572 research outputs found
Uncertainty Quantification of Electronic and Photonic ICs with Non-Gaussian Correlated Process Variations
Since the invention of generalized polynomial chaos in 2002, uncertainty
quantification has impacted many engineering fields, including variation-aware
design automation of integrated circuits and integrated photonics. Due to the
fast convergence rate, the generalized polynomial chaos expansion has achieved
orders-of-magnitude speedup than Monte Carlo in many applications. However,
almost all existing generalized polynomial chaos methods have a strong
assumption: the uncertain parameters are mutually independent or Gaussian
correlated. This assumption rarely holds in many realistic applications, and it
has been a long-standing challenge for both theorists and practitioners.
This paper propose a rigorous and efficient solution to address the challenge
of non-Gaussian correlation. We first extend generalized polynomial chaos, and
propose a class of smooth basis functions to efficiently handle non-Gaussian
correlations. Then, we consider high-dimensional parameters, and develop a
scalable tensor method to compute the proposed basis functions. Finally, we
develop a sparse solver with adaptive sample selections to solve
high-dimensional uncertainty quantification problems. We validate our theory
and algorithm by electronic and photonic ICs with 19 to 57 non-Gaussian
correlated variation parameters. The results show that our approach outperforms
Monte Carlo by to in terms of efficiency. Moreover,
our method can accurately predict the output density functions with multiple
peaks caused by non-Gaussian correlations, which is hard to handle by existing
methods.
Based on the results in this paper, many novel uncertainty quantification
algorithms can be developed and can be further applied to a broad range of
engineering domains
High-Dimensional Uncertainty Quantification of Electronic and Photonic IC with Non-Gaussian Correlated Process Variations
Uncertainty quantification based on generalized polynomial chaos has been
used in many applications. It has also achieved great success in
variation-aware design automation. However, almost all existing techniques
assume that the parameters are mutually independent or Gaussian correlated,
which is rarely true in real applications. For instance, in chip manufacturing,
many process variations are actually correlated. Recently, some techniques have
been developed to handle non-Gaussian correlated random parameters, but they
are time-consuming for high-dimensional problems. We present a new framework to
solve uncertainty quantification problems with many non-Gaussian correlated
uncertainties. Firstly, we propose a set of smooth basis functions to well
capture the impact of non-Gaussian correlated process variations. We develop a
tensor approach to compute these basis functions in a high-dimension setting.
Secondly, we investigate the theoretical aspect and practical implementation of
a sparse solver to compute the coefficients of all basis functions. We provide
some theoretical analysis for the exact recovery condition and error bound of
this sparse solver in the context of uncertainty quantification. We present
three adaptive sampling approaches to improve the performance of the sparse
solver. Finally, we validate our methods by synthetic and practical
electronic/photonic ICs with 19 to 57 non-Gaussian correlated variation
parameters. Our approach outperforms Monte Carlo by thousands of times in terms
of efficiency. It can also accurately predict the output density functions with
multiple peaks caused by non-Gaussian correlations, which are hard to capture
by existing methods.Comment: arXiv admin note: substantial text overlap with arXiv:1807.0177
Stochastic Collocation with Non-Gaussian Correlated Process Variations: Theory, Algorithms and Applications
Stochastic spectral methods have achieved great success in the uncertainty
quantification of many engineering problems, including electronic and photonic
integrated circuits influenced by fabrication process variations. Existing
techniques employ a generalized polynomial-chaos expansion, and they almost
always assume that all random parameters are mutually independent or Gaussian
correlated. However, this assumption is rarely true in real applications. How
to handle non-Gaussian correlated random parameters is a long-standing and
fundamental challenge. A main bottleneck is the lack of theory and
computational methods to perform a projection step in a correlated uncertain
parameter space. This paper presents an optimization-based approach to
automatically determinate the quadrature nodes and weights required in a
projection step, and develops an efficient stochastic collocation algorithm for
systems with non-Gaussian correlated parameters. We also provide some
theoretical proofs for the complexity and error bound of our proposed method.
Numerical experiments on synthetic, electronic and photonic integrated circuit
examples show the nearly exponential convergence rate and excellent efficiency
of our proposed approach. Many other challenging uncertainty-related problems
can be further solved based on this work.Comment: 14 pages,11 figure. 4 table
Intrinsic Random Functions and Universal Kriging on the Circle
Intrinsic random functions (IRF) provide a versatile approach when the
assumption of second-order stationarity is not met. Here, we develop the IRF
theory on the circle with its universal kriging application. Unlike IRF in
Euclidean spaces, where differential operations are used to achieve
stationarity, our result shows that low-frequency truncation of the Fourier
series representation of the IRF is required for such processes on the circle.
All of these features and developments are presented through the theory of
reproducing kernel Hilbert space. In addition, the connection between kriging
and splines is also established, demonstrating their equivalence on the circle.Comment: 14 pages, initial versio
Magnetic dipolar interaction between correlated triplets created by singlet fission in tetracene crystals
Singlet fission (SF) can potentially break the Shockley-Queisser efficiency
limit in single-junction solar cells by splitting one photo-excited singlet
exciton (S1) into two triplets (2T1) in organic semiconductors. A dark
multi-exciton (ME) state has been proposed as the intermediate connecting S1 to
2T1. However, the exact nature of this ME state, especially how the
doubly-excited triplets interact, remains elusive. Here, we report a
quantitative study on the magnetic dipolar interaction between SF-induced
correlated triplets in tetracene crystals by monitoring quantum beats relevant
to the ME sublevels at room temperature. The resonances of ME sublevels
approached by tuning an external magnetic field are observed to be avoided,
which agrees well with the theoretical predictions considering a magnetic
dipolar interaction of ~ 0.008 GHz. Our work paves a way to quantify the
magnetic dipolar interaction in organic materials and marks an important step
towards understanding the underlying physics of the ME state
Intrinsic Random Functions on the sphere
Spatial stochastic processes that are modeled over the entire Earth's surface
require statistical approaches that directly consider the spherical domain.
Here, we extend the notion of intrinsic random functions (IRF) to model
non-stationary processes on the sphere and show that low-frequency truncation
plays an essential role. Then, the universal kriging formula on the sphere is
derived. We show that all of these developments can be presented through the
theory of reproducing kernel Hilbert space. In addition, the link between
universal kriging and splines is carefully investigated, whereby we show that
thin-plate splines are non-applicable for surface fitting on the sphere
Active Subspace of Neural Networks: Structural Analysis and Universal Attacks
Active subspace is a model reduction method widely used in the uncertainty
quantification community. In this paper, we propose analyzing the internal
structure and vulnerability and deep neural networks using active subspace.
Firstly, we employ the active subspace to measure the number of "active
neurons" at each intermediate layer and reduce the number of neurons from
several thousands to several dozens. This motivates us to change the network
structure and to develop a new and more compact network, referred to as
{ASNet}, that has significantly fewer model parameters. Secondly, we propose
analyzing the vulnerability of a neural network using active subspace and
finding an additive universal adversarial attack vector that can misclassify a
dataset with a high probability. Our experiments on CIFAR-10 show that ASNet
can achieve 23.98 parameter and 7.30 flops reduction. The
universal active subspace attack vector can achieve around 20% higher attack
ratio compared with the existing approach in all of our numerical experiments.
The PyTorch codes for this paper are available online
Stochastic Collocation with Non-Gaussian Correlated Parameters via a New Quadrature Rule
This paper generalizes stochastic collocation methods to handle correlated
non-Gaussian random parameters. The key challenge is to perform a multivariate
numerical integration in a correlated parameter space when computing the
coefficient of each basis function via a projection step. We propose an
optimization model and a block coordinate descent solver to compute the
required quadrature samples. Our method is verified with a CMOS ring oscillator
and an optical ring resonator, showing 3000x speedup over Monte Carlo.Comment: 3 pages, 5 figure, EPEPS 201
Holonomic quantum computation in the ultrastrong-coupling regime of circuit QED
We present an experimentally feasible scheme to implement holonomic quantum
computation in the ultrastrong-coupling regime of light-matter interaction. The
large anharmonicity and the Z2 symmetry of the quantum Rabi model allow us to
build an effective three-level {\Lambda}-structured artificial atom for quantum
computation. The proposed physical implementation includes two gradiometric
flux qubits and two microwave resonators where single-qubit gates are realized
by a two-tone driving on one physical qubit, and a two-qubit gate is achieved
with a time-dependent coupling between the field quadratures of both
resonators. Our work paves the way for scalable holonomic quantum computation
in ultrastrongly coupled systems.Comment: 9 pages, 6 figure
Tensor Methods for Generating Compact Uncertainty Quantification and Deep Learning Models
Tensor methods have become a promising tool to solve high-dimensional
problems in the big data era. By exploiting possible low-rank tensor
factorization, many high-dimensional model-based or data-driven problems can be
solved to facilitate decision making or machine learning. In this paper, we
summarize the recent applications of tensor computation in obtaining compact
models for uncertainty quantification and deep learning. In uncertainty
analysis where obtaining data samples is expensive, we show how tensor methods
can significantly reduce the simulation or measurement cost. To enable the
deployment of deep learning on resource-constrained hardware platforms, tensor
methods can be used to significantly compress an over-parameterized neural
network model or directly train a small-size model from scratch via
optimization or statistical techniques. Recent Bayesian tensorized neural
networks can automatically determine their tensor ranks in the training
process
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