Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Design Methods and Models Design Representations Computational Methods of Design”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

Safety Analysis of FeCrAl Accident-Tolerant Fuels with Increased Enrichment and Extended Burnup

The U.S. nuclear industry is facing a strong challenge to maintain regulatory-required levels of safety while ensuring economic competitiveness to stay in business. Safety remains a key parameter for all aspects related to the operation of light water reactor nuclear power plants (NPPs), and it can be achieved more economically by using a risk-informed ecosystem, such as that being developed by the Risk-Informed Systems Analysis Pathway under the U.S. Department of Energy Light Water Reactor Sustainability Program. This program is promoting a wide range of research and development activities to maximize both the safety and economically efficient performance of NPPs through improved scientific understanding, especially given that many plants are considering a second license renewal. The Risk-Informed Systems Analysis Pathway has two main goals: (1) The deployment of methodologies and technologies that enable a better representation of the safety margins and factors that contribute to cost and safety, and (2) The development of advanced applications that enable cost-effective plant operation. As part of this pathway, the Enhanced Resilient Plant project refers to an NPP where safety is improved by implementing various measures, such as accident-tolerant fuels, diverse and flexible coping strategies, enhancements to plant components and systems, incorporation of augmented or new passive cooling systems, and utilization of advanced battery technologies. The objective of the Enhanced Resilient Plant project is to use novel methods and computational tools to enhance existing reactors’ safety while reducing operational costs. This report documents research and development conducted in support of deployment of accident-tolerant fuels. This project performed safety analyses for the steady-state normal operation, anticipated operational occurrences, and design-basis accidents of a representative four-loop pressurized water reactor model with Zr and FeCrAl accident-tolerant fuel clad with higher enrichment and burnup supporting plant refueling cycles of 18 and 24 months. The source terms and environmental impacts were studied for a large-break loss of coolant accident, including uncertainty analyses.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Multi deep learning-based stochastic microstructure reconstruction and high-fidelity micromechanics simulation of time-dependent ceramic matrix composite response

A multi deep learning-based framework is developed for efficient, automated microstructure reconstruction and generation of stochastic representative volume elements (SRVEs) with periodic boundary conditions (PBCs) for accurate modeling of ceramic matrix composite (CMC) response. The methodology comprises a convolutional neural network coupled with regression layers to act as a vanilla regression network for semantic segmentation of the microstructure, allowing accurate characterization of the phases and their distributions at the microscale. Scanning electron microscope and confocal microscope are used to obtain C/SiNC and SiC/SiNC CMCs micrographs for vanilla regression testing. Microstructure variability in terms of fiber volume fraction and porosity are quantified through the output regression layer, ensuring accurate representation of material variability in SRVE construction. Generative adversarial network (GAN) and its variants are designed to produce high-fidelity SRVE, spanning CMCs microstructure variability space. A circular padding algorithm is developed to generate SRVEs with PBCs during training of GANs. The accuracy of the generated SRVEs is established through micromechanics simulations, where an efficient formulation of the high-fidelity generalized methods of cells (HFGMC) approach is used to compute the effective mechanical properties. Furthermore, an iterative algorithm is implemented in the HFGMC solver to simulate time-dependent deformation of SiC/SiNC subjected to creep loading conditions.

36 MATERIALS SCIENCE↗

A detailed study of interpretability of deep neural network based top taggers

Abstract Recent developments in the methods of explainable artificial intelligence (XAI) allow researchers to explore the inner workings of deep neural networks (DNNs), revealing crucial information about input–output relationships and realizing how data connects with machine learning models. In this paper we explore interpretability of DNN models designed to identify jets coming from top quark decay in high energy proton–proton collisions at the Large Hadron Collider. We review a subset of existing top tagger models and explore different quantitative methods to identify which features play the most important roles in identifying the top jets. We also investigate how and why feature importance varies across different XAI metrics, how correlations among features impact their explainability, and how latent space representations encode information as well as correlate with physically meaningful quantities. Our studies uncover some major pitfalls of existing XAI methods and illustrate how they can be overcome to obtain consistent and meaningful interpretation of these models. We additionally illustrate the activity of hidden layers as neural activation pattern diagrams and demonstrate how they can be used to understand how DNNs relay information across the layers and how this understanding can help to make such models significantly simpler by allowing effective model reoptimization and hyperparameter tuning. These studies not only facilitate a methodological approach to interpreting models but also unveil new insights about what these models learn. Incorporating these observations into augmented model design, we propose the particle flow interaction network model and demonstrate how interpretability-inspired model augmentation can improve top tagging performance.

97 MATHEMATICS AND COMPUTING↗

Application-Driven Creation of Building Metadata Models with Semantic Sufficiency

Semantic metadata models such as Brick, RealEstateCore, Project Haystack, and BOT promise to simplify and lower the cost of developing software for smart buildings, enabling the widespread deployment of energy efficiency applications. However, creating these models remains a challenge. Despite recent advances in creating models from existing digital representations like point labels and architectural models, there is still no feedback mechanism to ensure that the human input to these methods results in a model that can actually support the desired software. In this paper, we introduce the notion of semantic sufficiency, a practical principle for semantic metadata model creation that asserts that a model is "finished" when it contains the metadata necessary to support a given set of applications. To support semantic sufficiency, we design a standard representation for capturing application metadata requirements and a templating system for generating common metadata model components with limited user input. We then construct an iterative model creation workflow that integrates metadata requirements to direct the model creation effort, and present several novel optimizations that increase the model utility while minimizing the effort by a human operator. These new abstractions for model creation and validation lower model development costs and ensure the utility of the resulting model, thus facilitating the adoption of intelligent building applications.

applications↗

A symbolic framework to obtain mid-fidelity models of flexible multibody systems with application to horizontal-axis wind turbines

Abstract. The article presents a symbolic framework (also called computer algebra program) that is used to obtain, in symbolic mathematical form, the linear and nonlinear equations of motion of a mid-fidelity multibody system including rigid and flexible bodies. Our approach is based on Kane's method and a nonlinear shape function representation for flexible bodies. The shape function approach does not represent the state of the art for flexible multibody dynamics but is an effective trade-off to obtain mid-fidelity models with few degrees of freedom, taking advantage of the separation of space and time. The method yields compact symbolic equations of motion with implicit account of the constraints. The general and automatic framework facilitates the creation and manipulation of models with various levels of complexity by adding or removing degrees of freedom. The symbolic treatment allows for analytical gradients and linearized equations of motion. The linear and nonlinear equations can be exported to Python code or dedicated software. There are multiple applications, such as time domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, and digital twins. In this article, we describe the method we used to systematically generate the equations of motion of multibody systems and present the implementation of the framework using the Python package SymPy. We apply the framework to generate illustrative land-based and offshore wind turbine models. We compare our results with OpenFAST simulations and discuss the advantages and limitations of the method. The Python implementation is provided as an open-source project.

Branlard, Emmanuel (ORCID:0000000277506128)↗

Uncertainty Propagation within Chained Models for Machine Learning Reconstruction of Neutrino-LAr Interactions

Sequential or chained models are increasingly prevalent in machine learning for scientific applications, due to their flexibility and ease of development. Chained models are particularly useful when a task is separable into distinct steps with a hierarchy of meaningful intermediate representations. In reliability-critical tasks, it is important to quantify the confidence of model inferences. However, chained models pose an additional challenge for uncertainty quantification, especially when input uncertainties need to be propagated. In such cases, a fully uncertainty-aware chain of models is required, where each step accepts a probability distribution over the input space, and produces a probability distribution over the output space. In this work, we present a case study for adapting a single model within an existing chain, designed for reconstruction within neutrino-Argon interactions, developed for neutrino oscillation experiments such as MicroBooNE, ICARUS, and the future DUNE experiment. We test the performance of an input uncertainty-enabled model against an uncertainty-blinded model using a method for generating synthetic noise. By comparing these two, we assess the increase in inference quality achieved by exposing models to upstream uncertainty estimates.

97 MATHEMATICS AND COMPUTING↗

Decoding the protein–ligand interactions using parallel graph neural networks

Abstract Protein–ligand interactions (PLIs) are essential for biochemical functionality and their identification is crucial for estimating biophysical properties for rational therapeutic design. Currently, experimental characterization of these properties is the most accurate method, however, this is very time-consuming and labor-intensive. A number of computational methods have been developed in this context but most of the existing PLI prediction heavily depends on 2D protein sequence data. Here, we present a novel parallel graph neural network (GNN) to integrate knowledge representation and reasoning for PLI prediction to perform deep learning guided by expert knowledge and informed by 3D structural data. We develop two distinct GNN architectures: $$\hbox {GNN}_{\mathrm{F}}$$ GNN F is the base implementation that employs distinct featurization to enhance domain-awareness, while $$\hbox {GNN}_{\mathrm{P}}$$ GNN P is a novel implementation that can predict with no prior knowledge of the intermolecular interactions. The comprehensive evaluation demonstrated that GNN can successfully capture the binary interactions between ligand and protein’s 3D structure with 0.979 test accuracy for $$\hbox {GNN}_{\mathrm{F}}$$ GNN F and 0.958 for $$\hbox {GNN}_{\mathrm{P}}$$ GNN P for predicting activity of a protein–ligand complex. These models are further adapted for regression tasks to predict experimental binding affinities and $$\hbox {pIC}_{\mathrm{50}}$$ pIC 50 crucial for compound’s potency and efficacy. We achieve a Pearson correlation coefficient of 0.66 and 0.65 on experimental affinity and 0.50 and 0.51 on $$\hbox {pIC}_{\mathrm{50}}$$ pIC 50 with $$\hbox {GNN}_{\mathrm{F}}$$ GNN F and $$\hbox {GNN}_{\mathrm{P}}$$ GNN P , respectively, outperforming similar 2D sequence based models. Our method can serve as an interpretable and explainable artificial intelligence (AI) tool for predicted activity, potency, and biophysical properties of lead candidates. To this end, we show the utility of $$\hbox {GNN}_{\mathrm{P}}$$ GNN P on SARS-Cov-2 protein targets by screening a large compound library and comparing the prediction with the experimentally measured data.

59 BASIC BIOLOGICAL SCIENCES↗

Learning Optimal Aerodynamic Designs

This project created a framework for efficient, accurate, and scalable deep neural network representations of design optimization problem solutions. The inputs to these DNN representations are the vector of design requirement parameters, the outputs are the optimal design variables, and the goal is to learn the map from inputs to outputs (i.e., inverse design). The team addressed the problem of the optimal shape design of aerodynamic lifting surfaces—in particular aircraft wings—using a Reynolds-Average Navier Stokes model to govern the CFD-based aerodynamic shape optimization. The inverse design map for such problems is very complex and high-dimensional, involving inputs and outputs on the order of 1000s. To approximate this inverse design map, the team developed algorithms to construct parsimonious DNN architectures, which automatically identify low-dimensional manifolds in which design requirements affect optimal shape parameters, and trained these architectures with multifidelity optimization methods. The resulting methodology accurately and automatically designs optimal aerodynamic lifting surfaces with very high accuracy (99%) at interactive speeds, of the order of milliseconds, resulting in factors of one million or more speedup relative to CFD-based design optimization.

97 MATHEMATICS AND COMPUTING↗

Artificial Intelligence for Enhancing Multiscale Analysis: Buildings Focus

This project aims to develop multi-scale building energy data, potentially improving the representation of the U.S. buildings sector in GCAM-USA, an U.S.-focused human-energy-Earth systems model. Existing building energy datasets are typically limited to national or regional levels, which constrains the ability of models to capture fine-scale human-energy-Earth systems interactions and reduces their relevance for decision-making on issues such as energy security, resilience, and energy planning. By leveraging AI and advanced data integration methods, this work fuses multiple existing datasets to enhance the physical and geographic representation of both residential and commercial building energy use. So far, progress includes processing residential building data, designing the data structure for commercial buildings, and testing AI approaches for integrating datasets and addressing spatial-temporal gaps. This effort can not only advances GCAM-USA’s capability in modeling the buildings sector but also supports broader DOE missions, such as developing digital testbeds, enhancing grid resilience analysis, and improving building–energy system modeling at decision-relevant scales.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Active causal learning for decoding chemical complexities with targeted interventions

Abstract Predicting and enhancing inherent properties based on molecular structures is paramount to design tasks in medicine, materials science, and environmental management. Most of the current machine learning and deep learning approaches have become standard for predictions, but they face challenges when applied across different datasets due to reliance on correlations between molecular representation and target properties. These approaches typically depend on large datasets to capture the diversity within the chemical space, facilitating a more accurate approximation, interpolation, or extrapolation of the chemical behavior of molecules. In our research, we introduce an active learning approach that discerns underlying cause-effect relationships through strategic sampling with the use of a graph loss function. This method identifies the smallest subset of the dataset capable of encoding the most information representative of a much larger chemical space. The identified causal relations are then leveraged to conduct systematic interventions, optimizing the design task within a chemical space that the models have not encountered previously. While our implementation focused on the QM9 quantum-chemical dataset for a specific design task—finding molecules with a large dipole moment—our active causal learning approach, driven by intelligent sampling and interventions, holds potential for broader applications in molecular, materials design and discovery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Cathodic Protection Modeling for Hanford Underground Double-Shell Tank Farms

Hanford stores millions of gallons of radioactive and chemically hazardous waste from the production of weapon materials in tank farms consisting of underground carbon-steel storage tanks surrounded by reinforced concrete. Six of these Hanford tank farms use double-shell storage tanks (DSTs). The DST farms were constructed from 1968 to 1986 with a planned 40–50 year design life, so some are already operating beyond their initial life expectancy. Ultrasonic testing (UT) has indicated significant thinning on the bottom of the secondary (outer) liner of these tanks, believed to arise from groundwater intrusion driving concrete side corrosion. There is no direct access to the steel/concrete interface between the tank and the concrete pad, making it difficult to apply a chemical-based mitigation strategy or to conduct repairs, but cathodic protection (CP) is a possible method to inhibit further concrete-side corrosion. Hanford already uses CP to protect below grade steel piping within the tank farms and connected to the tanks, but this system was not designed to protect the tank bottoms. CP design must account for the structures surrounding the DSTs, including the steel reinforcing bars (rebar) within the concrete pad and vault, various process lines, and the existing CP system. In this study, finite element analysis (FEA) modeling was carried out to simulate CP protection of 1) a single tank and CP anode to develop options for modeling the rebar and to compare to a simpler circuit model and 2) the entire Hanford AN tank farm as a representative example consisting of seven tanks, associated piping, and both existing and new CP anodes. Both circuit and FEA models predict that significant protective current could be delivered to the bottoms of the tanks with the addition of tank-protection anodes below the depth of the tanks. Simulations with only the existing pipe-protection anodes active confirmed that only a very small current to the tank bottoms is predicted under present conditions. Multiple simplified representations of the dome and wall rebar were tested to reduce the computational complexity of the tank-farm simulations, resulting in modeling the rebar as edge elements with a prescribed effective circumference that matches the real rebar surface area. The geometry of the rebar is also simplified into horizontal hoops around the tank walls and radial rebar over the dome with increased effective circumference to retain the target surface area. This simplification was found to greatly reduce the complexity and solution time of the models without large changes in current distributions, especially to the tank bottom. A range of values were tested for model parameters such as soil and concrete resistivities and polarization resistance to investigate their impact on the current and electric potential distributions. Depending on the parameters used, FEA simulations predict some risk of overprotection, particularly on the piping system; since overprotection can also lead to surface damage associated with hydrogen gas generation at the interface (e.g. hydrogen embrittlement or damage to coatings), this needs to be considered when refining the design of the new CP system. Comparison between the FEA models and the circuit model representation demonstrated that the circuit model could not match the predicted FEA current distribution, even when using the exact same surface areas. This discrepancy appeared to be at least partly attributable to the impact of the relative positions of the tank components and anodes to each other and to the ground surface. The FEA model accounts for the relative positions since it solves the governing equations in three dimensions, but the circuit model cannot account for the positioning. In particular, the circuit model underpredicts the current to the tank bottom and overpredicts the current to the dome compared to FEA for the baseline geometry. The FEA models omitted the electrically isolated rebar in the bottom concrete slab. However, a circuit based stray current model estimated that only 2.1% of the total current through the slab would stray into the rebar, corresponding to ~0.21 A for a target current density of 2 mA/ft2 to the tank bottom. The estimated corrosion driven by this amount of stray current is predicted to yield a lifetime of >400 years for the minimum rebar diameter, assuming an acceptable cross-section area loss of 10%.

d'Entremont, Anna [Savannah River National Laborat↗

Multibody for Everybody (M4E): A Symbolic Dynamics Modeling Tool with Applications in Simulation, Control, and Optimization

Developing the analytical model of a multibody system is often the initial step in control and optimization. The analytical model (equations of motion) describes a system’s time evolution under specified forcing conditions. Although developing these equations is easy for simple systems, this process becomes more complex for systems composed of multiple bodies. Deriving equations of motion for complex multibody systems requires specialized expertise in multibody dynamics, is time-consuming, and is susceptible to error. To address this issue, this paper presents an open-source, easy-to-use, systematic framework to derive symbolic equations of motion in both Python and MATLAB using the joint coordinate formulation. This formulation results in a set of ordinary differential equations that use the minimum set of coordinates needed to model a system. The symbolic representation provides better insight into the influence of design parameters on system performance, facilitates sensitivity analysis and parameter studies, and supports direct implementation of control and optimization routines. The tool enables numerical simulation for specified parameter sets, is modular for straightforward integration with other tools and libraries, and allows incorporation of hydrodynamics, mooring, and other external forces. The result is a reproducible, extensible pipeline for modeling, simulation, and design of complex multibody systems. The proposed tool is versatile and can be applied to domains such as robotics, control, and design. In addition, we integrated external libraries that provide capabilities for modeling offshore systems such as underwater robots and marine energy converters.

16 TIDAL AND WAVE POWER↗

Machine learning with persistent homology and chemical word embeddings improves prediction accuracy and interpretability in metal-organic frameworks

Machine learning has emerged as a powerful approach in materials discovery. Its major challenge is selecting features that create interpretable representations of materials, useful across multiple prediction tasks. We introduce an end-to-end machine learning model that automatically generates descriptors that capture a complex representation of a material’s structure and chemistry. This approach builds on computational topology techniques (namely, persistent homology) and word embeddings from natural language processing. It automatically encapsulates geometric and chemical information directly from the material system. We demonstrate our approach on multiple nanoporous metal–organic framework datasets by predicting methane and carbon dioxide adsorption across different conditions. Our results show considerable improvement in both accuracy and transferability across targets compared to models constructed from the commonly-used, manually-curated features, consistently achieving an average 25–30% decrease in root-mean-squared-deviation and an average increase of 40–50% in R 2 scores. A key advantage of our approach is interpretability: Our model identifies the pores that correlate best to adsorption at different pressures, which contributes to understanding atomic-level structure–property relationships for materials design.

97 MATHEMATICS AND COMPUTING↗

A machine learning approach to emulation and biophysical parameter estimation with the Community Land Model, version 5

Abstract. Land models are essential tools for understanding and predicting terrestrial processes and climate–carbon feedbacks in the Earth system, but uncertainties in their future projections are poorly understood. Improvements in physical process realism and the representation of human influence arguably make models more comparable to reality but also increase the degrees of freedom in model configuration, leading to increased parametric uncertainty in projections. In this work we design and implement a machine learning approach to globally calibrate a subset of the parameters of the Community Land Model, version 5 (CLM5) to observations of carbon and water fluxes. We focus on parameters controlling biophysical features such as surface energy balance, hydrology, and carbon uptake. We first use parameter sensitivity simulations and a combination of objective metrics including ranked global mean sensitivity to multiple output variables and non-overlapping spatial pattern responses between parameters to narrow the parameter space and determine a subset of important CLM5 biophysical parameters for further analysis. Using a perturbed parameter ensemble, we then train a series of artificial feed-forward neural networks to emulate CLM5 output given parameter values as input. We use annual mean globally aggregated spatial variability in carbon and water fluxes as our emulation and calibration targets. Validation and out-of-sample tests are used to assess the predictive skill of the networks, and we utilize permutation feature importance and partial dependence methods to better interpret the results. The trained networks are then used to estimate global optimal parameter values with greater computational efficiency than achieved by hand tuning efforts and increased spatial scale relative to previous studies optimizing at a single site. By developing this methodology, our framework can help quantify the contribution of parameter uncertainty to overall uncertainty in land model projections.

54 ENVIRONMENTAL SCIENCES↗

Chemical reaction enhanced graph learning for molecule representation

Abstract Motivation Molecular representation learning (MRL) models molecules with low-dimensional vectors to support biological and chemical applications. Current methods primarily rely on intrinsic molecular information to learn molecular representations, but they often overlook effectively integrating domain knowledge into MRL. Results In this article, we develop a reaction-enhanced graph learning (RXGL) framework for MRL, utilizing chemical reactions as domain knowledge. RXGL introduces dual graph learning modules to model molecule representation. One module employs graph convolutions on molecular graphs to capture molecule structures. The other module constructs a reaction-aware graph from chemical reactions and designs a novel graph attention network on this graph to integrate reaction-level relations into molecular modeling. To refine molecule representations, we design a reaction-based relation learning task, which considers the relations between the reactant and product sides in reactions. In addition, we introduce a cross-view contrastive task to strengthen the cooperative associations between molecular and reaction-aware graph learning. Experiment results show that our RXGL achieves strong performance in various downstream tasks, including product prediction, reaction classification, and molecular property prediction. Availability and implementation The code is publicly available at https://github.com/coder-ACAC/RLM.

Biochemistry & Molecular Biology↗

Scalable training of graph convolutional neural networks for fast and accurate predictions of HOMO-LUMO gap in molecules

Abstract Graph Convolutional Neural Network (GCNN) is a popular class of deep learning (DL) models in material science to predict material properties from the graph representation of molecular structures. Training an accurate and comprehensive GCNN surrogate for molecular design requires large-scale graph datasets and is usually a time-consuming process. Recent advances in GPUs and distributed computing open a path to reduce the computational cost for GCNN training effectively. However, efficient utilization of high performance computing (HPC) resources for training requires simultaneously optimizing large-scale data management and scalable stochastic batched optimization techniques. In this work, we focus on building GCNN models on HPC systems to predict material properties of millions of molecules. We use HydraGNN, our in-house library for large-scale GCNN training, leveraging distributed data parallelism in PyTorch. We use ADIOS, a high-performance data management framework for efficient storage and reading of large molecular graph data. We perform parallel training on two open-source large-scale graph datasets to build a GCNN predictor for an important quantum property known as the HOMO-LUMO gap. We measure the scalability, accuracy, and convergence of our approach on two DOE supercomputers: the Summit supercomputer at the Oak Ridge Leadership Computing Facility (OLCF) and the Perlmutter system at the National Energy Research Scientific Computing Center (NERSC). We present our experimental results with HydraGNN showing (i) reduction of data loading time up to 4.2 times compared with a conventional method and (ii) linear scaling performance for training up to 1024 GPUs on both Summit and Perlmutter.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Incorporating the Impacts of Climate Change on Hydrology in a Performance Assessment Model - 20403

The evidence of climate change is increasingly well-documented and impacts should be incorporated in performance assessment studies. The current climate literature provides both observational evidence and climate model projections of climate trends and/or climate change in the late 20. and early 21. centuries for North America and the northeast United States. Probabilistic modeling is a core requirement for quantifying uncertainty and evaluating its impacts. Not evaluating future climate states in a performance assessment because of the existence of uncertainty is contradictory to good modeling practices - the most uncertain issues and parameters require the most attention in effective probabilistic modeling. Excluding climate change limits development of modeling information that could aid in effective decision making. In this work we develop methods to use the output from hydrologic models and analysis of historical aerial imagery to quantify and implement the impacts of climate change on hydrologic processes at a nuclear waste site in West Valley, New York. Specifically, we used the HELP (Hydraulic Performance of Landfill Performance) model to characterize key hydrologic processes under both current and future climate conditions to assess the impacts of changing climate on hydrology. A suite of previous climatic models were reviewed and synthesized to produce a cohesive representation of the current state of knowledge of the impact of climate change on important model inputs such as precipitation. Output from the HELP simulations was coupled to the GoldSim model that was used to develop the Probabilistic Performance Assessment (PPA) approach through the application of a novel 'nearest neighbor' technique. First, several thousand realizations were generated from the HELP model using a Latin Hypercube experimental design to ensure adequate coverage of the parameter space of explanatory variables used to drive HELP. For example, porosity is a physical parameter that is used as an input to both HELP and the GoldSim PA model. We then ran sensitivity analysis (SA) algorithms on the output of HELP for each of the responses of interest. For each predictor, each time we build an SA model we get a different value for the sensitivity index (SI). From the collection of all the SA models, the average was computed among all of the SIs to represent the predictor within the context of the nearest neighbor approach. That is, we conduct SA on each HELP outcome for each scenario. This gives us parameter sensitivity indices for the outcomes. We average the parameter sensitivity indices across the outcomes to get the average SI for a scenario. For each realization that is generated from the Goldsim PA model, Goldsim generates random values for physical/empirical parameters that HELP uses as well. For each vector of physical/empirical parameters that Goldsim generates, the vector from the 5,000 HELP runs that is most 'similar' to the Goldsim vector is computed using the nearest neighbor approach. In this context 'similar' means minimization of the SA-weighted sum of the absolute differences among the 5,000 values computed for this statistic, where each value corresponds to a different HELP realization. In order to account for the impacts of climate change, this process was repeated using the spatially downscaled future climate projections. For each of the key parameters of interest, it was assumed that a linear change depicted the relationship between the values for the present day and those for 2100. In this way, the climatically-driven changes in key parameters used to inform the GoldSim model are quantified and incorporated into the PA model output for the future. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

G2Aero: A Python package for separable shape tensors

G2Aero is a Python package for the design and deformation of discrete planar curves and tubular surfaces using a geometric data-driven approach. G2Aero utilizes a topology of product manifolds: the Grassmannian, $\mathcal{G}$($\mathcal{n}$, 2) - the set of 2-dimensional subspaces in $\mathbb{R}$ $\mathcal{n}$ - and the symmetric positive-definite (SPD) manifold, $\mathcal{S}^{2}_{++}$ - the set of 2x2 SPD matrices. The package provides a novel framework for representing separable deformations to shapes, which consist of stretching, scaling, rotating, and translating - also known as affine deformations - and a set of complementary deformations - which we refer to as undulation-type deformations. We focus on airfoil and blade design applications to emphasize the utility of the methods in an environment where the separation of affine and undulation-type deformations is critical. Notable functionalities of the framework for blade design include: 1) generating novel 2D (airfoil) shapes informed by a database of physically relevant airfoils, 2) building 3D blades by interpolating sequences of 2D airfoil cross-sections, and 3) generating blades with consistent perturbations along the blade span. We discuss the framework and provide examples in the context of wind energy applications, specifically wind turbine blade design. Figure 1 shows the wire frame obtained by interpolating airfoils defining the IEA 15-MW wind turbine blade and applying affine transformations corresponding to twist, chordal scaling, and bending. This, and all other figures in the paper, can be reproduced following examples and referencing supporting documentation provided in the G2Aero package.

97 MATHEMATICS AND COMPUTING↗