Estimation of Uncertainty Change of Reliability in Adaptive Sampling Under Prediction Uncertainty of Gaussian Process

2019 ◽  
Author(s):  
Sangjune Bae ◽  
Nam H. Kim
Keyword(s):  
Gaussian Process ◽  
Adaptive Sampling ◽  
Computational Cost ◽  
Probability Of Failure ◽  
Computational Burden ◽  
Single Loop ◽  
Prediction Uncertainty ◽  
Novel Approach ◽  
Estimation Of Variance ◽  
Estimation Of Uncertainty

Abstract A novel approach is introduced to estimate the change in the variance of the probability of failure by adding a sample to the Gaussian process (GP) in a conservative manner. Uncertainty in probability stems from prediction uncertainty and GP is used to represent the uncertainty. In the estimation of variance, a single-loop Monte Carlo Simulation (MCS) alleviates the computational burden. The result shows that the proposed methodology well predicts the change by a sample, maintaining the conservativeness by ignoring correlation in GP, yet the computational cost is at the same level as single-loop MCS.

A Generalized “Max-Min” Sample for Reliability Assessment With Dependent Variables

2014 ◽  
Author(s):  
Sylvain Lacaze ◽  
Samy Missoum
Keyword(s):  
Probability Density ◽  
Adaptive Sampling ◽  
Reliability Assessment ◽  
Joint Probability ◽  
Probability Of Failure ◽  
Sampling Scheme ◽  
Support Vector ◽  
Space Design ◽  
Novel Approach ◽  
Dependent Variables

This paper introduces a novel approach for reliability assessment with dependent variables. In this work, the boundary of the failure domain, for a computational problem with expensive function evaluations, is approximated using a Support Vector Machine and an adaptive sampling scheme. The approximation is sequentially refined using a new adaptive sampling scheme referred to as generalized “max-min”. This technique efficiently targets high probability density regions of the random space. This is achieved by modifying an adaptive sampling scheme originally tailored for deterministic spaces (Explicit Space Design Decomposition). In particular, the approach can handle any joint probability density function, even if the variables are dependent. In the latter case, the joint distribution might be obtained from copula. In addition, uncertainty on the probability of failure estimate are estimated using bootstrapping. A bootstrapped coefficient of variation of the probability of failure is used as an estimate of the true error to determine convergence. The proposed method is then applied to analytical examples and a beam bending reliability assessment using copulas.

Estimating Effect of Additional Sample on Uncertainty Reduction in Reliability Analysis Using Gaussian Process

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Sangjune Bae ◽  
Chanyoung Park ◽  
Nam H. Kim
Keyword(s):  
Gaussian Process ◽  
Reliability Analysis ◽  
Adaptive Sampling ◽  
Probability Of Failure ◽  
Sampling Uncertainty ◽  
Sampling Schemes ◽  
Probabilistic Classification ◽  
Prediction Variance ◽  
Additional Sample ◽  
Estimate Uncertainty

Abstract An approach is proposed to quantify the uncertainty in probability of failure using a Gaussian process (GP) and to estimate uncertainty change before actually adding samples to GP. The approach estimates the coefficient of variation (CV) of failure probability due to prediction variance of GP. The CV is estimated using single-loop Monte Carlo simulation (MCS), which integrates the probabilistic classification function while replacing expensive multi-loop MCS. The methodology ensures a conservative estimate of CV, in order to compensate for sampling uncertainty in MCS. Uncertainty change is estimated by adding a virtual sample from the current GP and calculating the change in CV, which is called expected uncertainty change (EUC). The proposed method can help adaptive sampling schemes to determine when to stop before adding a sample. In numerical examples, the proposed method is used in conjunction with the efficient local reliability analysis to calculate the reliability of analytical function as well as the battery drop test simulation. It is shown that the EUC converges to the true uncertainty change as the model becomes accurate.

Nanosecond Photodynamics Simulations of a Cis-Trans Isomerization Are Enabled by Machine Learning

2020 ◽  
Author(s):  
Jingbai Li ◽  
Patrick Reiser ◽  
André Eberhard ◽  
Pascal Friederich ◽  
Steven Lopez
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Excited State ◽  
Adaptive Sampling ◽  
Computational Cost ◽  
Ground Truth ◽  
Absolute Error ◽  
Photochemical Reactions ◽  
Computational Techniques ◽  
Full Potential

<p>Photochemical reactions are being increasingly used to construct complex molecular architectures with mild and straightforward reaction conditions. Computational techniques are increasingly important to understand the reactivities and chemoselectivities of photochemical isomerization reactions because they offer molecular bonding information along the excited-state(s) of photodynamics. These photodynamics simulations are resource-intensive and are typically limited to 1–10 picoseconds and 1,000 trajectories due to high computational cost. Most organic photochemical reactions have excited-state lifetimes exceeding 1 picosecond, which places them outside possible computational studies. Westermeyr <i>et al.</i> demonstrated that a machine learning approach could significantly lengthen photodynamics simulation times for a model system, methylenimmonium cation (CH<sub>2</sub>NH<sub>2</sub><sup>+</sup>).</p><p>We have developed a Python-based code, Python Rapid Artificial Intelligence <i>Ab Initio</i> Molecular Dynamics (PyRAI<sup>2</sup>MD), to accomplish the unprecedented 10 ns <i>cis-trans</i> photodynamics of <i>trans</i>-hexafluoro-2-butene (CF<sub>3</sub>–CH=CH–CF<sub>3</sub>) in 3.5 days. The same simulation would take approximately 58 years with ground-truth multiconfigurational dynamics. We proposed an innovative scheme combining Wigner sampling, geometrical interpolations, and short-time quantum chemical trajectories to effectively sample the initial data, facilitating the adaptive sampling to generate an informative and data-efficient training set with 6,232 data points. Our neural networks achieved chemical accuracy (mean absolute error of 0.032 eV). Our 4,814 trajectories reproduced the S<sub>1</sub> half-life (60.5 fs), the photochemical product ratio (<i>trans</i>: <i>cis</i> = 2.3: 1), and autonomously discovered a pathway towards a carbene. The neural networks have also shown the capability of generalizing the full potential energy surface with chemically incomplete data (<i>trans</i> → <i>cis</i> but not <i>cis</i> → <i>trans</i> pathways) that may offer future automated photochemical reaction discoveries.</p>

Structured Gaussian Process Regression of Music Mood

2020 ◽  
Vol 176 (2) ◽  
pp. 183-203
Author(s):  
Santosh Chapaneri ◽  
Deepak Jayaswal
Keyword(s):  
Gaussian Process ◽  
Computational Cost ◽  
Gaussian Process Regression ◽  
Gaussian Mixture ◽  
Feature Representation ◽  
Affective Content ◽  
Variational Bayesian Inference ◽  
Benchmark Datasets ◽  
Valence And Arousal ◽  
Structured Regression

Modeling the music mood has wide applications in music categorization, retrieval, and recommendation systems; however, it is challenging to computationally model the affective content of music due to its subjective nature. In this work, a structured regression framework is proposed to model the valence and arousal mood dimensions of music using a single regression model at a linear computational cost. To tackle the subjectivity phenomena, a confidence-interval based estimated consensus is computed by modeling the behavior of various annotators (e.g. biased, adversarial) and is shown to perform better than using the average annotation values. For a compact feature representation of music clips, variational Bayesian inference is used to learn the Gaussian mixture model representation of acoustic features and chord-related features are used to improve the valence estimation by probing the chord progressions between chroma frames. The dimensionality of features is further reduced using an adaptive version of kernel PCA. Using an efficient implementation of twin Gaussian process for structured regression, the proposed work achieves a significant improvement in R2 for arousal and valence dimensions relative to state-of-the-art techniques on two benchmark datasets for music mood estimation.

Two-dimensional Bayesian inversion of magnetotelluric data using trans-dimensional Gaussian processes

2021 ◽  
Author(s):  
Daniel Blatter ◽  
Anandaroop Ray ◽  
Kerry Key
Keyword(s):  
Gaussian Process ◽  
Process Model ◽  
Field Data ◽  
Probability Distributions ◽  
Bulk Composition ◽  
Computational Cost ◽  
Model Space ◽  
Bayesian Inversion ◽  
Adaptive Finite Element ◽  
Magnetotelluric Data

Summary Bayesian inversion of electromagnetic data produces crucial uncertainty information on inferred subsurface resistivity. Due to their high computational cost, however, Bayesian inverse methods have largely been restricted to computationally expedient 1D resistivity models. In this study, we successfully demonstrate, for the first time, a fully 2D, trans-dimensional Bayesian inversion of magnetotelluric data. We render this problem tractable from a computational standpoint by using a stochastic interpolation algorithm known as a Gaussian process to achieve a parsimonious parametrization of the model vis-a-vis the dense parameter grids used in numerical forward modeling codes. The Gaussian process links a trans-dimensional, parallel tempered Markov chain Monte Carlo sampler, which explores the parsimonious model space, to MARE2DEM, an adaptive finite element forward solver. MARE2DEM computes the model response using a dense parameter mesh with resistivity assigned via the Gaussian process model. We demonstrate the new trans-dimensional Gaussian process sampler by inverting both synthetic and field magnetotelluric data for 2D models of electrical resistivity, with the field data example converging within 10 days on 148 cores, a non-negligible but tractable computational cost. For a field data inversion, our algorithm achieves a parameter reduction of over 32x compared to the fixed parameter grid used for the MARE2DEM regularized inversion. Resistivity probability distributions computed from the ensemble of models produced by the inversion yield credible intervals and interquartile plots that quantitatively show the non-linear 2D uncertainty in model structure. This uncertainty could then be propagated to other physical properties that impact resistivity including bulk composition, porosity and pore-fluid content.

Adaptive sampling of potential-field data: A direct approach to compressive inversion

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. IM1-IM9 ◽  
Author(s):  
Nathan Leon Foks ◽  
Richard Krahenbuhl ◽  
Yaoguo Li
Keyword(s):  
Potential Field ◽  
Adaptive Sampling ◽  
Field Data ◽  
Computational Cost ◽  
Large Field ◽  
Magnetic Data ◽  
Data Sampling ◽  
Data Types ◽  
Data Set ◽  
Potential Field Data

Compressive inversion uses computational algorithms that decrease the time and storage needs of a traditional inverse problem. Most compression approaches focus on the model domain, and very few, other than traditional downsampling focus on the data domain for potential-field applications. To further the compression in the data domain, a direct and practical approach to the adaptive downsampling of potential-field data for large inversion problems has been developed. The approach is formulated to significantly reduce the quantity of data in relatively smooth or quiet regions of the data set, while preserving the signal anomalies that contain the relevant target information. Two major benefits arise from this form of compressive inversion. First, because the approach compresses the problem in the data domain, it can be applied immediately without the addition of, or modification to, existing inversion software. Second, as most industry software use some form of model or sensitivity compression, the addition of this adaptive data sampling creates a complete compressive inversion methodology whereby the reduction of computational cost is achieved simultaneously in the model and data domains. We applied the method to a synthetic magnetic data set and two large field magnetic data sets; however, the method is also applicable to other data types. Our results showed that the relevant model information is maintained after inversion despite using 1%–5% of the data.

scholarly journals A NOTE ON PHASING LONG GENOMIC REGIONS USING LOCAL HAPLOTYPE PREDICTIONS

2006 ◽  
Vol 04 (03) ◽  
pp. 639-647 ◽  
Author(s):  
ELEAZAR ESKIN ◽  
RODED SHARAN ◽  
ERAN HALPERIN
Keyword(s):  
Large Scale ◽  
Computational Cost ◽  
Nucleotide Polymorphisms ◽  
Single Nucleotide ◽  
Novel Approach ◽  
Maximum Likelihood Criterion ◽  
The Common ◽  
Genomic Regions ◽  
High Computational Cost ◽  
Combining Information

The common approaches for haplotype inference from genotype data are targeted toward phasing short genomic regions. Longer regions are often tackled in a heuristic manner, due to the high computational cost. Here, we describe a novel approach for phasing genotypes over long regions, which is based on combining information from local predictions on short, overlapping regions. The phasing is done in a way, which maximizes a natural maximum likelihood criterion. Among other things, this criterion takes into account the physical length between neighboring single nucleotide polymorphisms. The approach is very efficient and is applied to several large scale datasets and is shown to be successful in two recent benchmarking studies (Zaitlen et al., in press; Marchini et al., in preparation). Our method is publicly available via a webserver at .

Multiscale Topology Optimization With Gaussian Process Regression Models

2021 ◽  
Author(s):  
Joel C. Najmon ◽  
Homero Valladares ◽  
Andres Tovar
Keyword(s):  
Topology Optimization ◽  
Gaussian Process ◽  
Regression Models ◽  
Computational Cost ◽  
Gaussian Process Regression ◽  
Analytical Sensitivity ◽  
Inverse Homogenization ◽  
Discrete Location ◽  
Unit Cells ◽  
Periodic Microstructures

Abstract Multiscale topology optimization (MSTO) is a numerical design approach to optimally distribute material within coupled design domains at multiple length scales. Due to the substantial computational cost of performing topology optimization at multiple scales, MSTO methods often feature subroutines such as homogenization of parameterized unit cells and inverse homogenization of periodic microstructures. Parameterized unit cells are of great practical use, but limit the design to a pre-selected cell shape. On the other hand, inverse homogenization provide a physical representation of an optimal periodic microstructure at every discrete location, but do not necessarily embody a manufacturable structure. To address these limitations, this paper introduces a Gaussian process regression model-assisted MSTO method that features the optimal distribution of material at the macroscale and topology optimization of a manufacturable microscale structure. In the proposed approach, a macroscale optimization problem is solved using a gradient-based optimizer The design variables are defined as the homogenized stiffness tensors of the microscale topologies. As such, analytical sensitivity is not possible so the sensitivity coefficients are approximated using finite differences after each microscale topology is optimized. The computational cost of optimizing each microstructure is dramatically reduced by using Gaussian process regression models to approximate the homogenized stiffness tensor. The capability of the proposed MSTO method is demonstrated with two three-dimensional numerical examples. The correlation of the Gaussian process regression models are presented along with the final multiscale topologies for the two examples: a cantilever beam and a 3-point bending beam.

Robust Well Placement Optimization Through Universal Trace Kriging with Adaptive Sampling

2021 ◽  
Author(s):  
Carlo Cristiano Stabile ◽  
Marco Barbiero ◽  
Giorgio Fighera ◽  
Laura Dovera
Keyword(s):  
Adaptive Sampling ◽  
Pareto Front ◽  
Computing Time ◽  
Computational Cost ◽  
Oil Field ◽  
Computational Time ◽  
Decision Space ◽  
Adaptive Approach ◽  
Reservoir Simulations ◽  
Proxy Models

Abstract Optimizing well locations for a green field is critical to mitigate development risks. Performing such workflows with reservoir simulations is very challenging due to the huge computational cost. Proxy models can instead provide accurate estimates at a fraction of the computing time. This study presents an application of new generation functional proxies to optimize the well locations in a real oil field with respect to the actualized oil production on all the different geological realizations. Proxies are built with the Universal Trace Kriging and are functional in time allowing to actualize oil flows over the asset lifetime. Proxies are trained on the reservoir simulations using randomly sampled well locations. Two proxies are created for a pessimistic model (P10) and a mid-case model (P50) to capture the geological uncertainties. The optimization step uses the Non-dominated Sorting Genetic Algorithm, with discounted oil productions of the two proxies, as objective functions. An adaptive approach was employed: optimized points found from a first optimization were used to re-train the proxy models and a second run of optimization was performed. The methodology was applied on a real oil reservoir to optimize the location of four vertical production wells and compared against reference locations. 111 geological realizations were available, in which one relevant uncertainty is the presence of possible compartments. The decision space represented by the horizontal translation vectors for each well was sampled using Plackett-Burman and Latin-Hypercube designs. A first application produced a proxy with poor predictive quality. Redrawing the areas to avoid overlaps and to confine the decision space of each well in one compartment, improved the quality. This suggests that the proxy predictive ability deteriorates in presence of highly non-linear responses caused by sealing faults or by well interchanging positions. We then followed a 2-step adaptive approach: a first optimization was performed and the resulting Pareto front was validated with reservoir simulations; to further improve the proxy quality in this region of the decision space, the validated Pareto front points were added to the initial dataset to retrain the proxy and consequently rerun the optimization. The final well locations were validated on all 111 realizations with reservoir simulations and resulted in an overall increase of the discounted production of about 5% compared to the reference development strategy. The adaptive approach, combined with functional proxy, proved to be successful in improving the workflow by purposefully increasing the training set samples with data points able to enhance the optimization step effectiveness. Each optimization run performed relies on about 1 million proxy evaluations which required negligible computational time. The same workflow carried out with standard reservoir simulations would have been practically unfeasible.

Novel approach to predicting blast-induced ground vibration using Gaussian process regression

2019 ◽  
Vol 36 (1) ◽  
pp. 29-42 ◽  
Author(s):  
Clement Kweku Arthur ◽  
Victor Amoako Temeng ◽  
Yao Yevenyo Ziggah
Keyword(s):  
Gaussian Process ◽  
Gaussian Process Regression ◽  
Ground Vibration ◽  
Novel Approach
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