Categorical Composition of Discrete Exterior Calculus Climate Models
summary
A Julia DSL called Decapodes.jl encodes PDEs as Discrete Exterior Calculus objects, composes them via undirected wiring diagrams, and compiles the result into runnable simulation code. The workflow assembles Halfar ice-sheet dynamics, composes Halfar with a Budyko‑Sellers energy‑balance model, and encodes the Klausmeier vegetation PDEs; benchmarks reproduce the community ice‑sheet model v2.1 with expected boundary error accumulation, and a type system prevents mismatched differential‑form operations.
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chapters (19)
- 0:00Introduction
- 0:44Climate simulations overview
- 1:50Vegetation dynamics
- 2:31Scientific computing spectrum
- 5:16Low-level code improvements
- 6:21Open-source limits
- 7:02Discrete exterior calculus
- 8:26Physics with exterior calculus
- 9:52Composing physics systems
- 10:55Category theory for formalization
- 12:01Domain-specific language in Julia
- 13:05Wiring diagrams for composition
- 13:48C-sets for data structures
- 14:33Equations with C-sets
- 15:35Compiling to simulations
- 15:57Ice sheet benchmarks
- 16:40Hellfire model execution
- 17:02Workflow and vegetation
- 17:45Q&A
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