Multiscale thermal analysis in integrated circuits is required for capturing both device-level and package-level dynamics. Traditional analysis with the finite element (FE) method performs poor at multiscale tasks because of conflicting element size requirements and CPU time limitation. Machine learning (ML) algorithms can be trained with FE simulation data to perform fast and efficient temperature prediction. In this work, spatial and temporal aspects of the temperature field are treated independently and used to train two artificial neural networks (ANNs). Prior to ANN training, fundamental spatial modes (proper orthogonal decomposition, POD) are calculated to simplify the ANN structure. In the time domain a similar approach is used: the fundamental temporal modes, i.e. thermal step responses are calculated and used to train the ANN. By training the ANN on step response data, the final dynamic temperature profile can be reconstructed using the convolutional operator. Using this method, a physics-informed ML workflow is established as the step response is converted to the impulse response or Green’s function, which are a known part of the analytical solution to the heat equation. The final result is an extremely fast and accurate dynamic thermal model of a chip.

Multiscale thermal analysis in integrated systems is required for capturing both device-level and circuit-level dynamics. Traditional analysis with finite element (FE) models can be accelerated by using machine learning (ML) methods. In this article, a performance benchmarking between three ML methods for thermal simulation is carried out: 1) artificial neural networks (ANNs); 2) proper orthogonal decomposition with radial basis functions (POD-RBFs); and 3) finally, POD-RBF-ANN is used as a hybrid ML method. The (dis)advantages of the different methods are demonstrated for the thermal simulation of a multiscale photonic chip. The ML models are trained with FE data for both linear and nonlinear dynamics and are tested for inter- and extra-polation prediction accuracy. A computational speed increase with a factor >7500 compared to FE is obtained. Furthermore, ANNs prove to be the best suited for the simulation of nonlinear dynamics. POD-RBF is the best method for minimizing training time and combining the best of both methods in POD-RBF-ANN creates an ML model with a short training phase and highly accurate predictions.