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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates

This work develops a new multi delity ensemble Kalman lter (MFEnKF) algorithm based on linear control variate framework. The approach allows for rigorous multi delity extensions of the EnKF, where the uncertainty in coarser delities in the hierarchy of models represent control variates for the uncertainty in ner delities. Small ensembles of high delity model runs are com- plemented by larger ensembles of cheaper, lower delity runs, to obtain much improved analyses at only small additional computational costs. We investigate the use of reduced order models as coarse delity control variates in the MFEnKF, and provide analyses to quantify the improvements over the traditional ensemble Kalman lters. We apply these ideas to perform data assimilation with a quasi-geostrophic test problem, using direct numerical simulation and a corresponding POD-Galerkin reduced order model. Numerical results show that the two- delity MFEnKF provides better analyses than existing EnKF algorithms at comparable or reduced computational costs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates

Herein, the use of many control variates is proposed as a method to accelerate the second- and third-order Monte Carlo (MC) many-body perturbation (MC-MP2 and MC-MP3) calculations. A control variate is an exactly integrable function that is strongly correlated or anti-correlated with the target function to be integrated by the MC method. Evaluating both integrals as well as their covariances in the same MC run, one can effect a mutual cancellation of the statistical uncertainties and biases in the MC integrations, thereby accelerating its convergence considerably. Six and thirty-six control variates, whose integrals are known a priori, are generated for MC-MP2 and MC-MP3, respectively, by systematically replacing one or more two-electron-integral vertexes of certain configurations by zero-valued overlap-integral vertexes in their Goldstone diagrams. The variances and co- variances of these control variates are computed at a marginal cost, enhancing the overall efficiency of the MC-MP2 and MC-MP3 calculations by a factor of up to 14 and 20, respectively.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Mitigating the noise of DESI mocks using analytic control variates

In order to address fundamental questions related to the expansion history of the Universe and its primordial nature with the next generation of galaxy experiments, we need to model reliably large-scale structure observables such as the correlation function and the power spectrum. Cosmological N-body simulations provide a reference through which we can test our models, but their output suffers from sample variance on large scales. Fortunately, this is the regime where accurate analytic approximations exist. To reduce the variance, which is key to making optimal use of these simulations, we can leverage the accuracy and precision of such analytic descriptions using Control Variates (CV). The power of control variates stems from utilizing inexpensive but highly correlated surrogates of the statistics one wishes to measure. The stronger the correlation between the surrogate and the statistic of interest, the larger the variance reduction delivered by the method. We apply two control variate formulations to mock catalogs generated in anticipation of upcoming data from the Dark Energy Spectroscopic Instrument (DESI) to test the robustness of its analysis pipeline. Our CV-reduced measurements offer a factor of 5-10 improvement in the measurement error compared with the raw measurements. We explore the relevant properties of the galaxy samples that dictate this reduction and comment on the improvements we find on some of the derived quantities relevant to Baryon Acoustic Oscillation (BAO) analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Ensemble approximate control variate estimators: Applications to multi-fidelity importance sampling.

The recent growth in multifidelity uncertainty quantification has given rise to a large set of variance reduction techniques that leverage information from model ensembles to provide variance reduction for estimates of the statistics of a high-fidelity model. In this paper we provide two contributions: (1) we utilize an ensemble estimator to account for uncertainties in the optimal weights of approximate control variate (ACV) approaches and derive lower bounds on the number of samples required to guarantee variance reduction; and (2) we extend an existing multifidelity importance sampling (MFIS) scheme to leverage control variates. Our approach directly addresses a limitation of many multifidelity sampling strategies that require the usage of pilot samples to estimate covariances. As such we make significant progress towards both increasing the practicality of approximate control variates—for instance, by accounting for the effect of pilot samples—and using multifidelity approaches more effectively for estimating low-probability events. The numerical results indicate our hybrid MFIS-ACV estimator achieves up to 50% improvement in variance reduction over the existing state-of-the-art MFIS estimator, which had already shown an outstanding convergence rate compared to the Monte Carlo method, on several problems of computational mechanics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Covariance-Free Bifidelity Control Variates Importance Sampling for Rare Event Reliability Analysis

Multifidelity modeling has been steadily gaining attention as a tool to address the problem of exorbitant model evaluation costs that makes the estimation of failure probabilities a significant computational challenge for complex real-world problems, particularly when failure is a rare event. To implement multifidelity modeling, estimators that efficiently combine information from multiple models/sources are necessary. In past works, the variance reduction techniques of control variates (CV) and importance sampling (IS) have been leveraged for this task. In this paper, we present the CVIS framework—a creative take on a coupled CV and IS estimator for bifidelity reliability analysis. The framework addresses some of the practical challenges of the CV method by using an estimator for the control variate mean and sidestepping the need to estimate the covariance between the original estimator and the control variate through a clever choice for the tuning constant. Furthermore, the task of selecting an efficient IS distribution is also considered, with a view towards maximally leveraging the bifidelity structure and maintaining expressivity. Additionally, a diagnostic is provided that indicates both the efficiency of the algorithm as well as the relative predictive quality of the models utilized. Finally, the behavior and performance of the framework is explored through analytical and numerical examples.

Markov chain Monte Carlo↗
DOE OSTI2025

CoVVVR: Control Variates & Vegas Variance Reduction

This package is a wrapper over the vegas integration package. The control variate variance reduction method is applied to the function when integrated along with the techniques applied in vegas such as importance sampling. To understand control variates, lets first look at how Monte Carlo works.

Scott, JacobL. [Univ. of Kansas, Lawrence, KS (Uni↗
DOE OSTI2020

A generalized approximate control variate framework for multifidelity uncertainty quantification

We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost models — which are typically lower fidelity with unknown statistics — are used to reduce the variance in statistical estimators relative to a MC estimator with equivalent cost. We derive the conditions under which our proposed approximate control variate framework recovers existing multifidelity variance reduction schemes as special cases. We demonstrate that existing recursive/nested strategies are suboptimal because they use the additional low-fidelity models only to efficiently estimate the unknown mean of the first low-fidelity model. As a result, they cannot achieve variance reduction beyond that of a control variate estimator that uses a single low-fidelity model with known mean. However, there often exists about an order-of-magnitude gap between the maximum achievable variance reduction using all low-fidelity models and that achieved by a single low-fidelity model with known mean. We show that our proposed approach can exploit this gap to achieve greater variance reduction by using non-recursive sampling schemes. The proposed strategy reduces the total cost of accurately estimating statistics, especially in cases where only low-fidelity simulation models are accessible for additional evaluations. Several analytic examples and an example with a hyperbolic PDE describing elastic wave propagation in heterogeneous media are used to illustrate the main features of the methodology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Leveraging neural control variates for enhanced precision in lattice field theory

Results obtained with stochastic methods have an inherent uncertainty due to the finite number of samples that can be achieved in practice. In lattice QCD this problem is particularly salient in some observables like, for instance, observables involving one or more baryons and it is the main problem preventing the calculation of nuclear forces from first principles. The method of control variables has been used extensively in statistics and it amounts to computing the expectation value of the difference between the observable of interest and another observable whose average is known to be zero but is correlated with the observable of interest. Recently, control variates methods emerged as a promising solution in the context of lattice field theories. In our current study, instead of relying on an educated guess to determine the control variate, we utilize a neural network to parametrize this function. Using 1 + 1 dimensional scalar field theory as a testbed, we demonstrate that this neural network approach yields substantial improvements. Notably, our findings indicate that the neural network ansatz is particularly effective in the strong coupling regime. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2025

CV4Quantum: Reducing the Sampling Overhead in Probabilistic Error Cancellation Using Control Variates

Quasiprobabilistic decompositions (QPDs) play a key role in maximizing the utility of near-term quantum hardware. For example, Probabilistic Error Cancellation (PEC) (an error mitigation technique) and circuit cutting (which enables large quantum computations to be performed on quantum hardware with a limited number of qubits) both involve QPDs. Computations based on QPDs typically incur large sampling overheads that grow exponentially with the number of error-terms mitigated or number of circuit-cuts employed, limiting their practical feasibility. In this work, we adapt the control variates variance reduction technique from the statistics literature in order to reduce the sampling overhead in QPD-based computations. We demonstrate our method using simulation experiments that mimic a realistic PEC scenario. In our experiments, we observed a more than 50% reduction in the number of samples needed to achieve a given precision, in more than 50% of the PEC-based estimations performed in the study when using our approach. We discuss how future research on constructing good control variates can lead to even stronger sampling overhead reduction.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Control variates for lattice field theory

In most lattice field theories, correlators are plagued by a signal-to-noise problem of exponential difficulty in the time separation. We propose a method for improving the signal-to-noise ratio, in which control variates are systematically constructed from lattice Schwinger-Dyson relations. The method is demonstrated on various two-dimensional lattices in scalar field theory, and a strategy for scaling to larger systems is explored. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Variance reduction via simultaneous importance sampling and control variates techniques using vegas

Monte Carlo (MC) integration is an important calculational technique in the physical sciences. Practical considerations require that the calculations are performed as accurately as possible for a given set of computational resources. To improve the accuracy of MC integration, a number of useful variance reduction algorithms have been developed, including importance sampling and control variates. In this work, we demonstrate how these two methods can be applied simultaneously, thus combining their benefits. We provide a python wrapper, named CoVVVR, which implements our approach in the VEGAS program. The improvements are quantified with several benchmark examples from the literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1993

A controlled variation scheme for convection treatment in pressure-based algorithm

Convection effect and source terms are two primary sources of difficulties in computing turbulent reacting flows typically encountered in propulsion devices. The present work intends to elucidate the individual as well as the collective roles of convection and source terms in the fluid flow equations, and to devise appropriate treatments and implementations to improve our current capability of predicting such flows. A controlled variation scheme (CVS) has been under development in the context of a pressure-based algorithm, which has the characteristics of adaptively regulating the amount of numerical diffusivity, relative to central difference scheme, according to the variation in local flow field. Both the basic concepts and a pragmatic assessment will be presented to highlight the status of this work.

Shyy, Wei↗
DOE OSTI2024

High-precision Galaxy Clustering Predictions from Small-volume Hydrodynamical Simulations via Control Variates

Abstract Cosmological simulations of galaxy formation are an invaluable tool for understanding galaxy formation and its impact on cosmological parameter inference from large-scale structures. However, their high computational cost is a significant obstacle for running simulations that probe cosmological volumes comparable to those analyzed by contemporary large-scale structure experiments. In this work, we explore the possibility of obtaining high-precision galaxy clustering predictions from small-volume hydrodynamical simulations such as MillenniumTNG and FLAMINGO via control variates. In this approach, the hydrodynamical full-physics simulation is paired with a matched low-resolution gravity-only simulation. By learning the galaxy–halo connection from the hydrodynamical simulation and applying it to the gravity-only counterpart, one obtains a galaxy population that closely mimics the one in the more expensive simulation. One can then construct an estimator of galaxy clustering that combines the clustering amplitudes in the small-volume hydrodynamical and gravity-only simulations with clustering amplitudes in a large-volume gravity-only simulation. Depending on the galaxy sample, clustering statistic, and scale, this galaxy clustering estimator can have an effective volume of up to around 100 times the volume of the original hydrodynamical simulation in the nonlinear regime. With this approach, we can construct galaxy clustering predictions from existing simulations that are precise enough for mock analyses of next-generation large-scale structure surveys such as the Dark Energy Spectroscopic Instrument and the Legacy Survey of Space and Time.

Doytcheva, Alexandra (ORCID:0009000111254888)↗
DOE OSTI2023

Precision redshift-space galaxy power spectra using Zel'dovich control variates

Numerical simulations in cosmology require trade-offs between volume, resolution and run-time that limit the volume of the Universe that can be simulated, leading to sample variance in predictions of ensemble-average quantities such as the power spectrum or correlation function(s). Sample variance is particularly acute at large scales, which is also where analytic techniques can be highly reliable. This provides an opportunity to combine analytic and numerical techniques in a principled way to improve the dynamic range and reliability of predictions for clustering statistics. In this paper we extend the technique of Zel'dovich control variates, previously demonstrated for 2-point functions in real space, to reduce the sample variance in measurements of 2-point statistics of biased tracers in redshift space. We demonstrate that with this technique, we can reduce the sample variance of these statistics down to their shot-noise limit out to k ~ 0.2 h Mpc -1 . This allows a better matching with perturbative models and improved predictions for the clustering of e.g. quasars, galaxies and neutral Hydrogen measured in spectroscopic redshift surveys at very modest computational expense. We discuss the implementation of ZCV, give some examples and provide forecasts for the efficacy of the method under various conditions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Intraspecific Reaction Norm Variation Controls the Eco-Evolutionary Consequences of Environmental Change

As environmental change accelerates globally, understanding concurrent organismal, species, and community responses is increasingly vital. Here, we examine these collective responses by incorporating genotype-specific thermal reaction norms into an eco-evolutionary predator-prey model, allowing us to track simultaneous phenotypic, ecological, and evolutionary responses to environmental change within ecological communities. We show that the reaction norms expressed by genotypes within a population determine how a community switches between different eco-evolutionary outcomes with changes in temperature. We identify how different components of phenotypic variation in thermal reaction norms—environmental (E), additive environmental and genetic (E + G), and gene-by-environment interactions (G × E)—influence eco-evolutionary dynamics and outcomes as temperature changes. Furthermore, our findings underscore how complex eco-evolutionary responses to environmental change ultimately emerge from variation in reaction norms among genotypes, offering new mechanistic insights into environmental impacts on adaptation, the maintenance of phenotypic and genetic variation, and ecological stability, which is crucial for understanding and predicting eco-evolutionary effects of rapid environmental change in the future.

Eco-evolutionary↗