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At least 217 records · Page 12

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING

Karhunen–Loève deep learning method for surrogate modeling and approximate Bayesian parameter estimation

We evaluate the performance of the Karhunen-Loève Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunen-Loève (KL) expansions are used for the dimensionality reduction of the number of unknown parameters and variables, and a deep neural network is employed to relate the reduced space of parameters to that of the state variables. The KL-DNN surrogate model is used to formulate a maximum-a-posteriori-like least-squares problem, which is randomized to draw samples of the posterior distribution of the parameters. We test the proposed framework for a hypothetical unconfined aquifer via comparison with the forward MODFLOW and inverse PEST++ iterative ensemble smoother (IES) solutions as well as the state-of-the-art Fourier neural operator (FNO) and deep operator networks (DeepONets) operator learning surrogate models. Our results show that the KL-DNN surrogate model outperforms FNO and DeepONet for forward predictions. For solving inverse problems, the randomized algorithm provides the same or more accurate Bayesian predictions of the parameters than IES as evidenced by the higher log-predictive probability of both the estimated parameter field and the forecast hydraulic head. The posterior mean obtained from the randomized algorithm is closer to the reference parameter field than that obtained with FNO as the maximum a posteriori estimate.

Approximate Bayesian inference

Rapid assessment of the creep rupture life of metals: A model enabling experimental design

Prediction of the creep rupture life of engineering metals is critical for qualification and design of new materials. The use of long-term creep tests and the need to quantify the performance variability in a priori similar systems hinder the rapid creep assessment of a given material. Therefore, it is essential to develop methods that can extrapolate the long-term performance of alloys and the associated variability from short-term experiments. To this end, this study introduces a new model which enables the estimation of the rupture life of a material for a given stress and temperature. This model relies on two components. First, a new relation for the minimum creep rate (MCR) of materials is introduced. It includes a stress dependent stress exponent allowing the model to capture the variation of MCR across a wide range of temperatures and stresses. Second, employing the Monkman-Grant (MG) law, we establish a relation between stress, temperature and creep rupture life. Together, these two elements yield a new closed-form mathematical expression for the Larson Miller parameter as a function of stress and temperature. This expression captures the creep rupture time for many metals (Gr91, Copper, Gr122 and 347H) and compares favorably with alternate empirical approaches. The model is then used to assess the minimum duration of creep rates necessary to qualify the material up to 100000h. Furthermore, it is found that depending on the material system, creep tests as few as five limited to 5000 h for steels (Gr91, Gr122, 347H) and 100 h for copper are sufficient to model creep lifetimes. Finally, using a Bayesian inference-based approach to calibrate the model, we demonstrate that variability in rupture life can be captured via the quantification of the uncertainty in the model parameters and extrapolated from a limited number of short to moderately short creep tests; thereby paving the way for accelerated creep testing.

36 MATERIALS SCIENCE

Unlocking hidden information in sparse small-angle neutron scattering measurements

Hypothesis Small-Angle Neutron Scattering (SANS) is a powerful technique for studying soft matter systems such as colloids, polymers, and lyotropic phases, providing nanoscale structural insights. However, its effectiveness is limited by low neutron flux, leading to long acquisition times and noisy data. Here, we hypothesize that Bayesian statistical inference using Gaussian Process Regression (GPR) can reconstruct high-fidelity scattering data from sparse measurements by leveraging intensity smoothness and continuity. Experiments and Simulations The method was benchmarked computationally and validated through SANS experiments on various soft matter systems, including wormlike micelles, colloidal suspensions, polymeric structures, and lyotropic phases. GPR-based inference was applied to both experimental and synthetic data to evaluate its effectiveness in noise reduction and intensity reconstruction. Findings GPR significantly enhances SANS data quality and therefore reducing measurement times by up to two orders of magnitude. This cost-effective approach maximizes experimental efficiency, enabling high-throughput studies and real-time monitoring of dynamic systems. It is particularly beneficial for weakly scattering and time-sensitive studies. Beyond SANS, this framework applies to other low-SNR techniques, including laboratory-based small-angle X-ray scattering and various dynamical scattering methods. Furthermore, it offers transformative potential for compact neutron sources, enhancing their viability for structural analysis in resource-limited settings.

Small angle neutron scattering

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

Shear wave propagation in a liquid crystal: An inelastic X-ray scattering study

For this work, we investigated the spectrum of density fluctuations of a liquid crystal, CB7CB, in two different orientations by using high-resolution inelastic x-ray scattering. Our analysis, based on Bayesian principles, revealed that high-frequency collective excitations propagate through this mesoscale-ordered sample in a peculiar manner that lies somewhere between those observed in liquids and crystalline systems. Interestingly, when we probed longer length scales, a more pronounced solid-like response emerged. This was mainly characterized by anomalously sharp inelastic excitations and the onset of shear mode propagation. Comparison with previous x-ray diffraction results suggests a correlation between the observed behavior and the mesogen arrangement.

36 MATERIALS SCIENCE

ETHOS: An automated framework to generate multi-fidelity constitutive data tables and propagate uncertainties to hydrodynamic simulations

Accurate constitutive data, such as equations of state and plasma transport coefficients, are necessary for reliable hydrodynamic simulations of plasma systems such as fusion targets, planets, and stars. Here, we develop a framework for automatically generating transport-coefficient tables using a parameterized model that incorporates data from both high-fidelity sources (e.g., density functional theory calculations and reference experiments) and lower-fidelity sources (e.g., average-atom and analytic models). The framework incorporates uncertainties from these multi-fidelity sources, generating ensembles of optimally diverse tables that are suitable for uncertainty quantification of hydrodynamic simulations. We illustrate the utility of the framework with magnetohydrodynamic simulations of magnetically launched flyer plates, which are used to measure material properties in pulsed-power experiments. We explore how changes in the uncertainties assigned to the multi-fidelity data sources propagate to changes in simulation outputs and find that our simulations are most sensitive to uncertainties near the melting transition. The presented framework enables computationally efficient uncertainty quantification that readily incorporates new high-fidelity measurements or calculations and identifies plasma regimes where additional data will have high impact.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Scalable quantum computational science: A perspective from block-encodings and polynomial transformations

Significant developments made in quantum hardware and error correction recently have been driving quantum computing toward practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications in computational sciences. In this perspective article, we propose several properties that scalable quantum computational science methods should possess. We further discuss how block-encodings and polynomial transformations can potentially serve as a unified framework with the desired properties. Recent advancements on these topics are presented, including the construction and assembly of block-encodings, and various generalizations of quantum signal processing (QSP) algorithms to perform polynomial transformations. The scalability of QSP methods on parallel and distributed quantum architectures is also highlighted. Promising applications in simulation and observable estimation in chemistry, physics, and optimization problems are presented. We hope this perspective serves as a gentle introduction to state-of-the-art quantum algorithms for the computational science community and inspires future development of scalable quantum computational science methodologies that bridge theory and practice.

Bayesian inference

Assessing the design of integrated methane sensing networks

Abstract While methane is the second largest contributor to global warming after carbon dioxide, it has a larger warming effect over a much shorter lifetime. Despite accelerated technological efforts to radically reduce global carbon dioxide emissions, rapid reductions in methane emissions are needed to limit near-term warming. Being primarily emitted as a byproduct from agricultural activities and energy extraction, methane is currently monitored via bottom–up (i.e. activity level) or top–down (via airborne or satellite retrievals) approaches. However, significant methane leaks remain undetected and emission rates are challenging to characterize with current monitoring frameworks. In this paper, we study the design of a layered monitoring approach that combines bottom–up and top–down approaches as an integrated sensing network. By recognizing that varying meteorological conditions and emission rates impact the efficacy of bottom–up monitoring, we develop a probabilistic approach to optimal sensor placement in its bottom–up network. Subsequently, we derive an inverse Bayesian framework to quantify the improvement that a design-optimized integrated framework has on emission-rate quantifications and their uncertainties. We find that under realistic meteorological conditions, the overall error in estimating the true emission rates is approximately 1.3 times higher, with their uncertainties being approximately 2.4 times higher, when using a randomized network over an optimized network, highlighting the importance of optimizing the design of integrated methane sensing networks. Further, we find that optimized networks can improve scenario coverage fractions by more than a factor of 2 over experimentally-studied networks, and identify a budget threshold beyond which the rate of optimized-network coverage improvement exhibits diminishing returns, suggesting that strategic sensor placement is also crucial for maximizing network efficiency.

54 ENVIRONMENTAL SCIENCES

Analysis and optimization of seismic monitoring networks with Bayesian optimal experimental design

SUMMARY Monitoring networks increasingly aim to assimilate data from a large number of diverse sensors covering many sensing modalities. Bayesian optimal experimental design (OED) seeks to identify data, sensor configurations or experiments which can optimally reduce uncertainty and hence increase the performance of a monitoring network. Information theory guides OED by formulating the choice of experiment or sensor placement as an optimization problem that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge and models of expected observation data. Therefore, within the context of seismo-acoustic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize a sensor network’s ability to locate seismic events from arrival time data of detected seismic phases at the regional-scale. This framework requires five elements: (i) A likelihood function that describes the distribution of detection and traveltime data from the sensor network, (ii) A prior distribution that describes a priori belief about seismic events, (iii) A Bayesian solver that uses a prior and likelihood to identify the posterior distribution of seismic events given the data, (iv) An algorithm to compute EIG about seismic events over a data set of hypothetical prior events, (v) An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we explore many relevant questions to monitoring such as: how to trade off sensor fidelity and earth model uncertainty; how sensor types, number and locations influence uncertainty; and how prior models and constraints influence sensor placement.

58 GEOSCIENCES

Bayesian event categorization matrix approach for explosion monitoring

Current efforts to correctly categorize natural events from suspected explosion sources with data that is collected by ground- or space-based sensors presents historical challenges that remain unaddressed by the Event Categorization Matrix (ECM) model. Smaller historical events (lower yield explosions) may have data available from fewer measurement techniques than are available today, and therefore, a historical event record can lack a complete set of discriminants. The covariance structures can also differ between such observations of event (source-type) categories. Both obstacles are problematic for the classic ECM model. Our work addresses this gap and presents a Bayesian update to the previous ECM model, termed the Bayesian Event Categorization Matrix model, which can be trained on partial observations and does not rely on a pooled covariance structure. We further augment the ECM model with Bayesian Decision Theory so that false negative or false positive rates of an event categorization can be reduced in an intuitive manner. To demonstrate improved categorization rates for the Bayesian Event Categorization Matrix model, we compare an array of Bayesian and classic models with multiple performance metrics using Monte Carlo experiments. We use both synthetic and real data. Our Bayesian models show consistent gains in overall accuracy and lower false negative rates relative to the classic ECM model. Here, we propose future avenues to improve Bayesian Event Categorization Matrix models’ decision making and predictive capability.

58 GEOSCIENCES

Sharp detection of low-dimensional structure in probability measures via dimensional logarithmic Sobolev inequalities

Identifying low-dimensional structure in high-dimensional probability measures is an essential pre-processing step for efficient sampling. To identify this structure, we approximate the target measure as a perturbation of an arbitrary reference measure along a few directions in $\mathbb{R}^{d}$. These directions are determined by minimizing an upper bound on the Kullback–Leibler (KL) divergence between the target and its approximation. Our contribution improves upon previous works by leveraging dimensional logarithmic Sobolev inequalities to refine the bound on the KL divergence. These inequalities lead to a uniformly tighter bound on the KL divergence, thereby enhancing the identification of the most significant perturbation directions. In particular, when the target and reference are both Gaussian, minimizing the resulting bound is equivalent to minimizing the KL divergence. We further demonstrate the applicability of this analysis to the squared Hellinger distance, where analogous reasoning shows that the dimensional Poincaré inequality offers improved bounds.

Bayesian inference

Combining Observations and Models: A Review of the CARDAMOM Framework for Data‐Constrained Terrestrial Ecosystem Modeling

The rapid increase in the volume and variety of terrestrial biosphere observations (i.e., remote sensing data and in situ measurements) offers a unique opportunity to derive ecological insights, refine process‐based models, and improve forecasting for decision support. However, despite their potential, ecological observations have primarily been used to benchmark process‐based models, as many past and current models lack the capability to directly integrate observations and their associated uncertainties for parameterization. In contrast, data assimilation frameworks such as the CARbon DAta MOdel fraMework (CARDAMOM) and its suite of process‐based models, known as the Data Assimilation Linked Ecosystem Carbon Model (DALEC), are specifically designed for model‐data fusion. This review, motivated by a recent CARDAMOM community workshop, examines the development and applications of CARDAMOM, with an emphasis on its role in advancing ecosystem process understanding. CARDAMOM employs a Bayesian approach, using a Markov Chain Monte Carlo algorithm to enable data‐driven calibration of DALEC parameters and initial states (i.e., carbon pool sizes) through observation operators. CARDAMOM's unique ability to retrieve localized model process parameters from diverse datasets—ranging from in situ measurements to global satellite observations—makes it a highly flexible tool for analyzing spatially variable ecosystem responses to environmental change. However, assimilating these data also presents challenges, including data quality issues that propagate into model skill, as well as trade‐offs between model complexity, parameter equifinality, and predictive performance. We discuss potential solutions to these challenges, such as reducing parameter equifinality by incorporating new observations. This review also offers community recommendations for incorporating emerging datasets, integrating machine learning techniques, strengthening collaboration with remote sensing, field, and modeling communities, and expanding CARDAMOM's relevance for localized ecosystem monitoring and decision‐making. CARDAMOM enables a deep, mechanistic understanding of terrestrial ecosystem dynamics that cannot be achieved through empirical analyses of observational datasets or weakly constrained models alone.

Bayesian inference

Testing T2K’s Bayesian constraints with priors in alternate parameterisations

Bayesian analysis results require a choice of prior distribution. In long-baseline neutrino oscillation physics, the usual parameterisation of the mixing matrix induces a prior that privileges certain neutrino mass and flavour state symmetries. Here we study the effect of privileging alternate symmetries on the results of the T2K experiment. We find that constraints on the level of CP violation (as given by the Jarlskog invariant) are robust under the choices of prior considered in the analysis. On the other hand, the degree of octant preference for the atmospheric angle depends on which symmetry has been privileged.

Bayesian Inference

TCAD-Machine Learning Enabled TID Compact Model Development for Commercial SiC MOSFET

We propose a TCAD (Technology Computer Aided Design)-machine learning coupled approach that combines a TCAD tool (Charon), optimization/uncertainty quantification tool (Dakota), surrogate models, and Bayesian learning capabilities. The coupling approach is used for accurate modeling and calibration of total ionizing dose (TID) induced threshold voltage (V th ) shifts in Commercial-Off-The-Shelf (COTS) semiconductor devices and to develop physics-informed TID compact models. This versatile approach is applied to model the TID effect in an exemplar COTS 3.3 kV SiC power MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor). With the Charon-Dakota coupling, we can determine key device geometry and doping values based on device physics, which are difficult to obtain or not available for COTS devices but important for TCAD simulation; additionally, we can efficiently generate thousands of simulation results in a large parameter space, which makes it possible to develop data-driven surrogate models and perform Bayesian calibration. Utilizing the full tool-coupling approach, we achieve calibrated TCAD simulation models that accurately capture the average TID-induced V th shifts behavior with total doses and V th shifts saturation at high doses as observed in experimental data. More importantly, the calibrated TCAD simulations are obtained with determined TID model parameters (e.g., hole trap density and capture cross section) values that contain well quantified uncertainties. Furthermore, we can isolate and quantify the noises that are not captured by the TCAD models but exist in the measured data due to measurements and devices variabilities. Lastly, the calibrated surrogate models are used to develop physics-informed TID compact models. The method is generalizable to other devices and/or radiation conditions with few modifications and can provide well-determined uncertainties.

COTS

py-boomer v0.1.0

Py-BOOMER (Python Bayesian OWL Ontology MErgER in Python) is a probabilistic reasoning system for knowledge representation and ontological reasoning with uncertainty. Itnables reasoning over probabilistic facts and taxonomic relationships, finding the most likely consistent interpretation of potentially conflicting assertions. It uses a combination of graph-based reasoning and Bayesian probabilistic inference. Key features: Represent probabilistic ontological statements Reason over class subsumption hierarchies Evaluate class equivalence relationships Detect and resolve logical inconsistencies Calculate posterior probabilities for each assertion

Mungall, Chris [Lawrence Berkeley National Laborat

Preliminary Results on Bayesian Inverse UQ for OECD/NEA WPNCS Subgroup 14 Benchmark Exercise for Error Recovery and Experimental Coverage

The Organization for Economic Cooperation and Development (OECD) Working Party on Nucelar Criticality Safety (WPNCS) has proposed a benchmark exercise representative of neutronic behavior in criticality experiments. Here, the goal is to develop confidence in data assimilation techniques used to adjust nuclear data. Participants are given synthetic experimental models with associated measured data and asked to estimate the model parameters given the model and measurements as well as provide predictions for separate application models. In this work, we performed data assimilation using Bayesian inverse Uncertainty Quantification (UQ) with machine learning surrogate models to produce posterior parameter distributions for the requested parameters and posterior predictive distributions for the requested responses. Several experimental models are shown to insufficiently inform the posterior parameter distributions for the applications involved. However, given sufficient experimental data, posterior parameter estimates yielded reduced uncertainty in the response predictions of interest while covering the experimental data.

Bayesian Inference