Structure-mining: screening structure models by automated fitting to the atomic pair distribution function over large numbers of models
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99 GENERAL AND MISCELLANEOUS↗
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Continuous mutual improvement of macromolecular structure models in the PDB and of X-ray crystallographic software: the dual role of deposited experimental data
Macromolecular structures deposited in the PDB can and should be continually reinterpreted and improved on the basis of their accompanying experimental X-ray data, exploiting the steady progress in methods and software that the deposition of such data into the PDB on a massive scale has made possible. Accurate crystal structures of macromolecules are of high importance in the biological and biomedical fields. Models of crystal structures in the Protein Data Bank (PDB) are in general of very high quality as deposited. However, methods for obtaining the best model of a macromolecular structure from a given set of experimental X-ray data continue to progress at a rapid pace, making it possible to improve most PDB entries after their deposition by re-analyzing the original deposited data with more recent software. This possibility represents a very significant departure from the situation that prevailed when the PDB was created, when it was envisioned as a cumulative repository of static contents. A radical paradigm shift for the PDB is therefore proposed, away from the static archive model towards a much more dynamic body of continuously improving results in symbiosis with continuously improving methods and software. These simultaneous improvements in methods and final results are made possible by the current deposition of processed crystallographic data (structure-factor amplitudes) and will be supported further by the deposition of raw data (diffraction images). It is argued that it is both desirable and feasible to carry out small-scale and large-scale efforts to make this paradigm shift a reality. Small-scale efforts would focus on optimizing structures that are of interest to specific investigators. Large-scale efforts would undertake a systematic re-optimization of all of the structures in the PDB, or alternatively the redetermination of groups of structures that are either related to or focused on specific questions. All of the resulting structures should be made generally available, along with the precursor entries, with various views of the structures being made available depending on the types of questions that users are interested in answering.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Structural modeling of liquid and amorphous Al91Tb9 by Monte Carlo simulations
Not Available
Ovun, M.↗
Quantifying model structural error: Efficient Bayesian calibration of a regional groundwater flow model using surrogates and a data-driven error model
Groundwater model structural error is ubiquitous, due to simplification and/or misrepresentation of real aquifer systems. During model calibration, the basic hydrogeological parameters may be adjusted to compensate for structural error. This may result in biased predictions when such calibrated models are used to forecast aquifer responses to new forcing. Here, we investigate the impact of model structural error on calibration and prediction of a real-world groundwater flow model, using a Bayesian method with a data-driven error model to explicitly account for model structural error. The error-explicit Bayesian method jointly infers model parameters and structural error and thereby reduces parameter compensation. In this study, Bayesian inference is facilitated using high performance computing and fast surrogate models (based on machine learning techniques) as a substitute for the computationally expensive groundwater model. We demonstrate that with explicit treatment of model structural error, the Bayesian method yields parameter posterior distributions that are substantially different from those derived using classical Bayesian calibration that does not account for model structural error. We also found that the error-explicit Bayesian method gives signficantly more accurate prediction along with reasonable credible intervals. Finally, through variance decomposition, we provide a comprehensive assessment of prediction uncertainty contributed from parameter, model structure, and measurement uncertainty. The results suggest that the error-explicit Bayesian approach provides a solution to real-world modeling applications for which data support the presence of model structural error, yet model deficiency cannot be specifically identified or corrected.
54 ENVIRONMENTAL SCIENCES↗
The Role of Input Assumptions and Model Structures in Projections of Variable Renewable Energy: A Multi-Model Perspective of the U.S. Electricity System
Recent wind and solar deployment in the United States has grown at unprecedented rates, but the extent to which this growth will continue is a key question. Energy-economic planning models are often used to develop future projections of these technologies, and although it is well-understood that model outcomes are sensitive to assumptions about technology developments and market conditions, it is less clear how underlying model structures might impact outcomes. For wind and solar technologies, model structures might be an even larger driver due to the complexity required to represent their variability, uncertainty, and location-dependence. Here, we apply three state-of-the-art electric sector planning models to evaluate variable renewable generation under different conditions with both harmonized and native input assumptions to isolate the impact that model structures might have on deployment outcomes. We find growth in wind and solar deployment in all models under a business-as-usual scenario (without new policies), where the median value for variable renewable energy generation share is found to be 27% by 2050 - but with a wide range of estimates (18-43%), types of renewable technologies deployed, and regional distributions across models. With harmonized assumptions about technology costs and market conditions the range narrows slightly, but a large range in penetration outcomes remains (24-41% by 2050) suggesting that model representations play significant roles in projections of future wind and solar deployment. We also assess the implications of achieving 55% wind and solar penetration by 2050 - to assess potential challenges at higher penetration levels - and the magnitude of variable generation under a carbon-constrained future. Finally, we identify research needs to better assess the future deployment of variable renewable energy.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Hierarchical, rotation‐equivariant neural networks to select structural models of protein complexes
Abstract Predicting the structure of multi‐protein complexes is a grand challenge in biochemistry, with major implications for basic science and drug discovery. Computational structure prediction methods generally leverage predefined structural features to distinguish accurate structural models from less accurate ones. This raises the question of whether it is possible to learn characteristics of accurate models directly from atomic coordinates of protein complexes, with no prior assumptions. Here we introduce a machine learning method that learns directly from the 3D positions of all atoms to identify accurate models of protein complexes, without using any precomputed physics‐inspired or statistical terms. Our neural network architecture combines multiple ingredients that together enable end‐to‐end learning from molecular structures containing tens of thousands of atoms: a point‐based representation of atoms, equivariance with respect to rotation and translation, local convolutions, and hierarchical subsampling operations. When used in combination with previously developed scoring functions, our network substantially improves the identification of accurate structural models among a large set of possible models. Our network can also be used to predict the accuracy of a given structural model in absolute terms. The architecture we present is readily applicable to other tasks involving learning on 3D structures of large atomic systems.
Eismann, Stephan↗
Accounting for erroneous model structures in biokinetic process models
In engineering practice, model-based design requires not only a good process-based model, but also a good description of stochastic disturbances and measurement errors to learn credible parameter values from observations. However, typical methods use Gaussian error models, which often cannot describe the complex temporal patterns of residuals. Consequently, this results in overconfidence in the identified parameters and, in turn, optimistic reactor designs. Here, we assess the strengths and weaknesses of a method to statistically describe these patterns with autocorrelated error models. This method produces increased widths of the credible prediction intervals following the inclusion of the bias term, in turn leading to more conservative design choices. However, we also show that the augmented error model is not a universal tool, as its application cannot guarantee the desired reliability of the resulting wastewater reactor design.
42 ENGINEERING↗
A dynamic data-driven method for dealing with model structural error in soil moisture data assimilation
Attributing to the flexibility in considering various types of observation error and model error, data assimilation has been increasingly applied to dynamically improve soil moisture modeling in many hydrological practices. However, accurate characterization of model error, especially the part caused by defective model structure, presents a significant challenge to the successful implementation of data assimilation. Model structural error has received limited attention relative to parameter and input errors, mainly due to our poor understanding of structural inadequacy and the difficulties in parameterizing structural error. In this paper, we present a dynamic data-driven approach to estimate the model structural error in soil moisture data assimilation without the need for identifying error generation mechanism or specifying particular form for the error model. The error model is based on the Gaussian process regression and then integrated into the ensemble Kalman filter (EnKF) to form a hybrid method for dealing with multi-source model errors. Two variants of the hybrid method in terms of two different error correction manners are proposed. The effectiveness of the proposed method is tested through a suit of synthetic cases and a real-world case. Results demonstrate the potential of the proposed hybrid method for estimating model structural error and providing improved model predictions. Compared to the traditional EnKF without explicitly considering the model structural error, parameter compensation issue is obviously reduced and soil moisture retrieval is substantially improved.
54 ENVIRONMENTAL SCIENCES↗
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↗
Hierarchical mixture of experts and diagnostic modeling approach to reduce hydrologic model structural uncertainty
In most water resources applications, a single model structure might be inadequate to capture the dynamic multi-scale interactions among different hydrological processes. Calibrating single models for dynamic catchments, where multiple dominant processes exist, can result in displacement of errors from structure to parameters, which in turn leads to over-correction and biased predictions. An alternative to a single model structure is to develop local expert structures that are effective in representing the dominant components of the hydrologic process and adaptively integrate them based on an indicator variable. In this study, the Hierarchical Mixture of Experts (HME) framework is applied to integrate expert model structures representing the different components of the hydrologic process. Various signature diagnostic analyses are used to assess the presence of multiple dominant processes and the adequacy of a single model, as well as to identify the structures of the expert models. The approaches are applied for two distinct catchments, the Guadalupe River (Texas) and the French Broad River (North Carolina) from the Model Parameter Estimation Experiment (MOPEX), using different structures of the HBV model. Furthermore, the results show that the HME approach has a better performance over the single model for the Guadalupe catchment, where multiple dominant processes are witnessed through diagnostic measures. Whereas, the diagnostics and aggregated performance measures prove that French Broad has a homogeneous catchment response, making the single model adequate to capture the response.
54 ENVIRONMENTAL SCIENCES↗
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↗
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↗
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↗