Abstract: A computing system comprises a processor configured to receive, a plurality of simulations, a discrete distribution function, and one or more cumulative distribution models. One or more conditional cumulative distribution models are generated based at least in part on the discrete distribution function and the one or more cumulative distribution models. A range of the one or more cumulative distribution models and one or more conditional cumulative distribution models is stratified, and a sum of discrepancy scores is computed for the plurality of simulations. In each of one or more resampling iterations, one or more simulations are replaced with one or more resampled simulations based on a policy. An updated sum of discrepancy scores is generated for the plurality of simulations with the one or more simulations replaced by the one or more resampled simulations. The plurality of simulations are output subsequent to performing the one or more resampling iterations.

Abstract: A computing system including a processor configured to receive, for a plurality of correlated random variables, a simulation sample including a plurality of simulations. The processor may generate a surrogate cumulative distribution model at least in part by estimating a plurality of surrogate model parameters. Based at least in part on the surrogate cumulative distribution model, the processor may select one or more subsets of the plurality of simulations. In each of one or more resampling iterations, until a sum of respective discrepancy scores of the subsets is determined to meet an optimization threshold, the processor may compute the discrepancy scores. Based at least in part on the sum, the processor may sample one or more resampled simulations. The processor may replace one or more simulations included in the one or more subsets with the one or more resampled simulations. The processor may output the one or more subsets.

Abstract: A computing system is provided, including one or more processors configured to receive a plurality of input matrices M. Each input matrix M may include a plurality of estimated input correlation coefficients. The one or more processors may be further configured to compute a respective plurality of estimated closest correlation matrices X0 for the plurality of input matrices M at a semidefinite program solver. Each estimated closest correlation matrix X0 may be a positive definite matrix. The one or more processors may be further configured to generate a training data set including at least the plurality of estimated closest correlation matrices X0. The one or more processors may be further configured to train a machine learning model using the training data set.

Abstract: A computing system comprises a processor configured to receive, for a plurality of correlated variables, a first predetermined number of simulations from a Monte-Carlo simulation sample, each simulation including a plurality of initial simulation results for the plurality of the variables. A unit interval of a cumulative distribution function (CDF) is segmented into a plurality of bins corresponding to a second predetermined number of strata. An initial discrepancy score is determined based upon a quantity of values in each bin, the first predetermined number, and second predetermined number. At least one of the initial simulation results is removed based upon an initial sum of the initial discrepancy scores. At least one other simulation is added and a plurality of representative simulations is output that represents the CDF across the strata based upon an updated sum of updated discrepancy scores.

Abstract: A computing system including a processor configured to receive a plurality of marginal distribution samples and a copula support sample including a plurality of copula sample points. The processor may divide the copula support sample into copula sample blocks and divide each of the marginal distribution samples into marginal sample blocks. For each of the copula sample blocks, within each copula dimension, the processor may assign a respective copula value rank to each sampled copula value included in that copula sample block. For each of the marginal sample blocks, the processor may sort the sampled marginal values to match an order of the copula value ranks of the corresponding copula sample block. The processor may generate a plurality of joint distribution sample vectors that each include the sampled marginal values located at corresponding positions across the marginal distribution samples. The processor may output the joint distribution sample vectors.