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DOE OSTI2026

Semi-Analytical Hierarchical Bayesian Inference of Nonlinear Model Structure in Stochastic Dynamics: Applied to Compartmental Models of Infectious Diseases

A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1979

Optimal estimation of large structure model errors

In-flight estimation of large structure model errors is usually required as a means of detecting inevitable deficiencies in large structure controller/estimator models. The present paper deals with a least-squares formulation which seeks to minimize a quadratic functional of the model errors. The properties of these error estimates are analyzed. It is shown that an arbitrary model error can be decomposed as the sum of two components that are orthogonal in a suitably defined function space. Relations between true and estimated errors are defined. The estimates are found to be approximations that retain many of the significant dynamics of the true model errors. Current efforts are directed toward application of the analytical results to a reference large structure model.

Rodriguez, G.↗

DOE OSTI2024

De novo atomic protein structure modeling for cryoEM density maps using 3D transformer and HMM

Accurately building 3D atomic structures from cryo-EM density maps is a crucial step in cryo-EM-based protein structure determination. Converting density maps into 3D atomic structures for proteins lacking accurate homologous or predicted structures as templates remains a significant challenge. Here, we introduce Cryo2Struct, a fully automated de novo cryo-EM structure modeling method. Cryo2Struct utilizes a 3D transformer to identify atoms and amino acid types in cryo-EM density maps, followed by an innovative Hidden Markov Model (HMM) to connect predicted atoms and build protein backbone structures. Cryo2Struct produces substantially more accurate and complete protein structural models than the widely used ab initio method Phenix. Additionally, its performance in building atomic structural models is robust against changes in the resolution of density maps and the size of protein structures.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1986

STEP and STEPSPL: Computer programs for aerodynamic model structure determination and parameter estimation

The successful parametric modeling of the aerodynamics for an airplane operating at high angles of attack or sideslip is performed in two phases. First the aerodynamic model structure must be determined and second the associated aerodynamic parameters (stability and control derivatives) must be estimated for that model. The purpose of this paper is to document two versions of a stepwise regression computer program which were developed for the determination of airplane aerodynamic model structure and to provide two examples of their use on computer generated data. References are provided for the application of the programs to real flight data. The two computer programs that are the subject of this report, STEP and STEPSPL, are written in FORTRAN IV (ANSI l966) compatible with a CDC FTN4 compiler. Both programs are adaptations of a standard forward stepwise regression algorithm. The purpose of the adaptation is to facilitate the selection of a adequate mathematical model of the aerodynamic force and moment coefficients of an airplane from flight test data. The major difference between STEP and STEPSPL is in the basis for the model. The basis for the model in STEP is the standard polynomial Taylor's series expansion of the aerodynamic function about some steady-state trim condition. Program STEPSPL utilizes a set of spline basis functions.

Batterson, J. G.↗

DOE OSTI2021

Multi‐fidelity digital twin structural model for a sub‐scale downwind wind turbine rotor blade

Abstract This paper presents the development of a multi‐fidelity digital twin structural model (virtual model) of an as‐built wind turbine blade. The goal is to develop and demonstrate an approach to produce an accurate and detailed model of the as‐built blade for use in verifying the performance of the operating two‐bladed, downwind rotor. The digital twin model development methodology, presented herein, involves a novel calibration process to integrate a wide range of information including design specifications, manufacturing information, and structural testing data (modal and static) to produce a multi‐fidelity digital twin structural model: a detailed high‐fidelity model (i.e., 3D finite element analysis [FEA]) and consistent beam‐type models for aeroelastic simulation. A key element is that the multi‐fidelity structural digital twin method follows the rotor from the stages of design, to manufacturing, then to the ground testing and field operation. The result of this comprehensive approach is an accurate multi‐fidelity digital twin structural model for the geometric, structural, and structural dynamic properties of the as‐built blade within a 1% match in mass properties, 3.2% in blade frequencies, and 6% in deflection. The different stages of processing this information within the methodology are discussed. The rotor examined is the SUMR‐Demonstrator (SUMR‐D), which was installed on the Controls Advanced Research Testbed (CART‐2) wind turbine at the National Wind Technology Center. The digital twin model developed here was utilized to design controllers to safely operate SUMR‐D in field tests, which are providing additional data for further evaluation and development of the multi‐fidelity digital twin structural model.

Chetan, Mayank↗

NASA NTRS1991

Engine Structures Modeling Software System (ESMOSS)

Engine Structures Modeling Software System (ESMOSS) is the development of a specialized software system for the construction of geometric descriptive and discrete analytical models of engine parts, components, and substructures which can be transferred to finite element analysis programs such as NASTRAN. The NASA Lewis Engine Structures Program is concerned with the development of technology for the rational structural design and analysis of advanced gas turbine engines with emphasis on advanced structural analysis, structural dynamics, structural aspects of aeroelasticity, and life prediction. Fundamental and common to all of these developments is the need for geometric and analytical model descriptions at various engine assembly levels which are generated using ESMOSS.

Source record↗

DOE OSTI2019

Model Structural Inference Using Local Dynamic Operators

This paper focuses on the problem of quantifying the effects of model-structure uncertainty in the context of time-evolving dynamical systems. This is motivated by multi-model uncertainty in computer physics simulations: developers often make different modeling choices in numerical approximations and process simplifications, leading to different numerical codes that ostensibly represent the same underlying dynamics. We consider model-structure inference as a two-step methodology: the first step is to perform system identification on numerical codes for which it is possible to observe the full state; the second step is structural uncertainty quantification, in which the goal is to search candidate models "close" to the numerical code surrogates for those that best match a quantity of interest (QOI) from some empirical data sets. Here, we (1) define a discrete, local representation of the structure of a partial differential equation, which we refer to as the "local dynamical operator" (LDO); (2) identify model structure nonintrusively from numerical code output; (3) nonintrusively construct a reduced-order model (ROM) of the numerical model through POD-DEIM-Galerkin projection; (4) perturb the ROM dynamics to approximate the behavior of alternate model structures; and (5) apply Bayesian inference and energy conservation laws to calibrate a LDO to a given QOI. We demonstrate these techniques using the two-dimensional rotating shallow water equations as an example system.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Coupling of regional geophysics and local soil-structure models in the EQSIM fault-to-structure earthquake simulation framework

Accurate understanding and quantification of the risk to critical infrastructure posed by future large earthquakes continues to be a very challenging problem. Earthquake phenomena are quite complex and traditional approaches to predicting ground motions for future earthquake events have historically been empirically based whereby measured ground motion data from historical earthquakes are homogenized into a common data set and the ground motions for future postulated earthquakes are probabilistically derived based on the historical observations. This procedure has recognized significant limitations, principally due to the fact that earthquake ground motions tend to be dictated by the particular earthquake fault rupture and geologic conditions at a given site and are thus very site-specific. Historical earthquakes recorded at different locations are often only marginally representative. There has been strong and increasing interest in utilizing large-scale, physics-based regional simulations to advance the ability to accurately predict ground motions and associated infrastructure response. However, the computational requirements for simulations at frequencies of engineering interest have proven a major barrier to employing regional scale simulations. In a U.S. Department of Energy Exascale Computing Initiative project, the EQSIM application development is underway to create a framework for fault-to-structure simulations. This framework is being prepared to exploit emerging exascale platforms in order to overcome computational limitations. This article presents the essential methodology and computational workflow employed in EQSIM to couple regional-scale geophysics models with local soil-structure models to achieve a fully integrated, complete fault-to-structure simulation framework. Here, the computational workflow, accuracy and performance of the coupling methodology are illustrated through example fault-to-structure simulations.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2001

Structural models of the MscL gating mechanism

Three-dimensional structural models of the mechanosensitive channel of large conductance, MscL, from the bacteria Mycobacterium tuberculosis and Escherichia coli were developed for closed, intermediate, and open conformations. The modeling began with the crystal structure of M. tuberculosis MscL, a homopentamer with two transmembrane alpha-helices, M1 and M2, per subunit. The first 12 N-terminal residues, not resolved in the crystal structure, were modeled as an amphipathic alpha-helix, called S1. A bundle of five parallel S1 helices are postulated to form a cytoplasmic gate. As membrane tension induces expansion, the tilts of M1 and M2 are postulated to increase as they move away from the axis of the pore. Substantial expansion is postulated to occur before the increased stress in the S1 to M1 linkers pulls the S1 bundle apart. During the opening transition, the S1 helices and C-terminus amphipathic alpha-helices, S3, are postulated to dock parallel to the membrane surface on the perimeter of the complex. The proposed gating mechanism reveals critical spatial relationships between the expandable transmembrane barrel formed by M1 and M2, the gate formed by S1 helices, and "strings" that link S1s to M1s. These models are consistent with numerous experimental results and modeling criteria.

NASA Discipline Cell Biology↗

DOE OSTI2021

Feedback density and causal complexity of simulation model structure

Measures of simulation model complexity generally focus on outputs; we propose measuring the complexity of a model’s causal structure to gain insight into its fundamental character. This article introduces tools for measuring causal complexity. First, we introduce a method for developing a model’s causal structure diagram, which characterises the causal interactions present in the code. Causal structure diagrams facilitate comparison of simulation models, including those from different paradigms. Next, we develop metrics for evaluating a model’s causal complexity using its causal structure diagram. We discuss cyclomatic complexity as a measure of the intricacy of causal structure and introduce two new metrics that incorporate the concept of feedback, a fundamental component of causal structure. The first new metric introduced here is feedback density, a measure of the cycle-based interconnectedness of causal structure. The second metric combines cyclomatic complexity and feedback density into a comprehensive causal complexity measure. Finally, we demonstrate these complexity metrics on simulation models from multiple paradigms and discuss potential uses and interpretations. These tools enable direct comparison of models across paradigms and provide a mechanism for measuring and discussing complexity based on a model’s fundamental assumptions and design.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

The multi-assumption architecture and testbed (MAAT v1.0): R code for generating ensembles with dynamic model structure and analysis of epistemic uncertainty from multiple sources

Abstract. Here, computer models are ubiquitous tools used to represent systems across many scientific and engineering domains. For any given system, many computer models exist, each built on different assumptions and demonstrating variability in the ways in which these systems can be represented. This variability is known as epistemic uncertainty, i.e. uncertainty in our knowledge of how these systems operate. Two primary sources of epistemic uncertainty are (1) uncertain parameter values and (2) uncertain mathematical representations of the processes that comprise the system. Many formal methods exist to analyse parameter-based epistemic uncertainty, while process-representation-based epistemic uncertainty is often analysed post hoc, incompletely, informally, or is ignored. In this model description paper we present the multi-assumption architecture and testbed (MAAT v1.0) designed to formally and completely analyse process-representation-based epistemic uncertainty. MAAT is a modular modelling code that can simply and efficiently vary model structure (process representation), allowing for the generation and running of large model ensembles that vary in process representation, parameters, parameter values, and environmental conditions during a single execution of the code. MAAT v1.0 approaches epistemic uncertainty through sensitivity analysis, assigning variability in model output to processes (process representation and parameters) or to individual parameters. In this model description paper we describe MAAT and, by using a simple groundwater model example, verify that the sensitivity analysis algorithms have been correctly implemented. The main system model currently coded in MAAT is a unified, leaf-scale enzyme kinetic model of C 3 photosynthesis. In the Appendix we describe the photosynthesis model and the unification of multiple representations of photosynthetic processes. The numerical solution to leaf-scale photosynthesis is verified and examples of process variability in temperature response functions are provided. For rapid application to new systems, the MAAT algorithms for efficient variation of model structure and sensitivity analysis are agnostic of the specific system model employed. Therefore MAAT provides a tool for the development of novel or toy models in many domains, i.e. not only photosynthesis, facilitating rapid informal and formal comparison of alternative modelling approaches.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1992

Track structure model of cell damage in space flight

The phenomenological track-structure model of cell damage is discussed. A description of the application of the track-structure model with the NASA Langley transport code for laboratory and space radiation is given. Comparisons to experimental results for cell survival during exposure to monoenergetic, heavy-ion beams are made. The model is also applied to predict cell damage rates and relative biological effectiveness for deep-space exposures.

Katz, Robert↗

DOE OSTI2019

Model Structure and Climate Data Uncertainty in Historical Simulations of the Terrestrial Carbon Cycle (1850–2014)

Abstract The divergence among Earth system models in the terrestrial carbon cycle has prompted interest in how to reduce uncertainty. Previous studies have identified model structural uncertainty arising from process parameterizations and parameter values. The current study highlights the importance of climate forcing in generating carbon cycle uncertainty. We use simulations in which three models (Community Land Model version 4 (CLM4), CLM4.5, CLM5) with substantially different carbon cycles are forced with two climate reconstructions (CRUNCEPv7, Global Soil Wetness Project 3 version 1 (GSWP3v1)) to examine the contributions of model structure and climate to uncertainty in the carbon cycle over the period 1850–2014. Climate uncertainty for global annual net biome production exceeds one third of total uncertainty (defined as the sum of climate and model structure uncertainty) in the first half of the twentieth century, but declines after the 1950s. Global annual gross primary productivity, net primary productivity, heterotrophic respiration, and vegetation and soil carbon stocks have substantial climate uncertainty (relative to total uncertainty) throughout the simulation period. Climate forcing contributes more than one half of total uncertainty for these carbon cycle fluxes and stocks throughout boreal North America and Eurasia, some midlatitude regions, and in eastern Amazonia and western equatorial Africa during the decade 2000–2009. Comparison with observationally based data sets of the carbon cycle using model benchmarking methods provides insight into strengths and deficiencies among models and climate forcings, but we caution against overreliance on benchmarking to discriminate among models. The conceptualization of uncertainty arising from this study implies embracing multiple feasible model simulations rather than focusing on which model or simulation is best.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1944

Applicability of Similarity Principles to Structural Models

A systematic account is given in part I of the use of dimensional analysis in constructing similarity conditions for models and structures. The analysis covers large deflections, buckling, plastic behavior, and materials with nonlinear stress-strain characteristics, as well as the simpler structural problems. (author)

Goodier, J N↗

NASA NTRS1984

Applications of model structure determination to flight test data

Several statistical and information criteria need to be considered when selecting an adequate model. Incorrect stability and control derivates result from inadequate aerodynamic model structure. Stepwise regression is used to determine the structure for an adequate model. Flight data which covers a nonlinear aerodynamic model range may be analyzed as a single data set or partitioned into several distinct sets. Stepwise regression for model structure detemination and parameter estimation was successfully applied to three aircraft types (single engine general aviation, unaugmented modern jet fighter, jet transport).

Batterson, J. G.↗

NASA NTRS1983

NASTRAN structural model for the large 64-meter antenna pedestal. Part 2: Improved model

Static analysis and a computer structural model for the large 64-m antenna pedestal are developed using the MSC version of the NASTRAN program. This improved pedestal model includes the launch areas and the actual pressure pattern of the oil under the hydrostatic bearing pad. The results obtained from the new improved model have indicated that the deflections due to pad loads are in good agreement with field measurements. The top surface deflection of the pedestal obtained from the NASTRAN model is used as an input to the oil film computer program to determine the minimum oil film thickness under the pad.

Chian, C. T.↗

NASA NTRS1984

Development of a thermal and structural model for a NASTRAN finite-element analysis of a hypersonic wing test structure

The development of a thermal and structural model for a hypersonic wing test structure using the NASTRAN finite-element method as its primary analytical tool is described. A detailed analysis was defined to obtain the temperature and thermal stress distribution in the whole wing as well as the five upper and lower root panels. During the development of the models, it was found that the thermal application of NASTRAN and the VIEW program, used for the generation of the radiation exchange coefficients, were definicent. Although for most of these deficiencies solutions could be found, the existence of one particular deficiency in the current thermal model prevented the final computation of the temperature distributions. A SPAR analysis of a single bay of the wing, using data converted from the original NASTRAN model, indicates that local temperature-time distributions can be obtained with good agreement with the test data. The conversion of the NASTRAN thermal model into a SPAR model is recommended to meet the immediate goal of obtaining an accurate thermal stress distribution.

Lameris, J.↗

NASA NTRS1983

Determination of airplane model structure from flight data using splines and stepwise regression

A procedure for the determination of airplane model structure from flight data is presented. The model is based on a polynomial spline representation of the aerodynamic coefficients, and the procedure is implemented by use of a stepwise regression. First, a form of the aerodynamic force and moment coefficients amenable to the utilization of splines is developed. Next, expressions for the splines in one and two variables are introduced. Then the steps in the determination of an aerodynamic model structure and the estimation of parameters are discussed briefly. The focus is on the application to flight data of the techniques developed.

Klein, V.↗