Conventional Monte Carlo Sampling Research Articles

Climate-informed flood risk mapping using a GAN-based approach (ExGAN)

This study develops a class of robust models for flood risk mapping in highly vulnerable regions by focusing on accurately depicting extreme precipitation patterns aligned with regional climates. By implementing sophisticated hydrodynamics modeling and advanced probabilistic approaches, the present work underscores the efficacy of physical-based methodologies in the flood risk assessment. We propose a machine learning based ExGAN to address the challenge of synthesizing extreme precipitation scenarios which faithfully capture the nuances of local climatology. It is expected that through refined temporal disaggregation, the ExGAN approach exhibits exceptional proficiency in replicating a diverse spectrum of extreme precipitation patterns specific to the vulnerable region under scrutiny. Therefore, using these synthesized scenarios as inputs in a meticulously calibrated hydrological model would enable a comprehensive and detailed flood risk mapping exercise. To demonstrate the robustness of the developed mode, we perform a rigorous testing and validation within the highly susceptible Martil river basin, situated in the northern Mediterranean region of Morocco. The obtained results confirm that extending return periods would provide invaluable insights into the expanding geographical expanse of at-risk areas, clarifying the evolving landscape of vulnerability rather than merely amplifying inherent risk levels. Comparisons against the conventional Monte-Carlo sampling are also carried out in this study and the obtained results highlight significant overestimations within the latter, emphasizing the imperative need to account for diverse uncertainties beyond the basic sampling strategies within the realm of hydrodynamic modeling.

Directed walk in probability space that locates mean field solutions to spin models.

Despite their formal simplicity, most lattice spin models cannot be easily solved, even under the simplifying assumptions of mean field theory. In this paper, we present a method for generating mean field solutions to classical continuous spins. We focus our attention on systems with nonlocal interactions and nonperiodic boundaries, which require careful handling with existing approaches, such as Monte Carlo sampling. Our approach utilizes functional optimization to derive a closed-form optimality condition and arrive at self-consistent mean field equations. We show that this approach significantly outperforms conventional Monte Carlo sampling in convergence speed and accuracy. To convey the general concept behind the approach, we first demonstrate its application to a simple system: a finite one-dimensional dipolar chain in an external electric field. We then describe how the approach naturally extends to more complicated spin systems and to continuum field theories. Furthermore, we numerically illustrate the efficacy of our approach by highlighting its utility on nonperiodic spin models of various dimensionality.

Dimension-reduction of stochastic wave forces and probability density evolution analysis of wave-excited pile foundation

This paper discusses the reasonable description and simulation of the continuous stochastic wave force field at probabilistic level. Firstly, in order to overcome the challenge of high-dimensional random variables inherent in the conventional Monte Carlo sampling (MCS), the dimension-reduction (DR) simulations of stochastic processes are addressed based on both the non-deterministic spectral amplitude (NSA) method and the deterministic spectral amplitude (DSA) method. In the proposed method, merely one or two elementary random variables are required to describe the continuous stochastic wave force field at the level of probability density. Simultaneously, the simulation efficiency of the proposed scheme is significantly enhanced by employing the Fast Fourier Transform (FFT) algorithm. In addition, the DR simulations for continuous stochastic wave force field are conducted in accordance with the linear Morison's equation (LME) and the nonlinear Morison's equation (NLME). Finally, the stochastic wave force field acting on a single pile foundation is generated by the proposed method, followed by the refined linear dynamic analysis and reliability assessment of the employed single pile foundation combining the probability density evolution method (PDEM). The effectiveness, accuracy and engineering practicability of the DR methods are sufficiently illustrated by comparison with the MCS methods thereafter. The analysis results also show that the DR methods are of significance robustness in reliability assessment of offshore engineering structures.

Bayesian Approach to Probabilistic Design Space Characterization: A Nested Sampling Strategy

Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space characterization, which determine a feasibility probability that can be used as a measure of reliability and risk by the practitioner. An adaptation of nested sampling---a Monte Carlo technique introduced to compute Bayesian evidence---is presented. The nested sampling algorithm maintains a given set of live points through regions with increasing probability feasibility until reaching a desired reliability level. It furthermore leverages efficient strategies from Bayesian statistics for generating replacement proposals during the search. Features and advantages of this algorithm are demonstrated by means of a simple numerical example and two industrial case studies. It is shown that nested sampling can outperform conventional Monte Carlo sampling and be competitive with flexibility-based optimization techniques in low-dimensional design space problems. Practical aspects of exploiting the sampled design space to reconstruct a feasibility probability map using machine learning techniques are also discussed and illustrated. Finally, the effectiveness of nested sampling is demonstrated on a higher-dimensional problem, in the presence of a complex dynamic model and significant model uncertainty.

An adaptive Kriging surrogate method for efficient uncertainty quantification with an application to geological carbon sequestration modeling

In numerical modeling of geological carbon sequestration (GCS), uncertainty quantification (UQ) is usually needed to evaluate the impact of uncertain model parameters on model predictions caused by limited measurements and incomplete knowledge of the parameters. However, UQ for GCS is computationally expensive due to the large ensemble of complex and lengthy model simulations. In this study, we propose an adaptive Kriging method to build a fast-to-evaluate surrogate of the GCS model to alleviate the heavy computational burden. The surrogate model is efficiently generated using a Taylor expansion-based adaptive experimental design algorithm that combines a distance-based exploration criterion and an exploitation criterion to adaptively search for informative training samples. In addition, we analyze the uncertainty brought by substituting the surrogate for the actual simulation model and explore its influence on UQ results. Our method is demonstrated in a synthetic GCS model and its performance is evaluated in comparison with the conventional Monte Carlo sampling. Results indicate that our method can greatly improve the computational efficiency in UQ and provide an effective and reliable UQ solution with the consideration of surrogate uncertainty.

The Reliability Evaluation Method of Generation System Based on the Importance Sampling Method and States Clustering

Abstract: To improve the reliability evaluation efficiency of large scale power system, an efficient reliability evaluation method of generation system is proposed in this paper. It can improve the calculation efficiency both in the sampling method and states evaluation. Firstly, the importance sampling method is used to replace the conventional Monte Carlo sampling method, which can accelerate the convergence speed of iteration calculation. Secondly, the states clustering method is proposed to get several typical generating states to replace all sampling states, which can improve the calculation speed. Finally, the simulations based on the IEEE RTS-79 generating system and the actual power system are carried out, and the efficiency and accuracy of this evaluation method in this paper are verified.

Simulation study of the atomic resolution secondary electron imaging

It has been experimentally achieved atomic resolution imaging by using secondary electron (SE) signals in a scanning transmission electron microscope with aberration correction. The underlying physical mechanism needs to be understood and has attracted considerable theoretical interest. Several recent calculations taking account of the inner‐shell ionization for high‐energy SE production have not included the cascade production of low‐energy SE signals which was believed to destroy the local information in SE imaging. In this work, we have developed a new theoretical method, a quantum Monte Carlo simulation, to calculate atomic resolution SE image by including every physical factor in SE generation, transportation and emission for a crystalline solid. This quantum Monte Carlo simulation method combines the Bohmian quantum trajectory method for treating electron elastic scattering and diffraction in a crystal with a conventional Monte Carlo sampling of inelastic scattering events along quantum trajectory paths. Simulation of atomic resolution SE image for atom columns in a copper crystal is performed. The contribution of the inner‐shell excitation to atomic resolution SE imaging is studied. Copyright © 2014 John Wiley & Sons, Ltd.

Efficient uncertainty quantification of dynamical systems with local nonlinearities and uncertainties

Idealized modeling of most engineering structures yields linear mathematical models, i.e., linear ordinary or partial differential equations. However, features like nonlinear dampers and/or springs can render nonlinear an otherwise linear model. Often, the connectivity of these nonlinear elements is confined to only a few degrees-of-freedom (DOFs) of the structure. In such cases, treating the entire structure as nonlinear results in very computationally expensive solutions. Moreover, if system parameters are uncertain, their stochastic nature can render the analysis even more computationally costly. This paper presents an approach for computing the response of such systems in a very efficient manner. The proposed solution procedure first segregates the DOFs appearing in the nonlinear and/or stochastic terms from those DOFs that involve only linear deterministic operations. Second, the responses of nonlinear/stochastic terms are determined using a non-standard form of a nonlinear Volterra integral equation (NVIE). Finally, the responses of the remaining DOFs are computed through a convolution approach using the fast Fourier transform to further increase the computational efficiency. Three examples are presented to demonstrate the efficacy and accuracy of the proposed method. It is shown that, even for moderately sized systems (∼1000 DOFs), the proposed method is about three orders of magnitude faster than a conventional Monte Carlo sampling method ( i.e., solving the system of ODEs repeatedly).

Decision-Theoretic Sensitivity Analysis for Complex Computer Models

When using a computer model to inform a decision, it is important to investigate any uncertainty in the model and determine how that uncertainty may impact on the decision. In probabilistic sensitivity analysis, model users can investigate how various uncertain model inputs contribute to the uncertainty in the model output. However, much of the literature focuses only on output uncertainty as measured by variance; the decision problem itself often is ignored, even though uncertainty as measured by variance may not equate to uncertainty about the optimum decision. Consequently, traditional variance-based measures of input parameter importance may not correctly describe the importance of each input. We review a decision-theoretic framework for conducting sensitivity analysis that addresses this problem. Because computation of these decision-theoretic measures can be impractical for complex computer models, we provide efficient computational tools using Gaussian processes. We give an illustration in the field of medical decision making, and compare the Gaussian process approach with conventional Monte Carlo sampling.

Fast Permutation Tests that Maximize Power Under Conventional Monte Carlo Sampling for Pairwise and Multiple Comparisons

While the distribution-free nature of permutation tests makes them the most appropriate method for hypothesis testing under a wide range of conditions, their computational demands can be runtime prohibitive, especially if samples are not very small and/or many tests must be conducted (e.g. all pairwise comparisons). This paper presents statistical code that performs continuous-data permutation tests under such conditions very quickly – often more than an order of magnitude faster than widely available commercial alternatives when many tests must be performed and some of the sample pairs contain a large sample. Also presented is an efficient method for obtaining a set of permutation samples containing no duplicates, thus maximizing the power of a pairwise permutation test under a conventional Monte Carlo approach with negligible runtime cost (well under 1% when runtimes are greatest). For multiple comparisons, the code is structured to provide an additional speed premium, making permutation-style p-value adjustments practical to use with permutation test p-values (although for relatively few comparisons at a time). “No-replacement” sampling also provides a power gain for such multiple comparisons, with similarly negligible runtime cost.

Importance Sampling for Estimating Exact Probabilities in Permutational Inference

Abstract This article discusses importance sampling as an alternative to conventional Monte Carlo sampling for estimating exact significance levels in a broad class of two-sample tests, including all of the linear rank tests (with or without censoring), homogeneity tests based on the chi-squared, hypergeometric, and likelihood ratio statistics, the Mantel—Haenszel trend test, and Zelen's test for a common odds ratio in several 2 × 2 contingency tables. Inference is based on randomly selecting 2 × k contingency tables from a reference set of all such tables with fixed marginals. Through a network algorithm, the tables are selected in proportion to their importance for reducing the variance of the estimated Monte Carlo p-value. Spectacular gains, up to four orders of magnitude, are achieved relative to conventional Monte Carlo sampling. The technique is illustrated on four real data sets.