# Neural Closure

Co2ODE models only the part of a biochemical network that carries signal in a given cellular context: a conditional mask selects the markers tied to rewiring, and a variational autoencoder compresses the rest into a learned closure term trained jointly with a sparse ODE. On single-cell phosphoproteomic data spanning 30 cancer-relevant overexpressions, it compresses a 30-marker panel into a 10-dimensional state while matching the target-trajectory accuracy of a neural ODE fit to the full panel; adding a prior score shifts the selected markers at almost no cost in fit, indicating these data do not identify the true rewiring.

Co2ODE models only the part of a biochemical network that carries signal in a given cellular context: a conditional mask selects the markers tied to rewiring, and a variational autoencoder compresses the rest into a learned closure term trained jointly with a sparse ODE. On single-cell phosphoproteomic data spanning 30 cancer-relevant overexpressions, it compresses a 30-marker panel into a 10-dimensional state while matching the target-trajectory accuracy of a neural ODE fit to the full panel; adding a prior score shifts the selected markers at almost no cost in fit, indicating these data do not identify the true rewiring.

The authors present AEGIS, a differentiable Mars climate model that couples Mars radiation, surface, CO2 frost, and regolith physics to the Dinosaur spectral dynamical core; at T21/L12 it completes stable ten-Mars-year integrations, reproduces the seasonal CO2 cycle while conserving the total atmosphere–frost CO2 inventory to very small drift, produces surface pressure that follows MOLA topography, and yields automatic-differentiation gradients that agree with finite differences for physical calibration and neural-closure training.

The authors present AEGIS, a differentiable Mars climate model that couples Mars radiation, surface, CO2 frost, and regolith physics to the Dinosaur spectral dynamical core; at T21/L12 it completes stable ten-Mars-year integrations, reproduces the seasonal CO2 cycle while conserving the total atmosphere–frost CO2 inventory to very small drift, produces surface pressure that follows MOLA topography, and yields automatic-differentiation gradients that agree with finite differences for physical calibration and neural-closure training.