Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Intrepid MCMC: Metropolis-Hastings with exploration

In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive to evaluate the associated density function. For such cases, MCMC has proven to be an invaluable tool. Random-walk Metropolis Methods (also known as Metropolis-Hastings (MH)), in particular, are highly popular for their simplicity, flexibility, and ease of implementation. However, most MH algorithms suffer from significant limitations when attempting to sample from distributions with multiple modes (particularly disconnected ones). Here, in this paper, we present Intrepid MCMC - a novel MH scheme that utilizes a simple coordinate transformation to significantly improve the mode-finding ability and convergence rate to the target distribution of random-walk Markov chains while retaining most of the simplicity of the vanilla MH paradigm. Through multiple examples, we showcase the improvement in the performance of Intrepid MCMC over vanilla MH for a wide variety of target distribution shapes. We also provide an analysis of the mixing behavior of the Intrepid Markov chain, as well as the efficiency of our algorithm for increasing dimensions. A thorough discussion is presented on the practical implementation of the Intrepid MCMC algorithm. Finally, its utility is highlighted through a Bayesian parameter inference problem for a two-degree-of-freedom oscillator under free vibration.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Online MCMC Thinning with Kernelized Stein Discrepancy

A fundamental challenge in Bayesian inference is efficient representation of a target distribution. Many nonparametric approaches do so by sampling a large number of points using variants of Markov chain Monte Carlo (MCMC). Here, we propose an MCMC variant that retains only those posterior samples which exceed a kernelized Stein discrepancy (KSD) threshold, which we call KSD thinning. We establish the convergence and complexity trade-offs for several settings of KSD thinning as a function of the KSD threshold parameter, sample size, and other problem parameters. We provide experimental comparisons against other online nonparametric Bayesian methods that generate low-complexity posterior representations. We observe superior consistency/complexity trade-offs across a range of settings including MCMC sampling on two Bayesian inference problems from the biological sciences, and 10 × inference speedup and storage reduction for Bayesian neural networks with no loss of accuracy and no increase in training time. Our code is available at https://github.com/colehawkins/KSD-Thinning.

Bayesian inference↗
DOE OSTI2025

Hierarchical Bayesian Modeling for Cosmology: Can NPE reliably replace MCMC?

Hierarchical neural posterior estimation has its place Hierarchical Bayesian Modeling (HBM) combined with MCMC algorithms has been shown to provide more robust and accurate inference for real-world phenomena in which nature takes a nested form. However, MCMC-based inference can be computationally expensive, and its performance often suffers for complex posterior geometries. These costs are especially pertinent for HBM. Studies have recently demonstrated the potential for a flexible, expressive, and amortized hierarchical neural posterior estimator (HNPE) built on Normalizing Flows. These studies have mostly been performed on simple datasets, or they focus on a single parameter from each level of the hierarchy. A systematic study analyzing how both hierarchical methods compare for more complex and realistic datasets is necessary before applying HNPE for scientific measurements. Here, we re-explore the theory behind HNPE and conduct comparative numerical experiments of HNPE and MCMC-based HBM methods on real and synthetic data, including strong gravitational lensing simulations. In particular, we use a suite of diagnostics to show trade-offs in terms of accuracy, precision, time to train or sample, reproducibility, and the need for expert domain knowledge. Especially for higher dimensional and complex posteriors, HNPE is expected to drastically improve on time for inference, accuracy, and precision with an upfront training time cost.

Hur, Rachel [Chicago U.] (ORCID:000900089890445X)↗
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 OSTI2022

Solar data uncertainty impacts on MCMC methods for r-process nucleosynthesis

In recent work, we developed a Markov Chain Monte Carlo (MCMC) procedure to predict the ground state masses capable of forming the observed Solar r-process rare-earth abundance peak. By applying this method to nucleosynthesis calculations which make use of distinct astrophysical conditions and comparing our results to the latest precision mass measurements, we are able to shed light on the conditions/masses capable of producing a rare-earth peak which matches Solar data. Here we examine how our mass predictions change when using a few different sets of r-process Solar abundance residuals that have been reported in the literature. We explore how the differing error estimates of these Solar evaluations propagate through the Markov Chain Monte Carlo to our mass predictions. We find that Solar data which reports the rare-earth peak to have its highest abundance at mass number A = 162 can require distinctly different mass predictions from data with the peak centered at A = 164. Nevertheless, we find that two important general conclusions from past work, regarding the inconsistency of ‘cold’ astrophysical outflows with current mass measurements and the need for local stability at N = 104 in ‘hot’ scenarios, remain robust in the face of differing Solar data evaluations. Additionally, we show that the masses our procedure finds capable of producing a peak at A < 164 are not in line with the latest precision mass measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2017

Kepler Uniform Modeling of KOIs: MCMC Notes for Data Release 25

This document describes data products related to the reported planetary parameters and uncertainties for the Kepler Objects of Interest (KOIs) based on a Markov-Chain-Monte-Carlo (MCMC) analysis. Reported parameters, uncertainties and data products can be found at the NASA Exoplanet Archive . The codes used for this data analysis are available on the Github website (Rowe 2016). The relevant paper for details of the calculations is Rowe et al. (2015). The main differences between the model fits discussed here and those in the DR24 catalogue are that the DR25 light curves were used in the analysis, our processing of the MAST light curves took into account different data flags, the number of chains calculated was doubled to 200 000, and the parameters which are reported are based on a damped least-squares fit, instead of the median value from the Markov chain or the chain with the lowest 2 as reported in the past.

DR25↗
NASA NTRS2008

Hybrid Gibbs Sampling and MCMC for CMB Analysis at Small Angular Scales

A) Gibbs Sampling has now been validated as an efficient, statistically exact, and practically useful method for "low-L" (as demonstrated on WMAP temperature polarization data). B) We are extending Gibbs sampling to directly propagate uncertainties in both foreground and instrument models to total uncertainty in cosmological parameters for the entire range of angular scales relevant for Planck. C) Made possible by inclusion of foreground model parameters in Gibbs sampling and hybrid MCMC and Gibbs sampling for the low signal to noise (high-L) regime. D) Future items to be included in the Bayesian framework include: 1) Integration with Hybrid Likelihood (or posterior) code for cosmological parameters; 2) Include other uncertainties in instrumental systematics? (I.e. beam uncertainties, noise estimation, calibration errors, other).

Gibbs sampling↗
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 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 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 OSTI2026

Probing Non-Standard Interactions in NOvA with Bayesian MCMC Methods

We present a search for non-standard neutrino interactions (NSI) using NOvA's joint $\nu_e$ appearance and $\nu_\mu$ disappearance samples in both neutrino and antineutrino beam modes. A Bayesian Markov Chain Monte Carlo approach is used to map the posterior distribution over NSI parameters $\varepsilon_{e\mu}$, $\varepsilon_{e\tau}$, and $\varepsilon_{\mu\tau}$, simultaneously with standard oscillation parameters. We investigate the effect of prior choice for the complex NSI parameters and present projected sensitivity to off-diagonal NSI.

Huang, Xiaoyan [Mississippi U.]↗
NASA NTRS2013

Application and Evaluation of a Snowmelt Runoff Model in the Tamor River Basin, Eastern Himalaya Using a Markov Chain Monte Carlo (MCMC) Data Assimilation Approach

Previous studies have drawn attention to substantial hydrological changes taking place in mountainous watersheds where hydrology is dominated by cryospheric processes. Modelling is an important tool for understanding these changes but is particularly challenging in mountainous terrain owing to scarcity of ground observations and uncertainty of model parameters across space and time. This study utilizes a Markov Chain Monte Carlo data assimilation approach to examine and evaluate the performance of a conceptual, degree-day snowmelt runoff model applied in the Tamor River basin in the eastern Nepalese Himalaya. The snowmelt runoff model is calibrated using daily streamflow from 2002 to 2006 with fairly high accuracy (average Nash-Sutcliffe metric approx. 0.84, annual volume bias <3%). The Markov Chain Monte Carlo approach constrains the parameters to which the model is most sensitive (e.g. lapse rate and recession coefficient) and maximizes model fit and performance. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall compared with simulations using observed station precipitation. The average snowmelt contribution to total runoff in the Tamor River basin for the 2002-2006 period is estimated to be 29.7+/-2.9% (which includes 4.2+/-0.9% from snowfall that promptly melts), whereas 70.3+/-2.6% is attributed to contributions from rainfall. On average, the elevation zone in the 4000-5500m range contributes the most to basin runoff, averaging 56.9+/-3.6% of all snowmelt input and 28.9+/-1.1% of all rainfall input to runoff. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall versus snowmelt compared with simulations using observed station precipitation. Model experiments indicate that the hydrograph itself does not constrain estimates of snowmelt versus rainfall contributions to total outflow but that this derives from the degree-day melting model. Lastly, we demonstrate that the data assimilation approach is useful for quantifying and reducing uncertainty related to model parameters and thus provides uncertainty bounds on snowmelt and rainfall contributions in such mountainous watersheds.

runoff↗