Modeling of Heterogeneously Integrated Systems: Challenges and Strategies for Rapid Design Exploration

Design space exploration in Heterogeneously Integrated (HI) systems requires trade-off between electrical, thermal, and mechanical performance metrics. Therefore, modeling of HI systems is readily recognized as a multi-physics problem [1] , [2] . The challenge in these models is to capture the physical behavior with high degree of fidelity. However, since the models need to connect physical causes/effects at sub-micrometer features to effects/causes at centimeter sized modules, the modeling needs are also inherently multi-scale. This need for multi-scale modeling is less commonly recognized. Fully refined computational models spanning 6-8 orders of length scale are computationally impractical for design space exploration. Recently machine learning models are proposed as enabling rapid design exploration, but their fidelity to the partial differential equation solution surface that underlie the physical behavior remains to be proven. In this talk we systematically explore (1) adaptive grid solution strategies for systematic trade-off between solution accuracy and computational speed, (2) decomposition of problem domain to enable compact models of sub-domains [3] and to enable a coordinated multi-level analysis, (3) machine learning models as compact models of decomposed domains, and (4) the computational cost of training and using machine learning models relative to physical models. Relevant to the last item, our prior work has demonstrated that neural networks, although fast to use, are advantageous only when training time is not considered [4] , [5] , [6] . We will conclude with potential strategies for the efficient design exploration of HI systems including Physics Informed Neural Networks (PINNs).