Efficient computational inference using gaussian processes

A method comprising:

• determining a plurality of candidate sets of values for a plurality of enforceable parameters of a physical system;
• for each of the plurality of candidate sets of values:
• obtaining a respective performance measurement for the physical system;
• and
• generating a respective data point having an input portion indicative of the candidate set of values and an output portion indicative of the respective performance measurement, the input portion having a first number of dimensions;
• and
• at a computing system:
• augmenting each data point to include an additional dimension comprising a bias value;
• projecting each augmented data point onto a surface of a unit hypersphere of the first number of dimensions;
• determining, using the projected augmented data points, a set of parameter values for a sparse variational GP on said unit hypersphere, the sparse variational GP having a zonal kernel and depending on a set of inducing variables randomly distributed according to a multi-dimensional Gaussian distribution and each corresponding to a reproducing kernel Hilbert space inner product between the GP and a spherical harmonic of the first number of dimensions;
• and
• determining, using the sparse variational GP with the determined set of parameter values, a further set of values for the plurality of enforceable parameters.

A processing unit for use in a computing system, the processing unit comprising:

• a data interface configured to receive a plurality of data points each having an input portion and an output portion, the input portion having a first number of dimensions;
• and
• a plurality of processing nodes, each configured to, independently of each other processing node of the plurality of processing nodes:
• augment a respective subset of the data points to each include an additional dimension comprising a bias value;
• project each augmented data point of the respective subset onto a surface of a unit hypersphere of the first number of dimensions;
• process each projected augmented data point of the respective subset to determine a respective covariance vector with elements given by spherical harmonics in the first number of dimensions evaluated at the projected augmented data point;
• and
• determine at least a portion of a diagonal covariance matrix with each element given by a variance of a respective one of a set of inducing variables randomly distributed according to a multi-dimensional Gaussian distribution and each corresponding to a reproducing kernel Hilbert space inner product between a sparse variational GP on said unit hypersphere and a spherical harmonic of the first number of dimensions,
• wherein the processing unit is further configured to determine a set of parameter values for the sparse variational GP using the determined covariance vectors and the determined diagonal covariance matrix.