- Electrical Engineering and Computer Science
Top 3 Areas of Expertise:
I am a PhD student of Electrical Engineering at MIT, and I am expected to graduate in February of 2015. My PhD research is focused on numerical methods for uncertainty quantification, with application to the stochastic modeling and simulation of integrated circuits, microelectromechanical systems (MEMS) and silicon photonics that are influenced by significant nano-scale fabrication process variations.
I am much interested in academia, and I plan to apply for faculty positions in Fall 2015. From Feb. 2015 to Aug 2016, I plan to work as a postdoc or research scientist on some emerging engineering topics to enhance the diversity of my research background.
My PhD research has been focused on uncertainty quantification algorithms for the modeling and simulation of integrated circuits, MEMS and silicon photonics. I developed a stochastic testing simulator, which can simulate nonlinear integrated circuits in a non-Monte-Carlo way with 100x to 1000x speedup over Monte-Carlo simulation. This simulator can perform efficient stochastic DC, transient and periodic steady-state analysis. I have further developed a set of frameworks for hierarchical uncertainty quantification with both low and high parameter dimensionalities. Such algorithms have been verified by practical MEMS/IC co-design examples, showing 90x to 500x speedup over existing state-of-the-art algorithms. I have also done some research in deterministic MEMS simulation and model order reduction, leading to sevreal first-authored top journal and conference publications.
Now I am much interested in the following topics:
1. Uncertainty quantification for emerging engineering problems. I want to extend my uncertainty quantification to the stochastic analysis of power systems, MRI, genetic networks and data mining. On the theoretical side, I am much interested in some open problems in uncertainty quantification, including long-term integration, high-dimensional problems, hierarchical problems.
2. Tensor analysis (multilinear algebra) to solve high-dimensional engineering problems. Using tensor decompositon and tensor completion, many high-dimensional function approximation and integration problems can be solved without curse of dimensionality. Such algorithms can be applied to data compression, to solve integral equations arising from MRI coil design and compuatational modeling of MRI coild design, and to solve high-dimensional uncertainty quantification problems.
3. High-dimensional statistics (e.g., sparse principal component analysis and matrix completion). I am at the starting stage of this area. I am particullay interested in low-rank and sparse recovery of large-scale and high-dimensional data, add apply the results to solve some problems in MRI and uncertainty quantification.
Expected date of graduation:
This thesis investigates fast numerical methods for quantifying the uncertainties of semiconductor chips caused by manufacturing process variations. The contributions of this thesis include: 1) a fast stochastic testing method for analyzing integrated circuits, 2) hierarchical uncertainty quantification for complex stochastic systems with several subsystems, 3) efficient algorithms for handling high-dimensional subsystems in hierarchical uncertainty quantification, and 4) uncertainty quantification techniques for physical systems with correlated non-Gaussian random parameters. Theoretical results and numerical implementations are presented for each topic. Simulation results on integrated circuits, microelectromechanical systems (MEMS) and silicon photonic devices are reported to show the effectivness of the proposed stochastic simulators.
Top 5 Awards and honors (name of award, date received):
5 Recent Papers:
Z. Zhang, X. Yang, I. V. Oseledets, G. E. Karniadakis and L. Daniel, "Enabling high-dimensional hierarchical uncertainty quantification by ANOVA and tensor-train decomposition," submitted to IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems in June 2014 (arXiv:1407.3023v2)
Z. Zhang, T. A. El-Moselhy, I. M. Elfadel and L. Daniel, "Calculation of generalized polynomial-chaos basis functions and Gauss quadrature rules in hierarchical uncertainty quantification," IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, vol. 33, no. 5, pp. 728-740, May 2014 (TCAD Popular Paper)
Z. Zhang, T. A. El-Moselhy, P. Maffezzoni, I. M. Elfadel and L. Daniel, "Efficient uncertainty quantification for the periodic steady state of forced and autonomous circuits," IEEE Trans. Circuits and Systems II: Express Briefs, vol. 60, no.10, pp. 687-691, Oct. 2013.
Z. Zhang, T. A. El-Moselhy, I. M. Elfadel and L. Daniel, "Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos," IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, vol. 32, no. 10, pp. 1533-1545, Oct. 2013, (Donald O. Pederson TCAD Best Paper Award, TCAD Popular Paper)
Z. Zhang, M. Kamon and L. Daniel, "Continuation-based pull-in and lift-off simulation algorithms for microelectromechanical devices," IEEE/ASME Journal of Microelectromechanical Systems (JMEMS), vol.23, no.5, pp., Oct. 2014