Abstract: In one embodiment, several reduced order models (ROMs), each at a different scale, are developed to create a multiscale ROM for a given system, which can include one or more integrated circuits (ICs), for simulating thermal responses (e.g., heating in the ICs and the system) as a result of usage scenarios of the IC and system (in which power is applied on the IC and in the system) over time. An IC, package and system can be thermally characterized to determine transient temperature response to a power source in each IC; this characterization can use simulations of the power source to simulate temperature responses at points in the IC, package and system, and these responses provide a set of thermal training data. An algorithm generates a linear time-invariant (LTI) state-space thermal macromodel or ROM at each of the different scales on-chip and in system, from the set of thermal step response training data, and combines them into a multiscale ROM, which can be distributed and solved on many CPUs.

Abstract: Methods and systems for improved simulation of thermal characterization and thermal modeling of devices, such as smart phones, are described. In one embodiment, a method can characterize center, edge, and corner thermal decay behavior at different locations on a simulated IC. For each location, near and far field thermal effects are captured at the same time. A simulation system can generate a steady state thermal decay curve for each selected location that shows how the temperature changes with distance to a heat source. The system can then use a set of location dependent thermal decay curves to compute, based on an inputted power profile for the IC, a steady state thermal profile of the IC.

Abstract: A method and apparatus of a device of predicting a heat map for a die model is described. In an exemplary embodiment, the device receives a die model for representing the die and a boundary condition applicable to the die, the die model including dimensions of the die. In addition, the device may include scaling the dimensions of the die model and the boundary condition, wherein the dimensions of the die model are scaled to a target die size, the scaled dimensions including a scaled die thickness. Furthermore, each trained die model including a die surface of the target die size, different trained die models having different die thickness, the plurality of trained die models trained under a plurality of boundary conditions, each trained die model having a plurality of decay curves associated with the plurality of boundary conditions. The method may additionally include determining a relationship between the scaled boundary condition and the plurality of boundary conditions.