Definition
Plain language
A physics equation about a special kind of wave that holds its shape as it travels, used to test simulation methods.
As stated in the literature
The Korteweg-de Vries equation, a nonlinear PDE admitting soliton solutions; a standard benchmark in physics-informed ML evaluation suites.
Also called: KdV, Korteweg-de Vries
Why it matters: It's a standard benchmark for checking whether a method can faithfully model waves that preserve their form over time.
For example, it describes a soliton, a lone wave that keeps its shape as it rolls along a shallow canal.
Heard on the show
“And the broader picture across the four canonical benchmarks — Burgers, KdV, Helmholtz, Poisson — is that the converged residuals get down close to ten to the minus sixteen on some of them.”Episode 042 — An Agentic Scientific Computing System That Actually Remembers What It Learns