English: Non-linear least squares is a method of fitting data and consists in selecting the "best" model from within a non-linear family of mathematical models which should represent some aspects of the data. Models within a family usually differ from one another in the values of some parameters.

The criterion used to select the "best" model may be visualized by showing the surface of the sum of squared errors ${\displaystyle SSE\,\!}$  of each data with respect to its corresponding model approximation. The surface height varies with varying the parameters value ${\displaystyle \theta _{i},\cdots \theta _{j}}$. Where the surface reaches the minimum, the corresponding parameters identify the best model in the sense of least squares.

In the non-linear case, that selection may be more difficult due to the fact that the surface may have multiple local minima. Without exploring the whole surface, there may be no certainty to have reached the global minimum.

The surface shown in the diagram has been translated so that

${\displaystyle \operatorname {mean} (SSE)\equiv \int \limits _{\theta _{i},\theta _{j}}SSE(\theta _{i},\theta _{j})\,d\theta _{i}\,d\theta _{j}\quad {\overset {\underset {\mathrm {def} }{}}{=}}\quad 0}$

since this makes the diagram more visually expressive while not affecting the position of minima in the ${\displaystyle \theta _{i},\theta _{j}\,\!}$ domain.