In physics and mathematics, an ansatz (/ˈænsæts/; German: [ˈʔanzats] ⓘ, meaning: "initial placement of a tool at a work piece", plural ansatzes[1] or, from German, ansätze /ˈænsɛtsə/; German: [ˈʔanzɛtsə] ⓘ) is an educated guess or an additional assumption made to help solve a problem, and which may later be verified to be part of the solution by its results.
[2] An ansatz is the establishment of the starting equation(s), the theorem(s), or the value(s) describing a mathematical or physical problem or solution.
It typically provides an initial estimate or framework to the solution of a mathematical problem,[1] and can also take into consideration the boundary conditions (in fact, an ansatz is sometimes thought of as a "trial answer" and an important technique in solving differential equations[2]).
[3] It has been demonstrated that machine learning techniques can be applied to provide initial estimates similar to those invented by humans and to discover new ones in case no ansatz is available.
Another example could be the mass, energy, and entropy balance equations that, considered simultaneous for purposes of the elementary operations of linear algebra, are the ansatz to most basic problems of thermodynamics.