Chapter 11 closes Part IV with hybrid modeling: combining physics-based models with machine learning rather than treating ML as a standalone black box. The running example is glacier flow, replacing the most computationally expensive part of a numerical ice-flow model with a trained CNN emulator.
What knowledge-guided machine learning (KGML) is, why data-only and knowledge-only models each fall short on their own, and where hybrid models are applied across climate science, engineering, and medicine.
Simulating glacier flow with the shallow ice approximation, training a CNN to emulate the ice velocity field, then plugging that emulator into the numerical mass-conservation solver in place of the expensive physics-based calculation.
Resources¶
Textbooks and papers this chapter’s exercise adapts¶
The Instructed Glacier Model (IGM) — the CNN-emulator approach this exercise’s hybrid model is based on. (11.2)
The shallow ice approximation (SIA) used for the numerical ice-flow solver is standard in large-scale ice-sheet modeling; see e.g. Hutter, K. Theoretical Glaciology (1983) for its derivation. (11.2)
PyTorch¶
torch.nn.Conv2d— the fully-convolutional CNN architecture used to emulate ice-flow velocity from ice thickness and surface slope. (11.2)torch.nn.functional.padandtorch.where— the staggered-grid finite-difference operations behind the numerical ice-flow solver. (11.2)
Datasets¶
A bedrock topography grid for the exercise’s synthetic glacier domain (
bedrock.nc, committed todata/part-IV/). (11.2)The CNN’s training dataset (simulated glacier states from a high-order ice-flow model) is not yet committed to the repository — flagged as a pending follow-up; see the chapter’s port notes. (11.2)