Physics-constrained learning of dose-dependent spectral degradation in metal–organic frameworks from in situ low-loss EELS

Electron-beam irradiation limits atomic-resolution characterization of beam-sensitive hybrid materials, yet quantitative models that connect in situ spectroscopy to dose-dependent degradation remain scarce. Here, we use a physics-informed neural network (PINN) to model beam-induced spectral evolution in MIL-101(Fe) from an in situ low-loss electron energy-loss spectroscopy (EELS) dose series. Each spectrum is reduced to fixed-window low-loss descriptors, ñeff,j(Φ)=∫WjS(E,Φ)dE, evaluated over nominal π–π*, C–C, C–O, and M–O windows. These descriptors are relative window-integrated low-loss spectral areas, not absolute f-sum-rule effective electron numbers. For each spectral channel, a latent integrity variable Ci(Φ) obeys the same uncoupled power-law degradation equation in normalized dose space, dCi/dϕ=−kiCipi, regularized by monotonicity, boundedness, and a single hierarchy prior kC–O ≥ kC–C. Applied to nine dose frames spanning 152–1368 e−/Å2, the ensemble PINN identifies C–O and C–C as the most strongly dose-sensitive linker-associated channels, with half-integrity thresholds of ∼1.0 × 103 e−/Å2. The 1–3 eV π–π*-labeled window increases with dose and is, therefore, interpreted as a mixed low-energy response, likely involving oscillator-strength redistribution rather than direct monotonic loss of a single bond population. The framework provides a dose-dependent, spectroscopy-constrained description of MOF degradation while explicitly stopping short of chemical-mechanism assignment: fixed-window low-loss EELS descriptors are phenomenological and require additional chemical-state validation before they can be assigned to specific bond populations.