skip to main content


Title: An effective physics simulation methodology based on a data-driven learning algorithm
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.  more » « less
Award ID(s):
1852102 2003307 2118079
NSF-PAR ID:
10414014
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
PASC '22: Proceedings of the Platform for Advanced Scientific Computing Conference
Page Range / eLocation ID:
1 to 10
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. 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. 
    more » « less
  2. 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. 
    more » « less
  3. Low-dimensional and computationally less-expensive reduced-order models (ROMs) have been widely used to capture the dominant behaviors of high-4dimensional systems. An ROM can be obtained, using the well-known proper orthogonal decomposition (POD), by projecting the full-order model to a subspace spanned by modal basis modes that are learned from experimental, simulated, or observational data, i.e., training data. However, the optimal basis can change with the parameter settings. When an ROM, constructed using the POD basis obtained from training data, is applied to new parameter settings, the model often lacks robustness against the change of parameters in design, control, and other real-time operation problems. This paper proposes to use regression trees on Grassmann manifold to learn the mapping between parameters and POD bases that span the low-dimensional subspaces onto which full-order models are projected. Motivated by the observation that a subspace spanned by a POD basis can be viewed as a point in the Grassmann manifold, we propose to grow a tree by repeatedly splitting the tree node to maximize the Riemannian distance between the two subspaces spanned by the predicted POD bases on the left and right daughter nodes. Five numerical examples are presented to comprehensively demonstrate the performance of the proposed method, and compare the proposed tree-based method to the existing interpolation method for POD basis and the use of global POD basis. The results show that the proposed tree-based method is capable of establishing the mapping between parameters and POD bases, and thus adapt ROMs for new parameters.

     
    more » « less
  4. Abstract

    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.

     
    more » « less
  5. null (Ed.)
    The G-equation is a well-known model for studying front propagation in turbulent combustion. In this paper, we develop an efficient model reduction method for computing regular solutions of viscous G-equations in incompressible steady and time-periodic cellular flows. Our method is based on the Galerkin proper orthogonal decomposition (POD) method. To facilitate the algorithm design and convergence analysis, we decompose the solution of the viscous G-equation into a mean-free part and a mean part, where their evolution equations can be derived accordingly. We construct the POD basis from the solution snapshots of the mean-free part. With the POD basis, we can efficiently solve the evolution equation for the mean-free part of the solution to the viscous G-equation. After we get the mean-free part of the solution, the mean of the solution can be recovered. We also provide rigorous convergence analysis for our method. Numerical results for viscous G-equations and curvature G-equations are presented to demonstrate the accuracy and efficiency of the proposed method. In addition, we study the turbulent flame speeds of the viscous G-equations in incompressible cellular flows. 
    more » « less