Multi-variable polynomial modeling techniques for use in integrated circuit design

An apparatus for use in modeling a cell of an integrated circuit design, the apparatus comprising:

• a processing device comprising a memory and a processor coupled to the memory;
• wherein the processor is configured to perform the steps of:
• generating a polynomial model of a modeling space by fitting to cell information comprising measured data points associated with one or more independent variables;
• generating error values indicative of error between the measured data points and the polynomial model of the modeling space;
• partitioning the modeling space into domains having boundaries based on the error values;
• and
• for at least a given one of the domains, performing the following steps:
• (i) generating a first polynomial model of given domain by fitting to a plurality of data points including a subset of the measured data points and at least one additional data point determined by interpolation from one or more of the measured data points in the subset;
• (ii) generating error values indicative of error between the measured data points of the subset and the first polynomial model of step (i);
• (iii) generating a shifted model by applying correction factors determined from the error values of step (ii) to respective data points taken from the first polynomial model of step (i), wherein for a given such data point corresponding to the additional data point of step (i), the associated correction factor is determined by interpolation from one or more of the error values of step (ii);
• and
• (iv) generating a second polynomial model of the given domain by fitting to a plurality of data points from the shifted model of step (iii);
• wherein the integrated circuit design is processed using at least the second polynomial model of the given domain in order to determine if the integrated circuit design meets specified performance criteria.

An article of manufacture for use in modeling a cell of an integrated circuit design, the article of manufacture comprising a storage medium containing one or more software programs which, when executed by a processing device, perform the steps of:

• generating a polynomial model of a modeling space by fitting to cell information comprising measured data points associated with one or more independent variables;
• generating error values indicative of error between the measured data points and the polynomial model of the modeling space;
• partitioning the modeling space into domains having boundaries based on the error values;
• and
• for at least a given one of the domains, performing the following steps:
• (i) generating a first polynomial model of given domain by fitting to a plurality of data points including a subset of the measured data points and at least one additional data point determined by interpolation from one or more of the measured data points in the subset;
• (ii) generating error values indicative of error between the measured data points of the subset and the first polynomial model of step (i);
• (iii) generating a shifted model by applying correction factors determined from the error values of step (ii) to respective data points taken from the first polynomial model of step (i), wherein for a given such data point corresponding to the additional data point of step (i), the associated correction factor is determined by interpolation from one or more of the error values of step (ii);
• and
• (iv) generating a second polynomial model of the given domain by fining to a plurality of data points from the shifted model of step (iii);
• wherein the integrated circuit design is processed using at least the second polynomial model of the given domain in order to determine if the integrated circuit design meets specified performance criteria.