Invariant
A quantity that does not change while everything else does.
Like you're twelve
Watch a swing go back and forth. Height changes, speed changes, direction changes — high and slow at the top, low and fast at the bottom. But there is a combination of height and speed that stays exactly the same all the way through, and finding that combination tells you more about the swing than any single snapshot does.
The thing that refuses to change is usually the thing worth knowing.
Precisely
Given states observed along a trajectory, an invariant is a direction in which nothing changes between one state and the next. Lift the state into features, form the matrix of feature differences across every observed transition, and an invariant is a direction in that matrix's null space — a weighting of features whose value is the same before and after.
No equations are supplied and no model class is chosen. The data is the trajectories, and the true quantity, where one is known, is used only to grade the answer.
The property that makes this trustworthy is what it does when there is nothing to find. A damped system conserves nothing, and the same computation run on it must return a weak result rather than a plausible one — a method that reports a law for every input has not found one. Grading therefore means three numbers: the result, its score on a system with a known law, and its score on a system with none.
Where nothing is conserved, the useful reading is a rate rather than a constant — how fast the system decays, and at what frequency.