Sam Buercklin

Tools for performing autodifferentiation (AD) and dimensional work in Julia are robust, but not always compatible. This talk explores how we can understand rule-based AD in Julia by showing how to make dimensional quantities from `Unitful.jl` compose with `ChainRules.jl`. Combining these two projects produces an intuitive look at the building blocks of AD in Julia using only rudimentary calculus and dimensional analysis.

`Unitful.jl` provides efficient type-level support for dimensional quantities we encounter when simulating physical systems. Likewise, `ChainRules.jl` forms the backbone of robust but easily-extensible autodifferentiation (AD) systems. Exploring these two systems together yields an insightful look at Julia's rule-based AD. Calculus, dimensional analysis, and physical intuition are sufficient to explain how `ChainRules.jl` works by building AD rules for `Unitful.jl`.

The versatility of the `ChainRules.jl` ecosystem arises from implementing and extending a ruleset for fundamental functions, such as `*` and `inv`, as `rrule`s and `frule`s. What can often seem like a mysterious black box that computes derivatives is actually composed of many individual `rrule`s or `frule`s built on rudimentary calculus.

These `rrule`s and `frule`s are interpreted by thinking about differentiation as a problem of physical dimensions, and `Unitful.jl` is used to confirm these findings. However, arithmetic between `Unitful.jl` quantities is not immediately compatible with `ChainRules.jl`-based AD. This talk presents the pertinent AD rules to enable basic `ChainRules.jl` compatibility. These rules are also used as a lens to understand how to read and write AD rules for the `ChainRules.jl` ecosystem.

Sam Buercklin

Talks:

ChainRules.jl meets Unitful.jl: Autodiff via Unit Analysis

Platinum sponsors

Gold sponsors

Silver sponsors

Media partners

Community partners

Fiscal Sponsor