Thermal optimization plays a crucial role in the design of advanced systems in package. Due to the large number of thermal simulations needed for full design space exploration, reductions in simulation run-time are critical. Here, we propose a data-driven approach to physics simulation by using neural networks (NNs) to cast the temperature solution process into an image-to-image translation problem. We first model the power generation map, conductivity map, and boundary conditions (BCs) into separate channels of an image. We then generate temperature solutions by training a generative adversarial network, composed of a U-Net shaped generator and a discriminator. The resultant NN model can handle diverse thermal simulation scenarios with accuracy. More importantly, our model can handle BCs, power maps, and physical package designs which are unseen during the training. Experiments show that speed wise, it enables near real-time design, providing a$2581\times $and$9171\times $speedup over a custom sparse matrix optimized finite element method and ABAQUS, respectively. Comparisons with state-of-the-art methods have demonstrated the accuracy, efficiency, and versatility of the proposed work.

Listeners are able to very approximately estimate speakers’ ages, with a mean estimation error of around ten years. Interestingly, accuracy varies considerably, depending on a number of social aspects of both speaker and listener, including age, gender and native language or language variety. The present study considers the effects of four factors on age perception. It investigates whether there is a main effect of speakers’ native language (Arabic, Korean and Mandarin) even when speaking a second language, English. It also investigates a particular speaker-listener relationship, namely the degree of linguistic familiarity. Linguistic familiarity was expected to be greater between Mandarin and Korean than between Mandarin or Korean and Arabic. In addition, it considers the effect of the acoustic cues of mean fundamental frequency (F0) and speech rate on age estimates. Fifteen Arabic-accented, fifteen Korean-accented and twenty Mandarin-accented English speakers participated as listeners. They heard audio stimuli produced by forty-eight speakers, equally distributed between native Arabic, Korean and Mandarin speakers, reading a short passage in English. Listeners were instructed to estimate speakers’ ages in years. Listeners’ age estimates and reaction times were recorded. Results indicate a significant main effect of speaker native language on perceived age such that Mandarin speakers were estimated to be younger than Arabic speakers. There was also a significant effect of linguistic familiarity on age estimation accuracy. Age estimates were more accurate with greater linguistic familiarity, i.e., native Korean and Mandarin listeners estimated ages of speakers of their own native languages more accurately than native Arabic speakers’ ages and vice versa. In terms of acoustic cues, mean F0 and speech rate were significant predictors of age estimation. These effects suggest that in perception, age may be marked not only by biological changes that occur over the lifetime, but also by language-specific socio-cultural features.

We develop a direct finite-element solver of linear (optimal) complexity to extract broadband circuit parameters such as S-parameters of arbitrarily shaped 3-D interconnects in inhomogeneous dielectrics. Numerical experiments demonstrate a clear advantage of the proposed solver as compared with existing finite-element solvers that employ state-of-the-art direct sparse matrix solutions. A linear complexity in both CPU time and memory consumption is achieved with prescribed accuracy satisfied. A finite-element matrix from the analysis of a large-scale 3-D circuit in multiple dielectrics having 5.643 million unknowns is directly factorized in less than 2 hours on a single core running at 2.8 GHz.

We develop a linear-complexity direct matrix solution for the surface integral equation (IE)-based impedance extraction of arbitrarily shaped 3-D nonideal conductors embedded in a dielectric material. A direct inverse of a highly irregular system matrix composed of both dense and sparse matrix blocks is obtained inO(N) complexity withNbeing the matrix size. It outperforms state-of-the-art impedance solvers, be they direct solvers or iterative solvers, with fast central processing unit (CPU) time, modest memory consumption, and without sacrificing accuracy, for both small and large number of unknowns. The inverse of a 2.68-million-unknown matrix arising from the extraction of a large-scale 3-D interconnect having 128 buses, which is a matrix solution for 2.68 million right-hand sides, was obtained in less than 1.5 GB memory and 1.3 h on a single CPU running at 3 GHz.

It is of critical importance to efficiently and accurately predict global resonances of a 3-D integrated circuit system that involves arbitrarily shaped lossy conductors and inhomogeneous materials. A quadratic eigenvalue solver of linear complexity and electromagnetic accuracy is developed in this paper to fulfill this task. Without sacrificing accuracy, the proposed eigenvalue solver has shown a clear advantage over state-of-the-art eigenvalue solvers in fast CPU time. It successfully solves a quadratic eigenvalue problem of over 2.5 million unknowns associated with a large-scale 3-D on-chip circuit embedded in inhomogeneous materials in 40 min on a single 3 GHz 8222SE AMD Opteron processor.

A linear-complexity direct matrix solution is developed for the surface-integral based impedance extraction of arbitrarily-shaped 3-D non-ideal conductors embedded in dielectric materials. It outperforms state-of-the-art impedance solvers with fast CPU-time, modest memory-consumption, and without sacrificing accuracy. The inverse of a 2.6-million-unknown matrix arising from the extraction of large-scale 3-D interconnects was obtained in 1.5 GB memory and 1.3 hours on a 3 GHz CPU.

State-of-the-art integral-equation-based solvers rely on techniques that can perform a matrix-vector multiplication in O(N) complexity. In this work, a fast inverse of linear complexity was developed to solve a dense system of linear equations directly for the capacitance extraction of any arbitrary shaped 3D structure. The proposed direct solver has demonstrated clear advantages over state-of-the-art solvers such as FastCap and HiCap; with fast CPU time and modest memory consumption, and without sacrificing accuracy. It successfully inverts a dense matrix that involves more than one million unknowns associated with a large-scale on-chip 3D interconnect embedded in inhomogeneous materials. Moreover, we have successfully applied the proposed solver to full-wave extraction.

A time-domain orthogonal finite-element reduction-recovery method is developed to overcome the large problem sizes encountered in the simulation of large-scale integrated-circuit and package problems. In this method, a set of orthogonal prism vector basis functions is developed. Based on this set of bases, an arbitrary 3-D multilayered system such as a combined package and die is reduced to a single-layer system with negligible computational cost. More importantly, the reduced single-layer system is diagonal and, hence, can be solved readily. From the solution of the reduced system, the solution of the other unknowns is recovered in linear complexity. The method entails no theoretical approximation. It applies to any arbitrarily shaped multilayer structure involving inhomogeneous materials or any structure that can be geometrically modeled by triangular prism elements. In addition, it permits nonlinear device modeling and broadband simulation within one run. Numerical and experimental results have demonstrated its accuracy and high capacity in simulating on-chip, package, and die-package interface problems.

This paper proposes a fast and high-capacity electromagnetic solution, time-domain layered finite element reduction recovery (LAFE-RR) method, for high-frequency modeling and simulation of large-scale on-chip circuits. This method rigorously reduces the matrix of a multilayer system to that of a single-layer one regardless of the original problem size. More important, the matrix reduction is achieved analytically, and hence the CPU and memory overheads are minimal. The recovery of solutions in all other layers involves only forward and backward substitution of matrices of single-layer size. The memory cost is also modest-requiring only the memory needed for the factorization of a single layer sparse matrix. The improved performance applies to any arbitrarily shaped multilayer structure. Numerical and experimental results are presented to demonstrate the accuracy, efficiency, and capacity of the proposed method.