Neural ordinary differential equations (ODEs) for smooth, high-accuracy isotherm reconstruction, interpolation, and extrapolation

Machine learning (ML) surrogate models offer a promising route to accelerate material property prediction, bypassing costly atomistic simulations. Here, we introduce IsothermODE, a neural ordinary differential equation (NODE) framework for reconstructing full uptake and heat of adsorption $$\left(\Delta {H}_{{\rm{ads}}}\right)$$ isotherms for CO2 adsorption in metal-organic frameworks (MOFs) using only sparse pressure data. Unlike traditional ML models, IsothermODE leverages the intrinsic structure of differential equations to produce smooth, physically-consistent predictions that generalize across wide pressure ranges. We demonstrate high-fidelity interpolation and extrapolation, even with only five pressure points. To address the stochasticity inherent in Grand Canonical Monte Carlo (GCMC) simulations, we integrate uncertainty quantification, yielding tight bounds on predicted enthalpy curves. We further interpret the learned latent dynamics in terms of adsorption thermodynamics and textural properties, offering insight into structure-property relationships. Finally, we demonstrate IsothermODE’s long-range interpolation and extrapolation capabilities with sparse isotherm data (5 pressure points) and large incomplete intervals featuring missing data between 4–40 (case 1) and 25–50 (case 2) bars. IsothermODE provides a fast, robust alternative to simulation-heavy workflows, enabling scalable screening and design of next-generation carbon capture materials.