Advanced thermal compensation of mechanical processes

A computer program product for compensating errors of a mechanical process due to thermal disturbances, the computer program product having a non-transitory machine-readable storage medium that includes computer-executable instructions that when executed by a computer is configured to receive as input:

• a set of sensor input data points from a sensor input data point space, each sensor input data point comprising data from a set of sensors, wherein each sensor provides a sensor sequence of sensor values at sensor sequence times, and each sensor input data point corresponds to an evolution of the mechanical process, wherein different sensor input data points correspond to different evolutions of the mechanical process;
• a current sensor input data point;
• a set of thermal error compensation states of the mechanical process, wherein each thermal error compensation state comprises a thermal error compensation state sequence of thermal error compensation vectors, wherein the thermal error compensation vectors are provided at thermal error compensation state sequence times;
• a model of the mechanical process, the model comprising a set of free parameters and a set of internal parameters, the assignment of free parameters and internal parameters determining temporal and spatial evolution of the model, the free parameters having pre-assigned values, wherein the free parameters are parameters that are determined through a calibration step;
• constraints on the temporal and spatial evolution of the model in the form of possible sets of values which the free parameters can take and in the form of sets of relationships between the internal parameters of the model;
• an abstract representation embodied as a function mapping an input space onto the space of thermal error compensation states, wherein the input space comprises at least the sensor input data point space, the function having a set of function parameters;
• and
• a representation input function with assigned function parameter values, the representation input function corresponding in form to the abstract representation,
• wherein the computer program product possesses two modes of operation, wherein in a training mode a training data set comprising empirical training data or synthetic training data is used, wherein the empirical training data are comprised of the set of sensor input data points as empirical training data input and the set of thermal error compensation states as empirical training data output, and wherein the synthetic training data are constructed by way of simulations carried out using the model of the mechanical process and the constraints, the synthetic training data comprising a synthetic simulated set of sensor input data points as synthetic training data input and a synthetic simulated set of thermal error compensation states as synthetic training data output,
• wherein the training data set comprising the empirical or synthetic training data is used for adapting the representation input function by adapting the function parameters, an inference mode being configured to use the adapted representation input function, wherein the adapted representation input function is invoked with at least the current sensor input data point to calculate a current thermal error compensation state used for compensating the thermal errors arising during the execution of the mechanical process.