Physics-Informed Liquid Neural Network Emulator for CRTM with Atmospheric-Layer Jacobian Capability

Physics-based fast radiative transfer models (RTMs), such as the Community Radiative Transfer Model (CRTM), face increasing computational demands from growing satellite data volumes and model complexity. We developed a physics-informed Liquid Neural Network emulator for CRTM (CRTM-LNN) that draws on continuous dynamical-system concepts while retaining physical interpretability. The framework combines an Ordinary Differential Equation (ODE)-inspired Liquid Neural Network for layer-by-layer optical-depth modeling with an analytic, differentiable radiative-transfer solver. This design preserves the explicit optical-depth-to-radiance pathway and incorporates physical constraints directly into the forward calculation. In the implementation evaluated in this study, the LNN uses discrete hidden-state updates on the fixed European Centre for Medium-Range Weather 91-layer (ECMWF91L) grid under clear-sky, absorption-only assumptions. Evaluation using Infrared Atmospheric Sounding Interferometer (IASI) observations and ECMWF91L forecast profiles shows that CRTM–LNN closely reproduces the reference CRTM simulations, with global, channel-mean brightness-temperature biases below 0.1 K in magnitude. Regional bias magnitudes nevertheless reach approximately 0.2–0.4 K for selected channels and latitude bands. Correlations with CRTM exceed 0.97 for cumulative optical depth, transmittance, and weighting functions in regimes with cumulative optical depth below five. It accelerates forward calculations by up to 18-fold and efficiently generates Jacobians through automatic differentiation. Compared with a conventional multilayer perceptron CRTM emulator, CRTM-LNN produces smoother and more physically consistent Jacobians, with improved vertical localization and fewer spurious oscillations. Absolute centroid-pressure errors for temperature Jacobians are reduced across all evaluated channels, ranging from 1.77 to 5.01 hPa for CRTM-LNN versus 5.88–8.17 hPa for CRTM–MLP, although the magnitude of improvement varies by channel. These results highlight the potential of the integrated CRTM–LNN framework, which combines ODE-driven neural emulation with physics-based radiative-transfer modeling, to provide a scalable foundation for atmospheric retrievals, satellite data assimilation, and near-real-time radiative-transfer applications. Current limitations and opportunities for extension to more complex radiative processes are also discussed.