A methodology for thermal simulation of interconnects enabled by model reduction with material property variation

Jia, Wangkun; Cheng, Ming‐C.

doi:10.1016/j.jocs.2022.101665

Cited by 8 publications

(7 citation statements)

References 46 publications

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“…In each simulation, only the WFs in the first 6 ( N Q ) QSs are collected. Using data collected from the QD structure with variations of five pyramid potentials, together with the structure without any pyramid, there are in total 186 samples/snapshots (i.e., (6 × 5 + 1) × 6) of WF data collected to solve POD modes and eigenvalues from (4) via the method of snapshots 51 , 52 . Similar to Fig.…”

Section: Methodsmentioning

confidence: 99%

“…In a multi-dimension structure with a fine spatial resolution, the large dimension of R may be difficult to manage. The method of snapshots 51,52 is applied to convert the eigenvalue problem in (4) from a discrete space domain with a large dimension of the N r × N r to a sampling domain with a dimension of N s × N s , where N r and N s are the numbers of spatial grid points and data samples/snapshots, respectively, and in general N s < < N r . Instead of N r eigenvalues given in (4), the snapshot method solves only the first N s eigenvalues and POD modes.…”

Section: Methodsmentioning

confidence: 99%

“…The sampled WF data in the QD structure collected from the 2 sets of orthogonal electric fields, together with the unbiased WF data, are combined to generate one set of POD modes that represent all 6 trained QSs. With 6 selected QSs for each field, a total of 102 samples/snapshots of the WF data is implemented in the method of snapshots 51,52 to solve the first 102 eigenvalues and POD modes from (4). This quantum POD-Galerkin model for a given in ( 9) is therefore constructed with the coefficients evaluated from (11) to (13) via its POD modes.…”

Section: Demonstrationsmentioning

confidence: 99%

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Physics-informed reduced-order learning from the first principles for simulation of quantum nanostructures

Veresko

Cheng

2023

Sci Rep

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Multi-dimensional direct numerical simulation (DNS) of the Schrödinger equation is needed for design and analysis of quantum nanostructures that offer numerous applications in biology, medicine, materials, electronic/photonic devices, etc. In large-scale nanostructures, extensive computational effort needed in DNS may become prohibitive due to the high degrees of freedom (DoF). This study employs a physics-based reduced-order learning algorithm, enabled by the first principles, for simulation of the Schrödinger equation to achieve high accuracy and efficiency. The proposed simulation methodology is applied to investigate two quantum-dot structures; one operates under external electric field, and the other is influenced by internal potential variation with periodic boundary conditions. The former is similar to typical operations of nanoelectronic devices, and the latter is of interest to simulation and design of nanostructures and materials, such as applications of density functional theory. In each structure, cases within and beyond training conditions are examined. Using the proposed methodology, a very accurate prediction can be realized with a reduction in the DoF by more than 3 orders of magnitude and in the computational time by 2 orders, compared to DNS. An accurate prediction beyond the training conditions, including higher external field and larger internal potential in untrained quantum states, is also achieved. Comparison is also carried out between the physics-based learning and Fourier-based plane-wave approaches for a periodic case.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Demonstrationsmentioning

confidence: 99%

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Physics-informed reduced-order learning from the first principles for simulation of quantum nanostructures

Veresko

Cheng

2023

Sci Rep

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“…This rigorous procedure guides the POD thermal solution to comply with the dynamic heat transfer equation. Cheng's group has applied the POD simulation methodology to develop efficient and accurate thermal simulation models for SOI and FinFET devices, FinFET circuits at the gate level and interconnects [8].…”

Section: E Physics-based Learning Methodsmentioning

confidence: 99%

“…As described above, the POD based simulator, PODTherm-GP, is able to model a large-scale dynamic thermal problem using a small number of POD modes [8], [9]. These modes are trained by the thermal solution data of the physical domain obtained from DNSs subjected to a range of parametric variations including the BCs and dynamic power map.…”

Section: Pod Thermal Simulation Methodologymentioning

confidence: 99%

PODTherm-GP: A Physics-Based Data-Driven Approach for Effective Architecture-Level Thermal Simulation of Multi-Core CPUs

Lin

Dowling

Cheng

et al. 2023

IEEE Trans. Comput.

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A thermal simulation methodology derived from the proper orthogonal decomposition (POD) and the Galerkin projection (GP), hereafter referred to as PODTherm-GP, is evaluated in terms of its efficiency and accuracy in a multi-core CPU. The GP projects the heat transfer equation onto a mathematical space whose basis functions are generated from thermal data enabled by the POD learning algorithm. The thermal solution data are collected from FEniCS using the finite element method (FEM) accounting for appropriate parametric variations. The GP incorporates physical principles of heat transfer in the methodology to reach high accuracy and efficiency. The dynamic power map for the CPU in FEM thermal simulation is generated from gem5 and McPACT, together with the SPLASH-2 benchmarks as the simulation workload. It is shown that PODTherm-GP offers an accurate thermal prediction of the CPU with a resolution as fine as the FEM. It is also demonstrated that PODTherm-GP is capable of predicting the dynamic thermal profile of the chip with a good accuracy beyond the training conditions. Additionally, the approach offers a reduction in degrees of freedom by more than 5 orders of magnitude and a speedup of 4 orders, compared to the FEM.

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VarSim: A fast process variation-aware thermal modeling methodology using Green’s functions

Sultan,

Sarangi

2023

Microelectronics Journal

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A methodology for thermal simulation of interconnects enabled by model reduction with material property variation

Cited by 8 publications

References 46 publications

Physics-informed reduced-order learning from the first principles for simulation of quantum nanostructures

Physics-informed reduced-order learning from the first principles for simulation of quantum nanostructures

PODTherm-GP: A Physics-Based Data-Driven Approach for Effective Architecture-Level Thermal Simulation of Multi-Core CPUs

VarSim: A fast process variation-aware thermal modeling methodology using Green’s functions

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