Unbiased Monte Carlo cluster updates with autoregressive neural networks

Efficient sampling of complex high-dimensional probability distributions is a central task in computational science. Machine learning methods like autoregressive neural networks, used with Markov chain Monte Carlo sampling, provide good approximations to such distributions but suffer from either intrinsic bias or high variance. In this Letter, we propose a way to make this approximation unbiased and with low variance. Our method uses physical symmetries and variable-size cluster updates which utilize the structure of autoregressive factorization. We test our method for first- and second-order phase transitions of classical spin systems, showing its viability for critical systems and in the presence of metastable states.

Mixture models for multivariate extremes

Marc-Olivier Boldi

This thesis is a contribution to multivariate extreme value statistics. The tail of a multivariate distribution function is characterized by its spectral distribution, for which we propose a new semi-parametric model based on mixtures of Dirichlet distributions. To estimate the components of this model, reversible jump Monte Carlo Markov chain and EM algorithms are developed. Their performances are illustrated on real and simulated data, obtained using new representations of the extremal logistic and Dirichlet models. In parallel with the estimation of the spectral distribution, extreme value statistic machinery requires the selection of a threshold in order to classify data as extreme or not. This selection is achieved by a new method based on heuristic arguments. It allows a selection independent of the dimension of the data. Its performance is illustrated on real and simulated data. Primal scientific interests behind a multivariate extreme value analysis reside in the estimation of quantiles of rare events and in the exploration of the dependence structure, for which the estimation of the spectral measure is a means rather than an end. These two issues are addressed. For the first, a Monte Carlo method is developed based on simulation of extremes. It is compared with classical and new methods of the literature. For the second one, an original conditional dependence analysis is proposed, which enlightens various aspects of the dependence structure of the data. Examples using real data sets are given. In the last part, the semi-parametric model and the presented methods are extended to spatial extremes. It is made possible by considering the spectral distribution as the distribution of a random probability, an original viewpoint adopted throughout this thesis. Classical multivariate extremes are extended to extremes of random measures. The application is illustrated on rainfall data in China.

EPFL2004

Monte Carlo study of the critical properties of the three-dimensional 120 degrees model

Sandro Wenzel

We report on large scale finite-temperature Monte Carlo simulations of the classical 120 degrees or e(g) orbital-only model on the simple cubic lattice in three dimensions with a focus towards its critical properties. This model displays a continuous phase transition to an orbitally ordered phase. While the correlation length exponent nu approximate to 0.665 is close to the 3D XY value, the exponent eta approximate to 0.15 differs substantially from O(N) values. We also introduce a discrete variant of the e(g) model, called the e(g)-clock model, which is found to display the same set of exponents. Further, an emergent U( 1) symmetry is found at the critical point T-c, which persists for T < T-c below a crossover length scaling as Lambda similar to xi(a), with an unusually small a approximate to 1.3.

2011

Updated braking forces for the assessment of road bridges

João Miguel De Oliveira Durães Alves Martins

Safety assessments of road bridges to braking events combine the braking force, acting along the longitudinal axis of the deck, with a vertical load that accounts for the vertical component of the traffic action. In modern design standards the vertical load models result from probabilistic calibration procedures targeting predefined return periods. On the contrary, the braking force was derived from a deterministic characterization of the vehicle configurations and of the braking process. Therefore, the return period of the braking force is unclear and may not be consistent with that of the vertical load model. Significant deviations from the target return period might lead to either uneconomical decisions, e.g. uncalled-for retrofitting interventions, or to inaccurate structural safety verifications. This thesis presents an original stochastic model to compute site-specific values of the braking force as a function of the return period. The developed stochastic model takes into account the length of the bridge deck and its dynamic properties for vibrations in the longitudinal direction, as well as different sources of randomness related to braking events, all of which comply with real-world measurements, including: - vehicle configurations, resorting to a time-history of crossing vehicles; - driver response times, randomly generated from probability distributions defined in the scope of this project; - deceleration profiles of the vehicles, resampled from catalogues of realistic deceleration profiles. The stochastic model uses Monte Carlo simulation of braking events and computes the maximum of the dynamic response of the bridge to each event. The computed maxima are collected in an empirical distribution function of the braking force. In the end, the model returns the quantile of this distribution that is suitable for safety assessments. This value of braking force is specific to the bridge given properties, to the traffic characteristics, and to the target return period. An additional novelty of this research work is the estimation of a rate of occurrence on motorways of braking events per vehicle-distance travelled. This parameter enables the estimation of the period of time covered by the simulations of braking events as a function of traffic flow and of the total number of braking events simulated. This step is fundamental to determine the value of the braking force that has a given return period. The braking forces returned by the stochastic model show significant dependence on the bridge length, the natural vibration period of the deck in the longitudinal direction, and the number of directions of traffic on the deck. On the contrary, damping ratio, traffic on the fast-lane or on weekends, and an augmentation of traffic in 20% show no substantial influence on the braking force. Moreover, the two motorway locations considered as sources of traffic data, Denges and Monte Ceneri, both in Switzerland, yielded braking forces with similar magnitudes, despite the significant differences in traffic characteristics. Finally, the results compiled served to calibrate an updated braking force that depends explicitly on the parameters found relevant, as well as on the return period so that it can be adopted by different standards even if they enforce different safety targets. This updated expression evidences that the braking forces of current codes tend to be conservative and, hence, can be improved based on the findings of this project.

EPFL2016

Updated braking forces for the assessment of road bridges

João Miguel De Oliveira Durães Alves Martins

EPFL2016