Patent ID: 8843509

Claim:
A method of estimating a property for a query object in a corresponding query object configuration, the method comprising: accessing a database of database object configurations and a corresponding value of a property for each respective database object in each database configuration, wherein the query object configuration is different from any of the database object configurations; calculating an estimate of a query value of the property for the query object in the query object configuration as a mean of a posterior distribution over the query value for the query object under a Gaussian Process model, wherein the objects are atoms, groups of atoms or molecules; and providing the estimate in an answer to a query; wherein: (a) the database object configurations are stored in the database as a list of object coordinates relative to a respective object and calculating the estimate includes transforming the relative object coordinates into a representation which is invariant under rotation and permutation, or (b) the method includes transforming relative object coordinates of object configurations into a representation which is invariant under rotation and permutation and storing the transformed object configurations in the database as the database object configurations; wherein the transforming in (a) and (b) comprises: (c) transforming the relative object coordinates into a basis comprising a product of spherical harmonics and radial basis functions and calculating selected values of the bi-spectrum from the transformed coordinates, or (d) projecting the relative object coordinates onto a 4-dimensional sphere, calculating spherical harmonics of the projected coordinates, and calculating selected values of the bi-spectrum from the spherical harmonics of the projected coordinates.