# Differentiable Programming

Multiaxial strength tests give only a few dozen failure stress states, and choosing which limit surface to fit has long relied on manual comparison and visual checks. Researchers recast that choice as sparse model discovery with differentiable penalties, define the surface by the first root along rays so the equivalent stress is explicitly solvable, and add PBP atoms with learnable shape parameters plus competition-gated mixtures of experts. On concrete data the PBP model's cross-validated error is about a quarter of the monomial library's, and measured strength ratios are reproduced within a few per cent.

Multiaxial strength tests give only a few dozen failure stress states, and choosing which limit surface to fit has long relied on manual comparison and visual checks. Researchers recast that choice as sparse model discovery with differentiable penalties, define the surface by the first root along rays so the equivalent stress is explicitly solvable, and add PBP atoms with learnable shape parameters plus competition-gated mixtures of experts. On concrete data the PBP model's cross-validated error is about a quarter of the monomial library's, and measured strength ratios are reproduced within a few per cent.

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.