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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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↗
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↗
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↗
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↗
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↗
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↗
OpenMDlr: parallel, open-source tools for general protein structure modeling and refinement from pairwise distances
Easy-to-use, open-source, general-purpose programs for modeling a protein structure from inter-atomic distances are needed for modeling from experimental data and refinement of predicted protein structures. OpenMDlr is an open-source Python package for modeling protein structures from pairwise distances between any atoms, and optionally, dihedral angles. Finally, we provide a user-friendly input format for harnessing modern biomolecular force fields in an easy-to-install package that can efficiently make use of multiple compute cores.
59 BASIC BIOLOGICAL SCIENCES↗
Structural Models of the Rhodopseudomonas palustris Proteome
This dataset contains the structural models for the primary transcripts of the Rhodopseudomonas palustris proteome. For each protein, the five models inferred from AlphaFold 2 are provided. The largest pTM-scoring model for each protein was energy minimized; this minimized structure as well as its AlphaFold pickle output file are also provided. This set of structures represent an alternate source of models for the R. palustris proteome to those available in the AlphaFold Protein Structure Database.
59 BASIC BIOLOGICAL SCIENCES↗
Federating Structural Models and Data: Outcomes from A Workshop on Archiving Integrative Structures
Structures of biomolecular systems are increasingly computed by integrative modeling. In this approach, a structural model is constructed by combining information from multiple sources, including varied experimental methods and prior models. In 2019, a Workshop was held as a Biophysical Society Satellite Meeting to assess progress and discuss further requirements for archiving integrative structures. The primary goal of the Workshop was to build consensus for addressing the challenges involved in creating common data standards, building methods for federated data exchange, and developing mechanisms for validating integrative structures. The summary of the Workshop and the recommendations that emerged are presented here.
59 BASIC BIOLOGICAL SCIENCES↗