Xuan Zeng

Chanhao Yan, Wei Cai, Xuan Zeng

In this paper, we will present a new approach for solving Laplace equations in general 3-D domains. The approach is based on a local computation method for the DtN mapping of the Laplace equation by combining a deterministic (local) boundary integral equation method and the probabilistic Feynman-Kac formula of PDE solutions. This hybridization produces a parallel algorithm where the bulk of the computation has no need for data communications. Given the Dirichlet data of the solution on a domain boundary, a local boundary integral equation (BIE) will be established over the boundary of a local region formed by a hemisphere superimposed on the domain boundary. By using a homogeneous Dirichlet Green's function for the whole sphere, the resulting BIE will involve only Dirichlet data (solution value) over the hemisphere surface, but over the patch of the domain boundary intersected by the hemisphere, both Dirichlet and Neumann data will be used. Then, firstly, the solution value on the hemisphere surface is computed by the Feynman-Kac formula, which will be implemented by a Monte Carlo walk on spheres (WOS) algorithm. Secondly, a boundary collocation method is applied to solve the integral equation on the aforementioned local patch of the domain boundary to yield the required Neumann data there. As a result, a local method of finding the DtN mapping is obtained, which can be used to find all the Neumann data on the whole domain boundary in a parallel manner. Finally, the potential solution in the whole space can be computed by an integral representation using both the Dirichlet and Neumann data over the domain boundary.

Yiting Liu, Hai Zhou, Jia Wang et al.

Placement is a critical task with high computation complexity in VLSI physical design. Modern analytical placers formulate the placement objective as a nonlinear optimization task, which suffers a long iteration time. To accelerate and enhance the placement process, recent studies have turned to deep learning-based approaches, particularly leveraging graph convolution networks (GCNs). However, learning-based placers require time- and data-consuming model training due to the complexity of circuit placement that involves large-scale cells and design-specific graph statistics. This paper proposes GiFt, a parameter-free technique for accelerating placement, rooted in graph signal processing. GiFt excels at capturing multi-resolution smooth signals of circuit graphs to generate optimized placement solutions without the need for time-consuming model training, and meanwhile significantly reduces the number of iterations required by analytical placers. Experimental results show that GiFt significantly improving placement efficiency, while achieving competitive or superior performance compared to state-of-the-art placers. In particular, compared to DREAMPlace, the recently proposed GPU-accelerated analytical placer, GF-Placer improves total runtime over 45%.

Shuhan Zhang, Fan Yang, Changhao Yan et al.

A large body of literature has proved that the Bayesian optimization framework is especially efficient and effective in analog circuit synthesis. However, most of the previous research works only focus on designing informative surrogate models or efficient acquisition functions. Even if searching for the global optimum over the acquisition function surface is itself a difficult task, it has been largely ignored. In this paper, we propose a fast and robust Bayesian optimization approach via one-dimensional subspaces for analog circuit synthesis. By solely focusing on optimizing one-dimension subspaces at each iteration, we greatly reduce the computational overhead of the Bayesian optimization framework while safely maximizing the acquisition function. By combining the benefits of different dimension selection strategies, we adaptively balancing between searching globally and locally. By leveraging the batch Bayesian optimization framework, we further accelerate the optimization procedure by making full use of the hardware resources. Experimental results quantitatively show that our proposed algorithm can accelerate the optimization procedure by up to 9x and 38x compared to LP-EI and REMBOpBO respectively when the batch size is 15.

Shuhan Zhang, Fan Yang, Changhao Yan et al.

Bayesian optimization is a promising methodology for analog circuit synthesis. However, the sequential nature of the Bayesian optimization framework significantly limits its ability to fully utilize real-world computational resources. In this paper, we propose an efficient parallelizable Bayesian optimization algorithm via Multi-objective ACquisition function Ensemble (MACE) to further accelerate the optimization procedure. By sampling query points from the Pareto front of the probability of improvement (PI), expected improvement (EI) and lower confidence bound (LCB), we combine the benefits of state-of-the-art acquisition functions to achieve a delicate tradeoff between exploration and exploitation for the unconstrained optimization problem. Based on this batch design, we further adjust the algorithm for the constrained optimization problem. By dividing the optimization procedure into two stages and first focusing on finding an initial feasible point, we manage to gain more information about the valid region and can better avoid sampling around the infeasible area. After achieving the first feasible point, we favor the feasible region by adopting a specially designed penalization term to the acquisition function ensemble. The experimental results quantitatively demonstrate that our proposed algorithm can reduce the overall simulation time by up to 74 times compared to differential evolution (DE) for the unconstrained optimization problem when the batch size is 15. For the constrained optimization problem, our proposed algorithm can speed up the optimization process by up to 15 times compared to the weighted expected improvement based Bayesian optimization (WEIBO) approach, when the batch size is 15.

Zhengqi Gao, Jun Tao, Yangfeng Su et al.

Pareto Front (PF) modeling is essential in decision making problems across all domains such as economics, medicine or engineering. In Operation Research literature, this task has been addressed based on multi-objective optimization algorithms. However, without learning models for PF, these methods cannot examine whether a new provided point locates on PF or not. In this paper, we reconsider the task from Data Mining perspective. A novel projection based active Gaussian process regression (P- aGPR) method is proposed for efficient PF modeling. First, P- aGPR chooses a series of projection spaces with dimensionalities ranking from low to high. Next, in each projection space, a Gaussian process regression (GPR) model is trained to represent the constraint that PF should satisfy in that space. Moreover, in order to improve modeling efficacy and stability, an active learning framework has been developed by exploiting the uncertainty information obtained in the GPR models. Different from all existing methods, our proposed P-aGPR method can not only provide a generative PF model, but also fast examine whether a provided point locates on PF or not. The numerical results demonstrate that compared to state-of-the-art passive learning methods the proposed P-aGPR method can achieve higher modeling accuracy and stability.