The need for full-chip dynamic thermal simulation for effective run-time thermal management of multi-core 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 multi-core 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 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 goodquality data, the POD simulation offers an accurate prediction of the dynamic thermal distribution in the multi-core 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. 

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

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 paper a performance benchmarking between three ML methods for thermal simulation is carried out: Artificial Neural Networks (ANNs), Proper Orthogonal Decomposition with Radial Basis Functions (POD-RBF) and 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 non-linear dynamics and are tested for inter-and extrapolation prediction accuracy. A computational speed increase with factor >7500 compared to FE is obtained. Furthermore, ANNs prove to be the best suited for the simulation of non-linear dynamics. POD-RBF is the best method for minimizing training time and combining the best of both methods in POD-RBF-ANN creates a ML model with short training phase and highly accurate predictions. 

Benchmarking of Machine Learning Methods for Multiscale Thermal Simulation of Integrated Circuits

Silicon photonics (SiPho) is a promising technology for enabling low power and high-speed optical transceivers, which are commonly used in inter/intra-data center communication links. In order to scale the communication data rate, transceivers employ multiple channels in parallel. Each channel is handled by a unit cell consisting of multiple thermally sensitive elements, such as ring modulators and wavelength filters. To combat this sensitivity, the devices are equipped with integrated heater elements which allow for temperature stabilisation. In this paper a methodology is proposed which allows to do multiscale thermal modelling of a transceiver array. Proper orthogonal decomposition (POD) is combined with radial basis functions (RBF) as a machine learning method which reduces computational complexity of models with a large number of degrees of freedom. The reduced order circuit-level model is used for the calculation of thermal coupling coefficients between unit cells. Device level finite element (FE) simulations are done in order to calculate heater efficiency. Finally, all results are combined in a lumped-parameter circuit-level model. This model allows to predict exactly how much heater power is required within each unit cell in order to achieve uniform temperature stabilisation. 

Circuit-level Thermal Modelling of Silicon Photonic Transceiver Array using Machine Learning

To perform chip-level thermal simulation effectively for large-scale processors with multicores/manycores, a multi-block model enabled by proper orthogonal decomposition (POD) and domain decomposition is applied. This approach partitions a large-scale processor into smaller building blocks, such as cores, caches, I/O units, etc. For each building block, a set of temperature solution data accounting for parametric variations of interest is collected individually from FEniCS, a finite element simulation platform, to extract its basis functions (or POD modes). Using smaller building blocks, the multi-block approach significantly enhances the computational efficiency of POD mode generation to construct a POD model for the entire chip. In this work, a set of POD modes is trained by the solution data from each of two selected building blocks, a core and a level-2 cache, of AMD Athlon II X4 610e, a quad-core chip. A two-block POD thermal model is developed for Core 1 and L2 Cache by projecting these two blocks to a functional space represented by these 2 sets of POD modes. The discontinuous Galerkin method with the penalty number is applied to ensure the boundary continuity at the block interface. An optimal range of the penalty number for the two-block POD thermal model has been observed to provide an accurate prediction of the dynamic thermal distribution in Core 1 and L2 Cache. For the two-block POD model, a least square error below 3% is achieved with only 3 POD modes in each block. This results in a reduction in the numerical degrees of freedom by almost 4 orders in magnitude and thousands of times faster than FEniCS for the thermal simulation. 

Chip-level Thermal Simulation for a Multicore Processor Using a Multi-Block Model Enabled by Proper Orthogonal Decomposition

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

A data-driven reduced-order approach is applied to develop a thermal simulation model for a quad-core CPU, AMD ATHLON II X4 610e. The model is based on proper orthogonal decomposition (POD) that projects the physical domain of the CPU onto a functional space represented by a small set of basis functions (or modes). To generate an optimal set of modes, these modes are trained by thermal solution data collected from numerical simulation tools, FEniCS and HotSpot Grid. If good-quality data are used in the training process, the process optimizes the POD modes that are then able to offer a very accurate simulation model with a very small numerical degree of freedom (DoF). Each of the developed POD models is verified against its simulation tool used in its training. A very accurate prediction is observed in the POD model derived from FEniCS with a reduction in the numerical DoF by nearly 5 orders of magnitude, which amounts to more than a 3-order reduction in computing time. The POD model derived from HotSpot Grid is however not able to offer accurate simulation due to its inadequate data quality.

An Effective and Accurate Data-Driven Approach for Thermal Simulation of CPUs

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.

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

Modern real-time systems utilize considerable amounts of power while executing computation-intensive tasks. The execution of these tasks leads to significant power dissipation and heating of the device. It therefore results in severe thermal issues like temperature escalation, high thermal gradients, and excessive hot spot formation, which may result in degrading chip performance, accelerating device aging, and premature failure. Thermal-Aware Scheduling (TAS) enables the optimization of thermal dissipation to maintain a safe thermal state. In this work, we implement a new TAS algorithm, POD-TAS, which manages the thermal behavior of the cores based on a defined set of states and their transitions. We compare the performances of a dynamic Resistor-Capacitor (RC) thermal circuit simulator (HotSpot) and a reduced order Proper Orthogonal Decomposition (POD)-based thermal model and we select the latter for use in our POD-TAS algorithm. We implement a novel simulation-based evaluation methodology to compare TAS algorithms. This methodology is used to evaluate the performance of the proposed POD-TAS algorithm with high spatiotemporal resolution. Additionally, we compare the performance of a state of the art TAS algorithm, RT-TAS, to our proposed POD-TAS algorithm. Furthermore, we utilize the Clarkson Open-source Multi-physics Benchmark Suite (COMBS) to provide CPU workloads for task scheduling. Our experimental results on a multi-core processor using a set of 4 benchmarks demonstrate that the proposed POD-TAS method can improve thermal performance by decreasing the peak thermal variance by 53.0% and the peak chip temperature by 29.01%. Using a set of 8 benchmarks, the comparison of the algorithms demonstrates that POD-TAS decreases the peak spatial variance of the chip temperature and the peak chip temperature by 29.57% and 26.26% respectively.

pdf/regulating-cpu-temperature-with-thermal-aware-scheduling-3a6hfz947u.pdf

Regulating CPU Temperature With Thermal-Aware Scheduling Using a Reduced Order Learning Thermal Model

https://doi.org/10.1016/j.mex.2023.102204

Physics-driven proper orthogonal decomposition: A simulation methodology for partial differential equations

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