Novel Tensor-Based Circuit Modeling and Simulation
Dr Wong, Ngai (Principal investigator)
Circuit modeling, Circuit simulation, Nonlinear, Tensor, Model Order Reduction
RGC General Research Fund (GRF)
HKU Project Code
General Research Fund (GRF)
1) New theory with fast and robust algorithms for tensor decomposition and analysis ---- a prominent yet intriguing property of tensors is that they allow various decompositions into finite low-rank terms, in contrast to the singular value decomposition (SVD) of matrices that is unique up to signs of singular vectors. This translates into the quest for tensor analysis and synthesis algorithms that strike the balance between numerical efficiency, accuracy and robustness; 2) Expedited tensor-based circuit modeling and simulation ---- many circuit modeling exercises naturally give rise to multi-dimensional data representation which are unnecessarily "flattened" into matrix/vector format only to fit into existing computing platforms and linear algebra routines. In fact, preservation of the intrinsic tensor structures and direct computation in tensor formats often lead to significant speedup; 3) Open-source computer codes and benchmarks for generic tensor operations and specialized EDA routines ---- appreciation of the benefits of tensor-based algorithms is best achieved by making them available in the public domain. This permits promulgation of the tensor framework, as well as verification and improvement of tensor algorithms through collective talents and efforts; 4) Long-Term Impact: The long-term impact of this project is echoed by the recent flurry of research on tensor decompositions and applications. Our initiative to introduce tensors to the EDA field can also address the need for an efficient tool in handling nonlinear circuit design problems that are naturally captured in the tensor format. The success of the above goals and their streamlined integration into the EDA flow will lead to a revolution in the data structure and numerical routines for performing circuit modeling and simulation. Elements in this project can also provide students, researchers and practitioners with the breadth (general tensor knowledge) and depth (specialization to EDA algorithms) of knowledge necessary to contribute to the academia and industry. The contemporary content of the project can be readily merged into postgraduate courses at HKU to provide an interdisciplinary training in advanced multi-linear tensor algebra, numerical algorithms, nonlinear theory and circuit modeling.