Jinglai Li

An efficient surrogate-based method for computing rare failure probability

In this paper, we present an efficient numerical method for evaluating rare failure probability. The method is based on a recently developed surrogate-based method from Li and Xiu [J. Li, D. Xiu, Evaluation of failure probability via surrogate models, J. Comput. Phys. 229 (2010) 8966-8980] for failure probability computation. The method by Li and Xiu is of hybrid nature, in the sense that samples of both the surrogate model and the true physical model are used, and its efficiency gain relies on using only very few samples of the true model. Here we extend the capability of the method to rare probability computation by using the idea of importance sampling (IS). In particular, we employ cross-entropy (CE) method, which is an effective method to determine the biasing distribution in IS. We demonstrate that, by combining with the CE method, a surrogate-based IS algorithm can be constructed and is highly efficient for rare failure probability computation-it incurs much reduced simulation efforts compared to the traditional CE-IS method. In many cases, the new method is capable of capturing failure probability as small as 10^-^1^2~10^-^6 with only several hundreds samples.

Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems

The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or forward model. When these evaluations are computationally intensive, approximations of the forward model are essential to accelerating sample-based inference. Yet the construction of globally accurate approximations for nonlinear forward models can be computationally prohibitive and in fact unnecessary, as the posterior distribution typically concentrates on a small fraction of the support of the prior distribution. We present a new approach that uses stochastic optimization to construct polynomial approximations over a sequence of distributions adaptively determined from the data, eventually concentrating on the posterior distribution. The approach yields substantial gains in efficiency and accuracy over prior-based surrogates, as demonstrated via application to inverse ...

New chiral phases of superfluid 3He stabilized by anisotropic silica aerogel

A rich variety of Fermi systems condense by forming bound pairs, including high-temperature and heavy-fermion superconductors, Sr_2RuO_4 (ref. 3), cold atomic gases and superfluid ^3He (ref. 5). Some of these form exotic quantum states with non-zero orbital angular momentum. We have discovered, in the case of ^3He, that anisotropic disorder, engineered from highly porous silica aerogel, stabilizes a chiral superfluid state that otherwise would not exist. Furthermore, we find that the chiral axis of this state can be uniquely oriented with the application of a magnetic field perpendicular to the aerogel anisotropy axis. At sufficiently low temperature we observe a sharp transition from a uniformly oriented chiral state to a disordered structure consistent with locally ordered domains, contrary to expectations for a superfluid glass phase.

Identification of superfluid phases of He3 in uniformly isotropic 98.2% aerogel

Superfluid ^{3}He confined to high porosity silica aerogel is the paradigm system for understanding impurity effects in unconventional superconductors. However, a crucial first step has been elusive: exact identification of the microscopic states of the superfluid in the presence of quenched disorder. Using a new class of highly uniform aerogel materials, we report pulsed nuclear magnetic resonance experiments that demonstrate definitively that the two observed superfluid states in aerogel are impure versions of the isotropic and axial p-wave states. The theoretically predicted destruction of long-range orbital order (Larkin-Imry-Ma effect) in the impure axial state is not observed.

Anisotropic hinge model for polarization-mode dispersion in installed fibers.

We discuss a generalized waveplate hinge model to characterize anisotropic effects associated with the hinge model of polarization-mode dispersion in installed systems. In this model, the action of the hinges is a random time-dependent rotation about a fixed axis. We obtain the probability density function of the differential group delay and the outage probability of an individual wavelength band using a combination of importance sampling and the cross-entropy method, and we then compute the noncompliant capacity ratio by averaging over wavelength bands. The results show that there are significant differences between the outage statistics predicted by isotropic and anisotropic hinge models.

Outage Statistics in a Waveplate Hinge Model of Polarization-Mode Dispersion

The properties of the waveplate hinge model of polarization-mode dispersion (PMD) are studied in detail, and its statistics are compared to those of the traditional hinge model based on the assumption of an isotropic output after each hinge. In particular, the probability density function of the differential group delay for each individual frequency band is computed using a combination of importance sampling and the cross-entropy method. The outage probability is then obtained combining these results with the outage map method, allowing the fraction of bands with unacceptable outage probabilities to be quantified by the noncompliant capacity ratio (NCR). The results show that the traditional hinge model significantly overestimates the NCR compared to the waveplate hinge model.

Gaussian process surrogates for failure detection

An important task of uncertainty quantification is to identify the probability of undesired events, in particular, system failures, caused by various sources of uncertainties. In this work we consider the construction of Gaussian process surrogates for failure detection and failure probability estimation. In particular, we consider the situation that the underlying computer models are extremely expensive, and in this setting, determining the sampling points in the state space is of essential importance. We formulate the problem as an optimal experimental design for Bayesian inferences of the limit state (i.e., the failure boundary) and propose an efficient numerical scheme to solve the resulting optimization problem. In particular, the proposed limit-state inference method is capable of determining multiple sampling points at a time, and thus it is well suited for problems where multiple computer simulations can be performed in parallel. The accuracy and performance of the proposed method is demonstrated by both academic and practical examples.

The superfluid glass phase of 3He-A

Confined within a porous aerogel, superfluid 3He loses its long-range order owing to random microscopic disorder, and becomes a glassy superfluid. Intriguingly, this effect can be switched off and the superfluidity restored.

Zeeman Splitting and Nonlinear Field-Dependence in Superfluid 3He

We have studied the acoustic Faraday effect in superfluid 3He up to significantly larger magnetic fields than in previous experiments achieving rotations of the polarization of transverse sound as large as 1710°. We report nonlinear field effects, and use the linear results to determine the Zeeman splitting of the imaginary squashing mode (ISQ) frequency in 3He-B.

Noncompliant Capacity Ratio for Systems With an Arbitrary Number of Polarization Hinges

We study the statistics of transmission impairments due to polarization-mode dispersion in systems characterized by the hinge model. In particular, we validate the use of a computationally efficient expression for the probability density function (PDF) of the differential group delay (DGD) of systems with an arbitrary number of hinges. We then combine this expression for the PDF of the DGD with the outage map approach to compute outage probabilities and noncompliant capacity ratios for transmission links with varying numbers of sections (from 4 up to 20), each for several values of mean DGD and different system parameters.