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1. Fast Accurate Full-Chip Dynamic Thermal Simulation with Fine Resolution Enabled by a Learning Method

   https://doi.org/10.1109/TCAD.2022.3229598  

   Jiang, Lin ; Liu, Yu ; Cheng, Ming-C ( August 2023 , IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems)

   The need for full-chip dynamic thermal simulation for effective runtime thermal management of multicore processors has been growing in recent years due to the rising demand for high-performance computing. In addition to simulation efficiency and accuracy, a high resolution is desirable in order to accurately predict crucial hot spots in the chip. This work investigates a simulation technique derived from proper orthogonal decomposition (POD) for full-chip dynamic thermal simulation of a multicore processor. The POD projects a heat transfer problem onto a mathematical space constituted by a finite set of basis functions (or POD modes) that are generated (or trained) by thermal solution data collected from direct numerical simulation (DNS). Accuracy and efficiency of the POD simulation technique influenced by the quality of thermal data are examined thoroughly, especially in the areas with high thermal gradients. The results show that if the POD modes are trained by good-quality data, the POD simulation offers an accurate prediction of the dynamic thermal distribution in the multicore processor with an extremely small degree of freedom (DoF). A reduction in computational time over four orders of magnitude, compared to the DNS, can be achieved for full-chip dynamic thermal simulation with a resolution as fine as the DNS. The study has also demonstrated that the POD approach can be used to rigorously verify the accuracy of solutions offered by DNS tools. A practical approach is proposed to further enhance the accuracy and efficiency of the proposed full-chip thermal simulation technique. 

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2. An effective physics simulation methodology based on a data-driven learning algorithm

   https://doi.org/10.1145/3539781.3539799  

   Jiang, Lin ; Veresko, Martin ; Liu, Yu ; Cheng, Ming-C. ( June 2022 , PASC '22: Proceedings of the Platform for Advanced Scientific Computing Conference)

   A methodology of multi-dimensional physics simulations is investigated based on a data-driven learning algorithm derived from proper orthogonal decomposition (POD). The approach utilizes numerical simulation tools to collect solution data for the problems of interest subjected to parametric variations that may include interior excitations and/or boundary conditions influenced by exterior environments. The POD is applied to process the data and to generate a finite set of basis functions. The problem is then projected from the physical domain onto a mathematical space constituted by its basis functions. The effectiveness of the POD methodology thus depends on the data quality, which relies on the numerical settings implemented in the data collection (or the training). The simulation methodology is developed and demonstrated in a dynamic heat transfer problem for an entire CPU and in a quantum eigenvalue problem for a quantum-dot structure. Encouraging findings are observed for the POD simulation methodology in this investigation, including its extreme efficiency, high accuracy and great adaptability. The models constructed by the POD basis functions are even capable of predicting the solution of the problem beyond the conditions implemented in the training with a good accuracy. 

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3. Rapid and Rigorous Learning Simulation Methodology with High Accuracy for Electronic and Optical Superlattices

   Veresko, Martin ; Liu, Yu ; Hou, Daqing ; Cheng, Ming-Cheng ( July 2024 , 24th Int'l Conf. Computational Science (ICCS2024), Malaga, Spain)

   A rigorous physics-informed learning methodology is proposed for predictions of wave solutions and band structures in electronic and optical superlattice structures. The methodology is enabled by proper orthogonal decomposition (POD) and Galerkin projection of the wave equation. The approach solves the wave eigenvalue problem in POD space constituted by a finite set of basis functions (or POD modes). The POD ensures that the generated modes are optimized and tailored to the parametric variations of the system. Galerkin projection however enforces physical principles in the methodology to further enhance the accuracy and efficiency of the developed model. It has been demonstrated that the POD-Galerkin methodology offers an approach with a reduction in degrees of freedom by 4 orders of magnitude, compared to direct numerical simulation (DNS). A computing speedup near 15,000 times over DNS can be achieved with high accuracy for either of the superlattice structures if only the band structure is calculated without the wave solution. If both wave function solution and band structure are needed, a 2-order reduction in computational time can be achieved with a relative least square error (LSE) near 1%. When the training is incomplete or the desired eigenstates are slightly beyond the training bounds, an accurate prediction with an LSE near 1%-2% still can be reached if more POD modes are included. This reveals its remarkable learning ability to reach correct solutions with the guidance of physical principles provided by Galerkin projection. 

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4. An evolve‐then‐filter regularized reduced order model for convection‐dominated flows

   https://doi.org/10.1002/fld.4363  

   Wells, D. ; Wang, Z. ; Xie, X. ; Iliescu, T. ( February 2017 , International Journal for Numerical Methods in Fluids)

   In this paper, we propose a new evolve‐then‐filter reduced order model (EF‐ROM). This is a regularized ROM (Reg‐ROM), which aims to add numerical stabilization to proper orthogonal decomposition (POD) ROMs for convection‐dominated flows. We also consider the Leray ROM (L‐ROM). These two Reg‐ROMs use explicit ROM spatial filtering to smooth (regularize) various terms in the ROMs. Two spatial filters are used: a POD projection onto a POD subspace (Proj) and a POD differential filter (DF). The four Reg‐ROM/filter combinations are tested in the numerical simulation of the three‐dimensional flow past a circular cylinder at a Reynolds numberRe=1000. Overall, the most accurate Reg‐ROM/filter combination is EF‐ROM‐DF. Furthermore, the spatial filter has a higher impact on the Reg‐ROM than the regularization used. Indeed, the DF generally yields better results than Proj for both the EF‐ROM and L‐ROM. Finally, the CPU times of the four Reg‐ROM/filter combinations are orders of magnitude lower than the CPU time of the DNS. Copyright © 2017 John Wiley & Sons, Ltd.

    

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5. Ensemble learning model for effective thermal simulation of multi-core CPUs

   https://doi.org/10.1016/j.vlsi.2024.102201  

   Jiang, Lin ; Dowling, Anthony ; Liu, Yu ; Cheng, Ming-C ( July 2024 , Integration)

   An ensemble data-learning approach based on proper orthogonal decomposition (POD) and Galerkin projection (EnPOD-GP) is proposed for thermal simulations of multi-core CPUs to improve training efficiency and the model accuracy for a previously developed global POD-GP method (GPOD-GP). GPOD-GP generates one set of basis functions (or POD modes) to account for thermal behavior in response to variations in dynamic power maps (PMs) in the entire chip, which is computationally intensive to cover possible variations of all power sources. EnPOD-GP however acquires multiple sets of POD modes to significantly improve training efficiency and effectiveness, and its simulation accuracy is independent of any dynamic PM. Compared to finite element simulation, both GPOD-GP and EnPOD-GP offer a computational speedup over 3 orders of magnitude. For a processor with a small number of cores, GPOD-GP provides a more efficient approach. When high accuracy is desired and/or a processor with more cores is involved, EnPOD-GP is more preferable in terms of training effort and simulation accuracy and efficiency. Additionally, the error resulting from EnPOD-GP can be precisely predicted for any random spatiotemporal power excitation. 

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