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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 OSTI2024

The single-cell transcriptome program of nodule development cellular lineages in Medicago truncatula

Legumes establish a symbiotic relationship with nitrogen-fixing rhizobia by developing nodules. Nodules are modified lateral roots that undergo changes in their cellular development in response to bacteria, but the transcriptional reprogramming that occurs in these root cells remains largely uncharacterized. Here, we describe the cell-type-specific transcriptome response of Medicago truncatula roots to rhizobia during early nodule development in the wild-type genotype Jemalong A17, complemented with a hypernodulating mutant (sunn-4) to expand the cell population responding to infection and subsequent biological inferences. The analysis identifies epidermal root hair and stele sub-cell types associated with a symbiotic response to infection and regulation of nodule proliferation. Trajectory inference shows cortex-derived cell lineages differentiating to form the nodule primordia and, posteriorly, its meristem, while modulating the regulation of phytohormone-related genes. Gene regulatory analysis of the cell transcriptomes identifies new regulators of nodulation, including STYLISH 4, for which the function is validated.

Cell Biology↗

DOE OSTI2026

A Framework for Parametric and Predictive Uncertainty Quantification in the E3SM Land Model: Assessing Site and Observable Generalizability

Quantifying parametric uncertainty using observations from individual sites provides a critical foundation for Earth system modeling, serving as a necessary first step before scaling up to regional or global applications. This study introduces a novel computational framework designed to enhance model predictability by reducing parametric uncertainty and assessing site and observable generalizability using various observational constraints. The framework integrates five components: Model Simulation, Statistical Emulation, Global Sensitivity Analysis (GSA), Model Calibration, and Model Prediction. Using the E3SM land model, we simulated site-level land-atmosphere carbon and energy fluxes from 2003 to 2007 across five evergreen needleleaf FLUXNET sites, perturbing 26 vegetation-related model parameters. Gaussian process emulators were employed to expedite GSA and model calibration. Four critical parameters that strongly influence selected land-atmosphere fluxes were identified by GSA. Bayesian approaches were used to infer parameter probability distributions leveraging synthetic data and FLUXNET observations. The results reveal that posterior parameter distributions vary significantly across different sites and observables within the same plant functional type. Probabilistic predictions indicate that parameters calibrated at one site can enhance predictive accuracy at other sites, although site heterogeneity may sometimes outweigh parametric uncertainty. Additionally, the probabilistic predictions demonstrate that calibration for one variable can also improve predictability for other variables, thereby maximizing predictive capabilities with limited observations. This framework provides a powerful approach for reducing parametric uncertainty in Earth system models and deepening our understanding of carbon dynamics and energy cycles. Its adaptability makes it a valuable tool for broader applications in Earth system modeling.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes

Uncertainty propagation in complex engineering systems often poses significant computational challenges related to modeling and quantifying probability distributions of model outputs, as those emerge as the result of various sources of uncertainty that are inherent in the system under investigation. Gaussian Processes regression (GPs) is a robust meta-modeling technique that allows for fast model prediction and exploration of response surfaces. Multi-fidelity variations of GPs further leverage information from cheap and low fidelity model simulations in order to improve their predictive performance on the high fidelity model. In order to cope with the high volume of data required to train GPs in high dimensional design spaces, a common practice is to introduce latent design variables that are typically projections of the original input space to a lower dimensional subspace, and therefore substitute the problem of learning the initial high dimensional mapping, with that of training a GP on a low dimensional space. Here in this paper, we present a Bayesian approach to identify optimal transformations that map the input points to low dimensional latent variables. The \projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to be inferred jointly with the GP parameters, conditioned on the available training data. The proposed Bayesian inference scheme relies on a two-step iterative algorithm that samples from the marginal posteriors of the GP parameters and the projection matrix respectively, both using Markov Chain Monte Carlo (MCMC) sampling. In order to take into account the orthogonality constraints imposed on the orthonormal projection matrix, a Geodesic Monte Carlo sampling algorithm is employed, that is suitable for exploiting probability measures on manifolds. We extend the proposed framework to multi-fidelity models using GPs including the scenarios of training multiple outputs together. We validate our framework on three synthetic problems with a known lower-dimensional subspace. The benefits of our proposed framework, are illustrated on the computationally challenging aerodynamic optimization of a last-stage blade for an industrial gas turbine, where we study the effect of an 85-dimensional shape parameterization of a three-dimensional airfoil on two output quantities of interest, specifically on the aerodynamic efficiency and the degree of reaction

42 ENGINEERING↗

DOE OSTI2026

Strong Lensing Cosmology with Population-level Calibrated Neural Ratio Estimation

Strong gravitational lensing contains key information about cosmic acceleration. Modern and next-generation galaxy imaging surveys are expected to provide high-quality data on $\mathcal{O}(10^5)$ galaxy-galaxy lensing systems. The plethora and complexity of the data are likely to present computational challenges for parameter inference methods for fitting high-dimensional likelihoods, which are often analytically intractable. Neural Ratio Estimation (NRE) efficiently computes individual likelihood ratios that can be combined into population-level posteriors. We use simulations to study the capacity of NRE to jointly predict the dark energy equation-of-state parameter $w$ and the total matter density $Ω_{m}$ from lensing images and companion spectroscopic information. We also introduce a post hoc posterior coverage calibration procedure that mitigates the model overconfidence that is typically found in neural density estimation applications. Our experiments show that the errors on both parameters decrease with increasing inference population sizes. In particular, for 100 lenses in a standard $Λ$CDM Universe, our calibrated NRE model achieves median fractional uncertainty of $22.8\%$ in $w$ and $2.9\%$ in $Ω_{m}$. This proof of concept demonstrates a potentially scalable approach for efficient cosmological parameter inference with large populations of galaxy-scale lenses observed in future surveys.

Jarugula, Sreevani [Fermilab] (ORCID:0000000253867↗

DOE OSTI2022

Posterior Regularized Bayesian Neural Network incorporating soft and hard knowledge constraints

Neural Networks (NNs) have been widely used in supervised learning due to their ability to model complex nonlinear patterns, often presented in high-dimensional data such as images and text. However, traditional NNs often lack the ability for uncertainty quantification. Bayesian NNs (BNNS) could help measure the uncertainty by considering the distributions of the NN model parameters. Besides, domain knowledge is commonly available and could improve the performance of BNNs if it can be appropriately incorporated. In this work, we propose a novel Posterior-Regularized Bayesian Neural Network (PR-BNN) model by incorporating different types of knowledge constraints, such as the soft and hard constraints, as a posterior regularization term. Furthermore, we propose to combine the augmented Lagrangian method and the existing BNN solvers for efficient inference. Furthermore, the experiments in simulation and two case studies about aviation landing prediction and solar energy output prediction have shown the knowledge constraints and the performance improvement of the proposed model over traditional BNNs without the constraints.

14 SOLAR ENERGY↗

DOE OSTI2025

Forecasting Dark Matter Subhalo Constraints from Stellar Streams using Implicit Likelihood Inference

The evidence for dark matter (DM) remains compelling, although attempts to understand its particle nature remain inconclusive. One promising method to study DM is detecting DM subhalos through their gravitational interactions with stellar streams. In this study, we apply Neural Posterior Estimation (NPE) to constrain subhalo interaction parameters, including mass, scale radius, velocity, and encounter geometry, from stellar stream kinematics. We generate particle spray simulations based on the Lagrange Cloud stripping technique, focusing on the ATLAS-Aliqa Uma stream as a test case. We train multiple NPE models across multiple observational scenarios, quantifying how kinematic completeness affects inference and forecasting constraints from upcoming surveys including LSST, 4MOST, and 10-year Gaia data. Our results demonstrate that NPE can produce accurate and well-calibrated posteriors. In the idealized case with full 6D coordinates, we achieve subhalo mass uncertainties of 15-20% for a $10^7 \, \mathrm{M_\odot}$ subhalo, with 5D coordinates (excluding radial velocities) achieving similar performance. Under realistic observational conditions, mass uncertainties range from 50% (present-day) to 20-40% (future scenarios), with comparable performance between the photometric-only LSST sample and a smaller sample that includes Gaia proper motions and 4MOST radial velocities. Most notably, we find that velocity bimodality emerges when phase space is poorly sampled, whether due to missing kinematic information or limited stellar tracers. Combining large photometric samples with targeted spectroscopic follow-up can effectively resolves this degeneracy. These results demonstrate the power of implicit likelihood inference for optimizing stellar stream observational strategies and forecasting DM subhalo constraints from upcoming surveys.

Nguyen, Tri [Northwestern U. (main); SkAI, Chicago↗

DOE OSTI2022

Human reliability analysis studies from simulator experiments using Bayesian inference

Probabilistic Safety Assessment (PSA) of complex facilities is performed to arrive at the risk posed by them. PSA also accounts for the contribution of the human errors towards the overall risk through Human Reliability Analysis (HRA) in terms of Human Error Probability (HEP). Human operators are part of the system and do not work in isolation. Their performance is influenced by the context in which the actions are performed. As a result, quantification of HEP requires operator performance data under the given context. Some good sources of operator performance data are plant‘s operation data, simulator data and expert judgement. The plant operation data pertaining to HRA is generally sparse. In this situation, a full scope plant simulator provides a good alternative for operator performance data generation. Many of the currently practiced HRA methods have been developed by combining the empirical evidence with expert judgement and contain a lot of uncertainty in their estimates. Bayesian inference is suitable for updating the prior HRA estimates with the simulator evidence to obtain the posterior HEP. Here, posterior HEP has been calculated for postulated accident scenarios in advanced reactor (first of its kind) at design stage, using plant simulator.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Nuclear masses learned from a probabilistic neural network

Machine learning methods and uncertainty quantification have been gaining interest throughout the last several years in low-energy nuclear physics. In particular, Gaussian processes and Bayesian neural networks have increasingly been applied to improve mass model predictions while providing well-quantified uncertainties. In this work, we use the probabilistic Mixture Density Network (MDN) to directly predict the mass excess of the 2016 Atomic Mass Evaluation within the range of measured data, and we extrapolate the inferred models beyond available experimental data. The MDN provides not only mean values but also full posterior distributions both within the training set and extrapolated testing set. We show that the addition of physical information to the feature space increases the accuracy of the match to the training data as well as provides for more physically meaningful extrapolations beyond the the limits of experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Fast and Flexible Inference Framework for Continuum Reverberation Mapping Using Simulation-based Inference with Deep Learning

Continuum reverberation mapping (CRM) of active galactic nuclei (AGN) monitors multiwavelength variability signatures to constrain accretion disk structure and supermassive black hole (SMBH) properties. The upcoming Vera Rubin Observatory’s Legacy Survey of Space and Time will survey tens of millions of AGN over the next decade, with thousands of AGN monitored with almost daily cadence in the deep drilling fields. However, existing CRM methodologies often require long computation time and are not designed to handle such large amounts of data. In this paper, we present a fast and flexible inference framework for CRM using simulation-based inference (SBI) with deep learning to estimate SMBH properties from AGN light curves. We use a long short-term memory summary network to reduce the high dimensionality of the light curve data and then use a neural density estimator to estimate the posterior of SMBH parameters. Using simulated light curves, we find SBI can produce more accurate SMBH parameter estimation with 10 3 –10 5 times speed up in inference efficiency compared to traditional methods. The SBI framework is particularly suitable for wide-field CRM surveys as the light curves will have identical observing patterns, which can be incorporated into the SBI simulation. We explore the performance of our SBI model on light curves with irregular-sampled, realistic observing cadence and alternative variability characteristics to demonstrate the flexibility and limitation of the SBI framework.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Implementation of a practical Markov chain Monte Carlo sampling algorithm in PyBioNetFit

Abstract Summary Bayesian inference in biological modeling commonly relies on Markov chain Monte Carlo (MCMC) sampling of a multidimensional and non-Gaussian posterior distribution that is not analytically tractable. Here, we present the implementation of a practical MCMC method in the open-source software package PyBioNetFit (PyBNF), which is designed to support parameterization of mathematical models for biological systems. The new MCMC method, am, incorporates an adaptive move proposal distribution. For warm starts, sampling can be initiated at a specified location in parameter space and with a multivariate Gaussian proposal distribution defined initially by a specified covariance matrix. Multiple chains can be generated in parallel using a computer cluster. We demonstrate that am can be used to successfully solve real-world Bayesian inference problems, including forecasting of new Coronavirus Disease 2019 case detection with Bayesian quantification of forecast uncertainty. Availability and implementation PyBNF version 1.1.9, the first stable release with am, is available at PyPI and can be installed using the pip package-management system on platforms that have a working installation of Python 3. PyBNF relies on libRoadRunner and BioNetGen for simulations (e.g. numerical integration of ordinary differential equations defined in SBML or BNGL files) and Dask.Distributed for task scheduling on Linux computer clusters. The Python source code can be freely downloaded/cloned from GitHub and used and modified under terms of the BSD-3 license (https://github.com/lanl/pybnf). Online documentation covering installation/usage is available (https://pybnf.readthedocs.io/en/latest/). A tutorial video is available on YouTube (https://www.youtube.com/watch?v=2aRqpqFOiS4&t=63s). Supplementary information Supplementary data are available at Bioinformatics online.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Neural posterior unfolding

Differential cross section measurements are the currency of scientific exchange in particle and nuclear physics. A key challenge for these analyses is the correction for detector distortions, known as deconvolution or unfolding. Binned unfolding of cross section measurements traditionally rely on the regularized inversion of the response matrix that represents the detector response, mapping pre-detector (`particle level') observables to post-detector (`detector level') observables. In this paper we introduce Neural Posterior Unfolding, a modern, Bayesian approach that leverages normalizing flows for unfolding. By using normalizing flows for neural posterior estimation, NPU offers several key advantages including implicit regularization through the neural network architecture, fast amortized inference that eliminates the need for repeated retraining, and direct access to the full uncertainty in the unfolded result. In addition to introducing NPU, we implement a classical Bayesian unfolding method called Fully Bayesian Unfolding (FBU) in modern Python so it can also be studied. These tools are validated on simple Gaussian examples and then tested on simulated jet substructure examples from the Large Hadron Collider (LHC). We find that the Bayesian methods are effective and worth additional development to be analysis ready for cross section measurements at the LHC and beyond.

Analysis and statistical methods↗

DOE OSTI2021

Multi-fidelity Bayesian neural networks: Algorithms and applications

Here we propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential equations (PDEs). These multi-fidelity BNNs consist of three neural networks: The first is a fully connected neural network, which is trained following the maximum a posteriori probability (MAP) method to fit the low-fidelity data; the second is a Bayesian neural network employed to capture the cross-correlation with uncertainty quantification between the low- and high-fidelity data; and the last one is the physics-informed neural network, which encodes the physical laws described by PDEs. For the training of the last two neural networks, we first employ the mean-field variational inference (VI) to maximize the evidence lower bound (ELBO) to obtain informative prior distributions for the hyperparameters in the BNNs, and subsequently we use the Hamiltonian Monte Carlo (HMC) method to estimate accurately the posterior distributions for the corresponding hyperparameters. We demonstrate the accuracy of the present method using synthetic data as well as real measurements. Specifically, we first approximate a one- and four-dimensional function, and then infer the reaction rates in one- and two-dimensional diffusion-reaction systems. Moreover, we infer the sea surface temperature (SST) in the Massachusetts and Cape Cod Bays using satellite images and in-situ measurements. Taken together, our results demonstrate that the present method can capture both linear and nonlinear correlation between the low- and high-fidelity data adaptively, identify unknown parameters in PDEs, and quantify uncertainties in predictions, given a few scattered noisy high-fidelity data. Finally, we demonstrate that we can effectively and efficiently reduce the uncertainties and hence enhance the prediction accuracy with an active learning approach, using as examples a specific one-dimensional function approximation and an inverse PDE problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Uncertainty quantification in multivariable regression for material property prediction with Bayesian neural networks

With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be overstated. UQ in material property prediction poses unique challenges, including multi-scale and multi-physics nature of materials, intricate interactions between numerous factors, limited availability of large curated datasets, etc. In this work, we introduce a physics-informed Bayesian Neural Networks (BNNs) approach for UQ, which integrates knowledge from governing laws in materials to guide the models toward physically consistent predictions. To evaluate the approach, we present case studies for predicting the creep rupture life of steel alloys. Experimental validation with three datasets of creep tests demonstrates that this method produces point predictions and uncertainty estimations that are competitive or exceed the performance of conventional UQ methods such as Gaussian Process Regression. Additionally, we evaluate the suitability of employing UQ in an active learning scenario and report competitive performance. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters, as it provided more reliable results in comparison to BNNs based on variational inference approximation or related NNs with probabilistic outputs.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Multimodal parameter spaces of a complex multi-channel neuron model

One of the most common types of models that helps us to understand neuron behavior is based on the Hodgkin–Huxley ion channel formulation (HH model). A major challenge with inferring parameters in HH models is non-uniqueness: many different sets of ion channel parameter values produce similar outputs for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness of local optimality poses challenges for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe non-linearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges with a tractable method in high-dimensional parameter spaces, we propose using a particular Markov chain Monte Carlo (MCMC) algorithm, which has the advantage of inferring parameters in a Bayesian framework. The Bayesian approach is designed to be suitable for multimodal solutions to inverse problems. We introduce and demonstrate the method using a three-channel HH model. We then focus on the inference of nine parameters in an eight-channel HH model, which we analyze in detail. We explore how the MCMC algorithm can uncover complex relationships between inferred parameters using five injected current levels. The MCMC method provides as a result a nine-dimensional posterior distribution, which we analyze visually with solution maps or landscapes of the possible parameter sets. The visualized solution maps show new complex structures of the multimodal posteriors, and they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities and regions of higher model robustness. We envision these solution maps as enabling experimentalists to improve the design of future experiments, increase scientific productivity and improve on model structure and ideation when the MCMC algorithm is applied to experimental data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Robust sampling for weak lensing and clustering analyses with the Dark Energy Survey

Recent cosmological analyses rely on the ability to accurately sample from high-dimensional posterior distributions. A variety of algorithms have been applied in the field, but justification of the particular sampler choice and settings is often lacking. Here, we investigate three such samplers to motivate and validate the algorithm and settings used for the Dark Energy Survey (DES) analyses of the first 3 yr (Y3) of data from combined measurements of weak lensing and galaxy clustering. We employ the full DES Year 1 likelihood alongside a much faster approximate likelihood, which enables us to assess the outcomes from each sampler choice and demonstrate the robustness of our full results. We find that the ellipsoidal nested sampling algorithm multinest reports inconsistent estimates of the Bayesian evidence and somewhat narrower parameter credible intervals than the sliced nested sampling implemented in polychord. We compare the findings from multinest and polychord with parameter inference from the Metropolis–Hastings algorithm, finding good agreement. We determine that polychord provides a good balance of speed and robustness for posterior and evidence estimation, and recommend different settings for testing purposes and final chains for analyses with DES Y3 data. Our methodology can readily be reproduced to obtain suitable sampler settings for future surveys.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

Alcock-Paczynski Blinding Scheme for the Ly-$α$ Forest Analysis

We present and validate a blinding method for the Lyman-$α$ (Ly$α$) forest analysis based on a modification of the Alcock-Paczynski test. In order to hide the background expansion history, the method employs a geometrical shift of each quasar (QSO) forest in wavelength space, once the quasar continuum has been fitted and the fluctuation field is extracted. The redshift positions for the QSO sample are also changed in a consistent manner. We show that the method remains effective when applied to real data, where contamination from metals and Lyman-$β$ is intrinsically mixed with the Lyman-$α$ forest. This limitation is primarily visible in the 1D correlation function, where other blinding strategies can mitigate the effect. To assess its effectiveness, the prescription is tested against a series of datasets of increasing complexity: from idealized low-noise mocks, to realistic DESI year one synthetic datasets, and finally to data from DESI first data release (DR1), using both the auto (Ly$α\times$Ly$α$) and cross (Ly$α\times$ QSO) correlations. We find that the method robustly shifts the BAO peak position from the 3D correlation functions to the expected value for cosmology changes of around 5% in the matter content, without altering the shape of the posteriors in the model parameters. In conclusion, this catalog-level blinding strategy is a viable method for cosmological inference with the Lyman-$α$ forest, particularly if a cross-analysis with other tracers using the same blinding strategy is pursued.

Perez-Sanchez, G. [Guanajuato U.] (ORCID:000900096↗

DOE OSTI2025

Persistent Sampling: Enhancing the Efficiency of Sequential Monte Carlo

Sequential Monte Carlo (SMC) samplers are powerful tools for Bayesian inference but suffer from high computational costs due to their reliance on large particle ensembles for accurate estimates. We introduce persistent sampling (PS), an extension of SMC that systematically retains and reuses particles from all prior iterations to construct a growing, weighted ensemble. By leveraging multiple importance sampling and resampling from a mixture of historical distributions, PS mitigates the need for excessively large particle counts, directly addressing key limitations of SMC such as particle impoverishment and mode collapse. Crucially, PS achieves this without additional likelihood evaluations-weights for persistent particles are computed using cached likelihood values. This framework not only yields more accurate posterior approximations but also produces marginal likelihood estimates with significantly lower variance, enhancing reliability in model comparison. Furthermore, the persistent ensemble enables efficient adaptation of transition kernels by leveraging a larger, decorrelated particle pool. Experiments on high-dimensional Gaussian mixtures, hierarchical models, and non-convex targets demonstrate that PS consistently outperforms standard SMC and related variants, including recycled and waste-free SMC, achieving substantial reductions in mean squared error for posterior expectations and evidence estimates, all at reduced computational cost. PS thus establishes itself as a robust, scalable, and efficient alternative for complex Bayesian inference tasks.

Karamanis, Minas↗