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Results for “Constrained MCMC”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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16 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Generalized fiducial inference on differentiable manifolds

We introduce a novel approach to inference on parameters that take values in a Riemannian manifold embedded in a Euclidean space. Parameter spaces of this form are ubiquitous across many fields, including chemistry, physics, computer graphics, and geology. Here, this new approach uses generalized fiducial inference (GFI) to obtain a posterior-like distribution on the manifold, without needing to know local parameterizations that map to the constrained space from an unconstrained Euclidean space. Using mathematical tools from Riemannian geometry, we construct a constrained generalized fiducial distribution (CGFD). A Bernstein-von Mises-type result for the CGFD, which provides intuition for how the desirable asymptotic qualities of the unconstrained generalized fiducial distribution are inherited by the CGFD, is provided. To illustrate the practical use of the CGFD, we provide a proof-of-concept example in the context of a linear logspline density estimation problem, and demonstrate that CGFD-based confidence sets exhibit desirable coverage properties via simulation. As an application, we fit a CGFD to COVID-19 case count data from North Carolina, USA.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Hydro-based MCMC Analysis of SNR 0509–67.5: Revealing the Explosion Properties from Fluid Discontinuities Alone

Using Hubble Space Telescope/ACS Hα images of SNR 0509–67.5 taken ~10 yr apart, we measure the forward shock (FS) proper motions (PMs) at 231 rim locations. The average shock radius and velocity are 3.66 ± 0.036 pc and 6315 ± 310 km s –1 . Hydrodynamic simulations, recast as similarity solutions, provide models for the supernova remnant’s expansion into a uniform ambient medium. These are coupled to a Markov chain Monte Carlo (MCMC) analysis to determine explosion parameters, constrained by the FS measurements. For our baseline model, the MCMC posteriors yield an age of 315.5 ± 1.8 yr, a dynamical explosion center at 5 h 09 m 31. s 16, $-67^\circ 31^{\prime} 17\buildrel{\prime\prime}\over{.} 1$ and ambient medium densities at each azimuth ranging over 3.7–8.0 × 10 –25 g cm –3 . The age uncertainty can be an order of magnitude larger when considering other models, or subsets of the data. We detect stellar PMs corresponding to speeds in the Large Magellanic Cloud ≥ 770 km s –1 . Five stars in the remnant show measurable PMs but none are moving radially from the dynamical center. There are four stars 1."4 from the center, including three faint, previously unidentified ones. Using coronal [Fe XIV ] λ5303 emission as a proxy for the reverse shock location, we constrain the explosion energy (for a compression factor of 4) to a value of E = (1.30 ± 0.41) × 10 51 erg for the first time from shock kinematics alone. Higher compression factors (7 or more) are strongly disfavored based on multiple criteria, arguing for inefficient particle acceleration in the Balmer shocks of SNR 0509–67.5.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty

Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ, an extensible and scalable software framework that contains implementations of state-of-the art algorithms aimed to overcome the challenges of high-dimensional, PDE-constrained Bayesian inverse problems. These algorithms accelerate MCMC sampling by exploiting the geometry and intrinsic low-dimensionality of parameter space via derivative information and low rank approximation. The software integrates two complementary open-source software packages, hIPPYlib and MUQ. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients and Hessians to permit large-scale solution. By combining these two complementary libraries, we created a robust, scalable, and efficient software framework that realizes the benefits of each and allows us to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. To illustrate the capabilities of hIPPYlib-MUQ, we present a comparison of a number of MCMC methods available in the integrated software on several high-dimensional Bayesian inverse problems. These include problems characterized by both linear and nonlinear PDEs, various noise models, and different parameter dimensions. The results demonstrate that large (~ 50×) speedups over conventional black box and gradient-based MCMC algorithms can be obtained by exploiting Hessian information (from the log-posterior), underscoring the power of the integrated hIPPYlib-MUQ framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

EvoProtGrad (Directed Evolution for Proteins with Gradients) [SWR-23-48]

A Python package for directed evolution on a protein sequence with gradient-based discrete Markov chain monte carlo (MCMC). Users are able to compose custom models that map sequence to function with pretrained models, including protein language models (PLMs), to guide and constrain search. Our package natively integrates with the HuggingFace platform and supports PLMs from transformers. Our MCMC sampler identifies promising amino acids to mutate via model gradients taken with respect to the input (i.e., sensitivity analysis). We allow users to compose their own custom target function for MCMC by leveraging the Product of Experts MCMC paradigm. Each model is an "expert" that contributes its own knowledge about the protein's fitness landscape to the overall target function. The sampler is designed to be more efficient and effective than brute force and random search while maintaining most of the generality and flexibility. Additional information can be found in the related publication: https://iopscience.iop.org/article/10.1088/2632-2153/accacd

Emami, Patrick↗
DOE OSTI2025

Using Machine Learning to Generate a GISS ModelE Calibrated Physics Ensemble (CPE)

A neural network (NN) surrogate of the NASA GISS ModelE atmosphere (version E3) is trained on a perturbed parameter ensemble (PPE) spanning 45 physics parameters and 36 outputs. The NN is leveraged in a Markov Chain Monte Carlo (MCMC) Bayesian parameter inference framework to generate a second posterior constrained ensemble coined a “calibrated physics ensemble,” or CPE. The CPE members are characterized by diverse parameter combinations and are, by definition, close to top-of-atmosphere radiative balance, and must broadly agree with numerous hydrologic, energy cycle and radiative forcing metrics simultaneously. Global observations of numerous cloud, environment, and radiation properties (provided by global satellite products) are crucial for CPE generation. The inference framework explicitly accounts for discrepancies (or biases) in satellite products during CPE generation. We demonstrate that product discrepancies strongly impact calibration of important model parameter settings (e.g., convective plume entrainment rates; fall speed for cloud ice). Structural improvements new to E3 are retained across CPE members (e.g., stratocumulus simulation). Notably, the framework improved the simulation of shallow cumulus and Amazon rainfall while not degrading radiation fields, an upgrade that neither default parameters nor Latin Hypercube parameter searching achieved. Analyses of the initial PPE suggested several parameters were unimportant for output variation. However, many “unimportant” parameters were needed for CPE generation, a result that brings to the forefront how parameter importance should be determined in PPEs. From the CPE, two diverse 45-dimensional parameter configurations are retained to generate radiatively-balanced, auto-tuned atmospheres that were used in two E3 submissions to CMIP6.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Can the angular scale of cosmic homogeneity be used as a cosmological test?

Abstract In standard cosmology, the cosmic homogeneity scale is the transition scale above which the patterns arising from non-uniformities – such as groups and clusters of galaxies, voids, and filaments – become indistinguishable from a random distribution of sources. Recently, different groups have investigated the feasibility of using such a scale as a cosmological test and arrived at different conclusions. In this paper, we complement and extend these studies by exploring the evolution of the spatial ( $$R_{\textrm{H}}$$ R H ) and angular ( $$\theta _{\textrm{H}}$$ θ H ) homogeneity scales with redshift, assuming a spatially flat, $$\varLambda $$ Λ -Cold Dark Matter universe and linear cosmological perturbation theory. We confirm previous results concerning the non-monotonicity of $$R_{\textrm{H}}$$ R H with the matter density parameter $$\varOmega _{\textrm{m0}}$$ Ω m0 but also show that it exhibits a monotonical behavior with the Hubble constant $$H_{0}$$ H 0 within a large redshift interval. More importantly, we find that, for $$z \gtrsim 0.6$$ z ≳ 0.6 , $$\theta _{\textrm{H}}$$ θ H presents a monotonical behavior with $$\varOmega _{\textrm{m0}}$$ Ω m0 , as well as for $$H_0$$ H 0 the entire redshift interval analyzed. We find also that the angular homogeneity scale is sensitive to $$H_{0}$$ H 0 , especially at higher redshifts. Using the currently available $$\theta _{\textrm{H}}$$ θ H measurements, we illustrate the constraints on the $$\varOmega _{\textrm{m0}}$$ Ω m0 – $$H_{0}$$ H 0 plane through a MCMC analysis and show the feasibility of using the angular homogeneity scale as a new, model-independent way to constrain cosmological parameters.

Physics↗
DOE OSTI2024

Constraining multi-field inflation using the SPHEREx all-sky survey power spectra

Abstract We investigate how well the SPHEREx all-sky survey can constrain local primordial non-Gaussianity beyond the parameterf NL using galaxy power spectra. We forecast joint constraints on the parametersf NL ,g NL andτ NL obtained assuming a simple two-field curvaton model of inflation. The parametersf NL andg NL characterise the squeezed limits of the primordial bispectrum and trispectrum respectively, and lead to a characteristic scale-dependence of the galaxy bias that increases out to arbitrarily large scales. Values of the parameterτ NL > (6/5f NL ) 2 cause the galaxy power spectrum to have a stochastic component which also increases out to arbitrarily large scales. Our MCMC forecasts indicate that SPHEREx can provide joint constraints on any two of the three parametersf NL ,g NL andτ NL . Due to strong degeneracies among these parameters, measurements of the galaxy power spectra alone may not be sufficient to jointly constrain all three. Constraints onf NL ,g NL andτ NL obtained from galaxy power spectrum observations depend on the modelling of underlying nuisance parameters. We study the robustness of our forecast constraints to modelling choices and note that even with relatively conservative modelling assumptions, SPHEREx galaxy power spectra can provide strong evidence of local non-Gaussianity, even if the particular values off NL andg NL cannot be measured precisely.

Astronomy & Astrophysics↗
DOE OSTI2022

Stringent σ8 constraints from small-scale galaxy clustering using a hybrid MCMC + emulator framework

ABSTRACT We present a novel simulation-based hybrid emulator approach that maximally derives cosmological and Halo Occupation Distribution (HOD) information from non-linear galaxy clustering, with sufficient precision for DESI Year 1 (Y1) analysis. Our hybrid approach first samples the HOD space on a fixed cosmological simulation grid to constrain the high-likelihood region of cosmology + HOD parameter space, and then constructs the emulator within this constrained region. This approach significantly reduces the parameter volume emulated over, thus achieving much smaller emulator errors with fixed number of training points. We demonstrate that this combined with state-of-the-art simulations result in tight emulator errors comparable to expected DESI Y1 LRG sample variance. We leverage the new abacussummit simulations and apply our hybrid approach to CMASS non-linear galaxy clustering data. We infer constraints on σ8 = 0.762 ± 0.024 and fσ8(zeff = 0.52) = 0.444 ± 0.016, the tightest among contemporary galaxy clustering studies. We also demonstrate that our fσ8 constraint is robust against secondary biases and other HOD model choices, a critical first step towards showcasing the robust cosmology information accessible in non-linear scales. We speculate that the additional statistical power of DESI Y1 should tighten the growth rate constraints by at least another 50–60 ${{\ \rm per\ cent}}$, significantly elucidating any potential tension with Planck. We also address the ‘lensing is low’ tension, which we find to be in the same direction as a potential tension in fσ8. We show that the combined effect of a lower fσ8 and environment-based bias accounts for approximately $50{{\ \rm per\ cent}}$ of the discrepancy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Plug & play directed evolution of proteins with gradient-based discrete MCMC

Abstract A long-standing goal of machine-learning-based protein engineering is to accelerate the discovery of novel mutations that improve the function of a known protein. We introduce a sampling framework for evolving proteins in silico that supports mixing and matching a variety of unsupervised models, such as protein language models, and supervised models that predict protein function from sequence. By composing these models, we aim to improve our ability to evaluate unseen mutations and constrain search to regions of sequence space likely to contain functional proteins. Our framework achieves this without any model fine-tuning or re-training by constructing a product of experts distribution directly in discrete protein space. Instead of resorting to brute force search or random sampling, which is typical of classic directed evolution, we introduce a fast Markov chain Monte Carlo sampler that uses gradients to propose promising mutations. We conduct in silico directed evolution experiments on wide fitness landscapes and across a range of different pre-trained unsupervised models, including a 650 M parameter protein language model. Our results demonstrate an ability to efficiently discover variants with high evolutionary likelihood as well as estimated activity multiple mutations away from a wild type protein, suggesting our sampler provides a practical and effective new paradigm for machine-learning-based protein engineering.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Bayesian Exploration of Phenomenological EoS of Neutron/Hybrid Stars with Recent Observations

The description of the stellar interior of compact stars remains as a big challenge for the nuclear astrophysics community. The consolidated knowledge is restricted to density regions around the saturation of hadronic matter ρ 0 =2.8 × 10 14 g cm -3 , regimes where our nuclear models are successfully applied. As one moves towards higher densities and extreme conditions up to the quark/gluons deconfinement, little can be said about the microphysics of the equation of state (EoS). Here, we employ a Markov Chain Monte Carlo (MCMC) strategy to access the variability at high density regions of polytropic piecewise models for neutron star (NS) EoS or possible hybrid stars, i.e., a NS with a small quark-matter core. With a fixed description of the hadronic matter for low density, below the nuclear saturation density, we explore a variety of models for the high density regimes leading to stellar masses near to 2.5 M ⊙ , in accordance with the observations of massive pulsars. The models are constrained, including the observation of the merger of neutrons stars from VIRGO-LIGO and with the pulsar observed by NICER. In addition, we also discuss the possibility of the use of a Bayesian power regression model with heteroscedastic error. The set of EoS from the Laser Interferometer Gravitational-Wave Observatory (LIGO) was used as input and treated as the data set for the testing case.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Constraining Bedrock Groundwater Residence Times in a Mountain System With Environmental Tracer Observations and Bayesian Uncertainty Quantification

Groundwater residence time distributions provide fundamental insights on the hydrological processes within watersheds. Yet, observations that can constrain groundwater residence times over broad timescales remain scarce in mountain catchment studies. We use environmental tracers (CFC-12, SF 6 , 3 H, and 4 He) to investigate groundwater residence times along a hillslope in the East River Watershed, Colorado, USA. We develop a Bayesian inference framework that applies a Markov-chain Monte Carlo (MCMC) approach to estimate noble gas recharge temperature, elevation, and excess-air parameters and the resulting environmental tracer concentrations. MCMC is then used to propagate the environmental tracer uncertainties to estimates of groundwater mean residence times inferred with lumped parameter models. All samples contain 3 H, CFC-12, and SF 6 in addition to terrigenic 4 He, suggesting a mixture of water characterized by modern and premodern residence times. 4He exponential mean residence times range from hundreds of years at the upslope well to thousands of years at the toe-slope well assuming average crustal production rates. We find that binary mixing residence time distributions with separate young and old mixing fractions are needed to predict the 4 He, CFC-12, SF 6 , and 3 H observations, supporting the importance of flow path mixing in this bedrock system. Our findings that the fractured bedrock hosts groundwater with a mixture of residence times ranging from decades to millennia suggest variable recharge dynamics and flow path mixing along the hillslope and highlight the importance of characterizing groundwater systems with observations that are sensitive to transport over a broad range of residence times.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Constraining Cosmology with Simulation-based inference and Optical Galaxy Cluster Abundance

We test the robustness of simulation-based inference (SBI) in the context of cosmological parameter estimation from galaxy cluster counts and masses in simulated optical datasets. We construct ``simulations'' using analytical models for the galaxy cluster halo mass function (HMF) and for the observed richness (number of observed member galaxies) to train and test the SBI method. We compare the SBI parameter posterior samples to those from an MCMC analysis that uses the same analytical models to construct predictions of the observed data vector. The two methods exhibit comparable performance, with reliable constraints derived for the primary cosmological parameters, ($\Omega_m$ and $\sigma_8$), and richness-mass relation parameters. We also perform out-of-domain tests with observables constructed from galaxy cluster-sized halos in the Quijote simulations. Again, the SBI and MCMC results have comparable posteriors, with similar uncertainties and biases. Unsurprisingly, upon evaluating the SBI method on thousands of simulated data vectors that span the parameter space, SBI exhibits worsened posterior calibration metrics in the out-of-domain application. We note that such calibration tests with MCMC is less computationally feasible and highlight the potential use of SBI to stress-test limitations of analytical models, such as in the use for constructing models for inference with MCMC.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Photometric redshift uncertainties in weak gravitational lensing shear analysis: models and marginalization

ABSTRACT Recovering credible cosmological parameter constraints in a weak lensing shear analysis requires an accurate model that can be used to marginalize over nuisance parameters describing potential sources of systematic uncertainty, such as the uncertainties on the sample redshift distribution n(z). Due to the challenge of running Markov chain Monte Carlo (MCMC) in the high-dimensional parameter spaces in which the n(z) uncertainties may be parametrized, it is common practice to simplify the n(z) parametrization or combine MCMC chains that each have a fixed n(z) resampled from the n(z) uncertainties. In this work, we propose a statistically principled Bayesian resampling approach for marginalizing over the n(z) uncertainty using multiple MCMC chains. We self-consistently compare the new method to existing ones from the literature in the context of a forecasted cosmic shear analysis for the HSC three-year shape catalogue, and find that these methods recover statistically consistent error bars for the cosmological parameter constraints for predicted HSC three-year analysis, implying that using the most computationally efficient of the approaches is appropriate. However, we find that for data sets with the constraining power of the full HSC survey data set (and, by implication, those upcoming surveys with even tighter constraints), the choice of method for marginalizing over n(z) uncertainty among the several methods from the literature may modify the 1σ uncertainties on Ωm–S8 constraints by ∼4 per cent, and a careful model selection is needed to ensure credible parameter intervals.

Zhang, Tianqing (ORCID:000000025596198X)↗
DOE OSTI2025

A Markov chain Monte Carlo (MCMC) Bayesian inference approach to analyze apparent activation barriers and reaction orders from microreactor data

Statistical analysis of steady-state catalytic kinetic data is often limited by data sparsity due to the slow pace at which the data is collected. Data sparsity and limitations in statistical analysis make it difficult to differentiate between mechanistic models and catalytic sites. A Bayesian inference tool is reported for catalysis researchers to estimate error in the determination of reaction orders from steady state microreactor data. The benefits of a Bayesian inference approach are discussed, as an alternative to the more common frequentist approach. The approach incorporates prior knowledge of the system and the data collected to form an error estimate on reaction orders. We investigated the effects of three distinct data treatments—individual fitting of trials, pooled analysis, and constrained regression methods—on the precision and uncertainty of reaction order determinations. To assess the robustness of our findings, we conducted sensitivity analyses to evaluate the influence of Bayesian parameters on uncertainty estimation. Additionally, we utilized synthetic data to illustrate how data quality impacts the precision of uncertainty assessments. We show Bayesian analysis can obtain a more precise estimation of error with a sparse data set than a frequentist analysis. Finally, this work provides strong evidence that the adoption of Bayesian analysis of kinetic data may help researchers make more precise arguments as to the strength of their evidence for a particular mechanistic hypothesis, or in comparing across different catalysts.

42 ENGINEERING↗
DOE OSTI2025

Indirect Measurement of the 23 Na(p, γ) 24 Mg Direct Capture Reaction Rate via ( 3 He,d) Spectroscopy

The cross section of the $^{23}\text{Na}(p,γ)^{24}\text{Mg}$ reaction is dominated by direct capture at low energies relevant for stellar burning. Such cross sections can be constrained using spectroscopic factors($C^2S$) or asymptotic normalization coefficients(ANCs) from transfer reactions. In this work, the $^{23}\text{Na}(^3\text{He},d)^{24}\text{Mg}$ reaction was measured at $E_{lab}=21$ MeV to extract spectroscopic factors for $^{24}\text{Mg}$ states with excitation energies in $E_x=7 - 12$ MeV using the Enge split-pole spectrograph at the Triangle Universities Nuclear Laboratory. A new non-resonant astrophysical S factor and the direct capture reaction rate for the $^{23}\text{Na}(p,γ)$ reaction are calculated and presented based on this measurement. The new rate at $T<0.04$ GK is 43$\%$ smaller than in previous studies. Rigorous treatments of uncertainties are presented using a Bayesian Markov Chain Monte Carlo (MCMC) method. Finally, sources of uncertainties for computing the direct capture cross section are also discussed in detail.

electromagnetic moments↗
DOE OSTI2022

A warm super-Neptune around the G-dwarf star TOI-1710 revealed with TESS, SOPHIE, and HARPS-N

We report the discovery and characterization of the transiting extrasolar planet TOI-1710 b. It was first identified as a promising candidate by the Transiting Exoplanet Survey Satellite. Its planetary nature was then established with SOPHIE and HARPS-N spectroscopic observations via the radial-velocity method. The stellar parameters for the host star are derived from the spectra and a joint Markov chain Monte-Carlo adjustment of the spectral energy distribution and evolutionary tracks of TOI-1710. A joint MCMC analysis of the TESS light curve and the radial-velocity evolution allows us to determine the planetary system properties. From our analysis, TOI 1710 b is found to be a massive warm super-Neptune (M p = 28.3 ± 4.7 M ⊕ and R p = 5.34 ± 0.11 R ⊕ ) orbiting a G5V dwarf star (T eff = 5665 ± 55 K) on a nearly circular 24.3-day orbit (e = 0.16 ± 0.08). The orbital period of this planet is close to the estimated rotation period of its host star P rot = 22.5 ± 2.0 days and it has a low Keplerian semi-amplitude K = 6.4 ± 1.0 m s -1 ; we thus performed additional analyses to show the robustness of the retrieved planetary parameters. With a low bulk density of 1.03 ± 0.23 g cm -3 and orbiting a bright host star (J = 8.3, V = 9.6), TOI-1710 b is one of the best targets in this mass-radius range (near the Neptunian desert) for atmospheric characterization via transmission spectroscopy, a key measurement in constraining planet formation and evolutionary models of sub-Jovian planets.

79 ASTRONOMY AND ASTROPHYSICS↗