_{\rm ML}$), the lens number density ($n_0$), and the fraction of dark matter in compact lenses ($f_{\rm DM}$). Using simulated microlensed GW signals drawn from a realistic binary black hole population, we find that $\sim 100$ detected microlensed events are able to constrain both $α_{\rm ML}$ and $n_0$, although a degeneracy between the two remains. For a low-mass-dominated lens population ($α_{\rm ML}=2$) with $n_0=10^6~\mathrm{Mpc}^{-3}$, a three-year observation at the O4 sensitivity yields $\sim 130$ detectable microlensed events and recovers the injected dark-matter fraction, $f_{\rm DM}\simeq 1.2 \times 10^{-4}$, with a 90% credible interval of $7.3 \times 10^{-5} \lesssim f_{\rm DM} \lesssim 1.8 \times 10^{-4}$.
Observed populations of rotating neutron stars~(NSs) with millisecond-order periods are powerful probes of fundamental physics. Mass-radius measurements inform poorly constrained properties of degenerate nuclear matter, whereas high-fidelity population synthesis connects unknowns in NS formation and binary evolution to large radio-timing surveys. However, repeated structure calculations are prohibitive due to the computational cost of solving the highly coupled partial differential equations of axisymmetric general relativistic hydrostatic equilibrium that govern rotating NS interiors. Non-rotating calculations or approximate rotational corrections can bias equation of state inference and limit the fidelity of population synthesis in tracing the evolutionary history of progenitors and propagating equation of state uncertainties. In this \textit{Letter}, we develop physics-informed neural operators that can solve the axisymmetric problem with high accuracy and negligible computational cost. \textit{Our solvers are trained in a fully unsupervised setting, with the training objective informed solely by the partial differential equations, and achieve a $10^3\times$ speed-up with negligible accuracy loss}. These solvers enable scalable EoS inference that self-consistently accounts for rotation and repeated stellar-structure calculations during binary evolution, making spin predictions that account for rotational structure and EoS uncertainties computationally accessible to population synthesis.
The atmospheric boundary layer (ABL) presents turbulence regimes that diverge from the classical Kolmogorov 1941 (K41) power-law spectrum widely assumed in optical atmospheric profiling, yet turbulence characterization for astronomical applications remains predominantly based on K41 assumptions. Using high-frequency sonic anemometer data from site-testing campaigns at the Giant Magellan Telescope (GMT) and Thirty Meter Telescope (TMT) sites in Chile, we apply detrended fluctuation analysis (DFA)---a technique from fractal time-series analysis---to identify the inertial sub-range and evaluate statistical isotropy in the ABL, comparing our approach with the Fourier-based algorithm for robust identification of the inertial subrange (ARIIS). Strict Kolmogorov conditions---simultaneous isotropy and $k^{-5/3}$ scaling across all fields---are satisfied in fewer than 7 per cent of observations. Temperature fields systematically decouple from velocity components under stable stratification, exhibiting Bolgiano-Obukhov scaling ($k^{-7/5}$) during nighttime hours, indicating active rather than passive scalar behaviour. DFA-detected regime transitions correlate with characteristic turbulence scales, providing objective, model-free boundaries for the inertial subrange. Comparative $C_n^2$ estimation reveals that structure function methods assuming K41 scaling diverge significantly from flux-based parameterizations under stable conditions. The rarity of true Kolmogorov conditions at these sites necessitates stratification-aware methodologies for accurate optical turbulence characterization at next-generation extremely large telescope facilities.