Imperial College Uses PyTorch to Solve Climate Models Without Hand-Coded Adjoints

Climate and weather models use land-surface models to calculate how heat, water, and radiation move between the ground and atmosphere. Parameters such as thermal conductivity, heat capacity, and surface albedo are difficult to measure and costly to infer. Imperial College London researchers report in a journal article that they can estimate these parameters by implementing the governing equations in PyTorch and differentiating the solver with autograd.

The approach, called Neural Physics in the arXiv preprint , represents finite-difference stencils as convolution operations. The forward pass still solves the discretized physical equations. PyTorch supplies tensor operations, gradient propagation, and optimizers. The authors call the method training-free because the convolution kernels encode numerical operators and no network weights learn a surrogate from examples. The inversion still uses iterative gradient descent to estimate physical parameters.

One backward pass replaces an adjoint

Inverse problems estimate physical parameters by minimizing the difference between model outputs and observations. Gradient-based methods need the derivative of that loss with respect to every unknown parameter. Geoscience codes traditionally obtain those derivatives from an adjoint, a separate sensitivity model that must remain synchronized with the forward solver as equations and numerical schemes change.

A finite-difference heat solver already applies small numerical stencils across a grid. In one dimension, a three-point stencil approximates the second spatial derivative at each soil level; a conv1d operation can apply the same calculation. PyTorch records how parameters affect each operation and propagates the loss backward through the time steps. The resulting gradients correspond to the discretized solver that ran, keeping the derivative aligned with differentiable changes to the code.