Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “cost function”

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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

FAIR Data and Interpretable AI Framework for Architectured Metamaterials

Our interdisciplinary effort successfully generated FAIR (Findable, Accessible, Interoperable, and Reusable) benchmark datasets for mechanical metamaterials while introducing a novel Artificial Intelligence (AI) framework known as Learning Refined Compositional Rules (LRCR). This framework was specifically designed to bridge the gap across varying computational length scales and extract the underlying physical mechanisms that connect a material's structural geometry to its bulk acoustic properties. Historically, the discovery of such structured materials relied heavily on human intuition or opaque, black-box optimization algorithms that were difficult to generalize. By combining interpretable machine learning techniques with rigorous experimental validation, this project established clear, generalizable design guidelines for tuning wave dispersion and controlling vibrations. Ultimately, the public availability of these structured datasets and algorithms will significantly reduce computational costs and accelerate the design of advanced multi-functional acoustic devices, offering broad societal impacts across fields like aerospace engineering, telecommunications, and biomedical implant design.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Reference floating wind array designs for three representative regions

This work presents the systematic development of three open-source reference floating wind array designs. The designs are tailored to representative site conditions for three regions of the United States: Humboldt Bay off the coast of California, the Gulf of Maine, and the Gulf of America. We adopted existing reference designs for the individual 15 MW turbines, semisubmersible floating platforms, substations, mooring systems, and power cables – integrating and adapting them as needed for each location. We adapted existing dynamic cable designs to use larger conductor sizes to meet the arrays' power transmission requirements, and we set up redundant mooring systems for each substation. The layout of each array is a uniform-grid design optimized to approximately minimize the levelized cost of energy (LCOE) within a square lease area while satisfying spatial constraints. These constraints ensure adequate clearances between adjacent turbines and between underwater components during the layout optimization to prevent clashing and ensure that all components reside within the lease boundaries. Substations are included to allow accounting for intra-array cable costs. They are placed within the uniform grid to maintain the navigability of the arrays. For each feasible layout considered, annual energy production and cable routing costs are calculated and updated in the LCOE objective function. After the optimization, we refined the cable routing with a mix of algorithmic and manual methods to ensure that the cables avoid mooring system components and approach the substation with adequate clearances. We confirmed the suitability of each reference array's layout by comparing the wake losses at each wind heading angle to the wind rose, observing that the optimized layouts largely avoid wake losses in the predominant wind directions. These reference arrays provide open-source baseline designs to enable future research and innovation of floating wind technology at the array scale.

17 WIND ENERGY↗
DOE OSTI2025

CERF Visualization: Projected locations of new natural gas combined cycle power plants (with recirculating cooling) in Wyoming, USA (2020-2050)

Visualization of CERF outputs for years 2030-2050 in 5-year time steps for a region in Wyoming, USA. This visualization was built using a custom CesiumJS application. The region of interest was zoomed into and then the app shows the layered application of natural gas combined cycle power plants (with recirculating cooling) suitability criteria, show the siting for each year in planform, simulates the selection of a site using Net Locational Cost, and then zooms into to show a single functional gas plant and simulates its connection to the grid.

CERF↗
DOE OSTI2020

Reliability-Informed Life-Cycle Warranty Cost Analysis: A Case Study on a Transmission in Agricultural Equipment

In agricultural and industrial equipment, both new and remanufactured systems are often available for warranty coverage. In such cases, it may be challenging for equipment manufacturers to properly trade-off between the system reliability and the cost associated with a replacement option (e.g., replace with a new or remanufactured system). To address this problem, we present a reliability-informed life-cycle warranty cost (LCWC) analysis framework that enables equipment manufacturers to evaluate different warranty policies. These warranty policies differ in whether a new or remanufactured system is used for replacement in the case of product failure. The novelty of this LCWC analysis framework lies in its ability to incorporate real-world field reliability data into warranty policy assessment using probabilistic warranty cost models that consider multiple life cycles. First, the reliability functions for the new and remanufactured systems are built as the time-to-failure distributions that provide the best-fit to the field reliability data. Then, these reliability functions and their corresponding warranty policies are used to build the LCWC models according to the specific warranty terms. Finally, Monte Carlo simulation is used to propagate the time-to-failure uncertainty of each system, modeled by its reliability function, through each LCWC model to produce a probability distribution of the LCWC. The effectiveness of the proposed reliability-informed LCWC analysis framework is demonstrated with a real-world case study on a transmission used in some agricultural equipment.

agricultural equipment↗
DOE OSTI2025

Quick-and-Easy Validation of Protein–Ligand Binding Models Using Fragment-Based Semiempirical Quantum Chemistry

Electronic structure calculations in enzymes converge very slowly with respect to the size of the model region that is described using quantum mechanics (QM), requiring hundreds of atoms to obtain converged results and exhibiting substantial sensitivity (at least in smaller models) to which amino acids are included in the QM region. As such, there is considerable interest in developing automated procedures to construct a QM model region based on well-defined criteria. However, testing such procedures is burdensome due to the cost of large-scale electronic structure calculations. Here, we show that semiempirical methods can be used as alternatives to density functional theory (DFT) to assess convergence in sequences of models generated by various automated protocols. The cost of these convergence tests is reduced even further by means of a many-body expansion. We use this approach to examine convergence (with respect to model size) of protein–ligand binding energies. Fragment-based semiempirical calculations afford well-converged interaction energies in a tiny fraction of the cost required for DFT calculations. Two-body interactions between the ligand and single-residue amino acid fragments afford a low-cost way to construct a “QM-informed” enzyme model of reduced size, furnishing an automatable active-site model-building procedure. This provides a streamlined, user-friendly approach for constructing ligand binding-site models that needs neither a priori information nor manual adjustments. Extension to model-building for thermochemical calculations should be straightforward.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Machine Learning a Simple Interpretable Short-Range Potential for Silica

A wide array of models, spanning from computationally expensive ab initio methods to a spectrum of force-field approaches, have been developed and employed to probe silica polymorphs and understand growth processes and atomic-level dynamical transitions in silica. However, the quest for a model capable of making accurate predictions with high computational efficiency for various silica polymorphs is still ongoing. Recent developments in short-range machine-learned models, such as GAP and NNPScan, have shown promise in providing reasonable descriptions of silica, but their computational cost remains high compared to force fields such as BKS which are based on simple interpretable functional forms. Here, in this study, we build on the recent success of our reinforcement learning (RL) workflow to derive a new set of optimal parameters for a promising short-range BKS-based model proposed by Soules. We use RL to navigate the eight-dimensional parameter space of the Soules potential using an experimental training data set that includes both local and global structural features from approximately 21 experimentally realized silica polymorphs, including high density phases and porous zeolites. We compare the performance of our machine-learned ML-Soules model with other high quality models including our recent machine-learned parametrization of BKS (ML-BKS), a machine-learned potential (GAP), as well as predictions of ab initio calculations with the highly fidelity SCAN functional. The ML-Soules accurately captures the relative energetic ordering of various polymorphs as well as their structural features at a significantly reduced computational expense. The ML-Soules model also reasonably captures the structure, density, and elastic constants of quartz, as well as metastable silica polymorphs. We further discuss the limitations of the Soules functional form and propose potential enhancements, including the incorporation of additional three-body terms and/or the utilization of different short-ranged functional forms to achieve greater accuracy for both global and local features in the modeling of silica while retaining low computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Optimizing and Exploring Untapped Micro-Hydro Hybrid Systems: a Multi-Objective Approach for Crystal Lake as a Large-Scale Energy Storage Solution

Increasing electricity demand and concerns about climate change and fossil fuel consumption have highlighted the importance of renewable energy resources and storage systems. This paper proposes a method for exploring untapped pumped hydro storage potentials to accommodate intermittent renewable energy generation profiles. Hourly measured data from 2022 in Benzie County, Michigan, United States, were gathered for system sizing and a thorough, realistic analysis. By employing the multi-objective grey wolf optimization algorithm, we formulated optimal sizing and energy-management strategies for three different scenarios. Unlike similar studies, the 3rd with triple objective functions (OFs) scenario aims to maximize both reliability and ecological OFs while minimizing the cost OF. It has shown promising results with multiple solutions, considering economic, environmental, and reliability factors. A case study conducted in Crystal Lake, Michigan, revealed that although Crystal Lake would function only as a micro-hydro power facility, it is a promising and huge storage unit with a substantial storage capacity of around 14.9734GWh. The system investigated is significant in the USA due to its rapid deployment capabilities, minimal construction requirements, and ease of integration with the distribution grid. The fuzzy logic method was employed to identify the best non-dominant solution among the other solutions. Furthermore, these outcomes include a notably low levelized cost of energy at 0.046147$/kWh, a robust index of reliability of 99.705%, and a significant reduction in CO₂ emissions amounting to 7.9142×10 3 tons/year, when considering the triple OFs. The paper’s methodology provides valuable insights for regions aiming to utilize renewable energy from untapped storage sources.

13 HYDRO ENERGY↗
DOE OSTI2021

AC Power Flow Based DLMP Calculation and Decomposition Method to Smooth Power Fluctuation of Distributed Renewable Energy Sources

As the penetration of renewable energy sources increases, the growing renewable power variability brings ramping issues to power systems. Meanwhile, the development of distributed energy resources (DERs) makes the distribution systems to provide both energy and ancillary services. To incentivise individual resources and customers to alleviate ramping issues on the demand side, a two-stage distribution locational marginal price (DLMP) calculation and decomposition method is developed to formulate the marginal power ramping price for DERs. In the first stage of the proposed method, a distribution system operator market scheduling model based on AC optimal power flow is designed to estimate the optimal operating point of the distribution system. Subsequently, the voltage and power flow constraints are linearised in stage two to calculate DLMP. Finally, based on the Lagrange function and sensitivity factors, DLMP is decomposed to the marginal costs for active/reactive power, voltage management, power loss and power variability. Case studies demonstrate that the proposed model can effectively smooth the power fluctuation and reduce the ramping flexibility requirements of distribution systems.

AC optimal power flow↗
DOE OSTI2021

Resilience-based Recovery Scheduling of Transportation Network in Mixed Traffic Environment: A Deep-Ensemble-Assisted Active Learning Approach

Devising effective post-hazard recovery strategies is critical in enhancing the resilience of transportation networks (TNs). However, existing work does not consider the multiclass users’ travel behavior in network functionality quantification and the metaheuristic solution procedures often suffer from extensive computational burden due to the exploration need in large solution space and the expensive functionality quantification. Here, this study develops a bilevel decision-making framework for the resilience-based recovery scheduling of the TN in a mixed traffic environment with connected and autonomous vehicles (CAVs) and human-driven vehicles (HDVs). The lower level quantifies the TN's functionality over time considering different travel behavior of CAV and HDV users arisen from their different levels of information perception. The upper level presents a novel deep-ensemble-assisted active learning approach to balance optimization performance and computational cost. This framework can help decision makers better quantify the TN's functionality to support effective recovery scheduling of TN with different mixed traffic scenarios ranging from HDV-only to future CAV-dominant traffic. The optimization approach bears the potential to be extended to solving general large-scale network recovery scheduling problems effectively and efficiently. The proposed methodology is demonstrated using a real-world traffic network in Southern California under earthquake considering deterministic and stochastic repair durations.

42 ENGINEERING↗
DOE OSTI2025

Rapid Bayesian High Entropy Alloy Designs Fabricated via Wire Arc Additive Manufacturing

Purpose: This project seeks to demonstrate a new high-throughput (rapid) alloy design technique applied to creating new high entropy alloys (HEAs) for extreme environments. High entropy alloys shift the design paradigm from being focused on a single principal element (e.g. nickel-based alloys) to target alloys that include high atomic fractions (X >10%) of multiple elements. These HEA materials can exhibit sluggish diffusion and enhanced corrosion resistance, ideal for potential applications in advanced ultra supercritical (A-USC) steam cycles for power generation. Scope: The addition of multiple elements in high atomic fractions creates an enormous design space that cannot easily be investigated by traditional material design strategies such as designed of experiments (DOE). This project utilizes a Bayesian machine learning algorithm that has been modified to work with calculation of phase diagrams (CALPHAD) software. This Bayesian algorithm reduces manual inputs and increase the likelihood of achieving an optimal solution. Compositional inputs to this algorithm will be assessed using existing material property models for high temperature strength and corrosion resistance. The target for alloy performance will be a 15% (~100 ⁰C) increase in allowable service temperature beyond heat-resistant stainless steels while maintaining or improving alloy cost and corrosion resistance. Haynes 230 was selected as a baseline, which is 57 wt% Ni with 22 wt% Cr 14 wt% W, and 2 wt% Mo as solid solution strengtheners. In addition to rapid design via Bayesian machine learning, the alloys were rapidly fabricated using a multi-wire arc additive manufacturing (mWAAM) technique which allows for precise control of alloy composition and assessing of alloy design “windows” to study composition effects. Build speeds for wire-arc additive processes are among the highest for additive technologies enabling rapid and reliable sample fabrication when compared to conventional methods such as arc button melting. The mWAAM samples will be rapidly characterized via instrumented indentation for room temperature modulus and strength and for elevated temperature strength via hot hardness tests. After being screened with hardness testing, potential alloys will be further evaluated with conventional microscopy techniques including scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to assess agreement with modeling results. The most promising compositions will also be evaluated by printing full sized tensile specimens for mechanical behavior tests at elevated temperatures. Results: Bayesian machine learning of a single performance function was initially used to optimize five performance metrics: 1) single phase stability, 2) yield strength, 3) creep resistance (low diffusion coefficient), 4) freezing range (weldability), and 5) material cost. The single performance function was suboptimal as assumptions had to be made about the results while formulating the optimization. A goal-oriented Bayesian optimization strategy (Hanaoka, 2021) was implemented with CALPHAD for use with the five metrics above. This multi-objective Bayesian optimization (MOBO) enabled the design of NiCrCoFe alloys with V and W additions. A base composition of NiCoCr was selected as Ni provides a stable FCC matrix, Cr aids corrosion/oxidation resistance, and Co is a solid-solutions strengthener that also improves creep by increasing the activation energy. Fe helps reduce diffusion coefficients and cost. Finally, V and W were selected for their reasonable solubility and high atomic misfit to aid in solid solution strengthening. Cracking of the mWAAM specimens was an early issue, and the Easton solidification cracking model (Easton et al., 2014a) was selected for addition to the MOBO function. High performing alloys fabricated by mWAAM included Ni 28 Cr 25 Co 26 Fe 15 V 8 and Ni 62 Cr 18 Co 1 Fe 3 W 15 . It was observed that even after adapting the mWAAM process for W, the W did not fully dissolve. To fully evaluate the Ni 62 Cr 18 Co 1 Fe 3 W 15 composition, a cored wire (80-20 NiCr sheath/powder core) was manufactured and printed via WAAM, and HIP’ing was utilized to homogenize and densify the printed alloy. The V and W alloys produced met metrics 1 (solid solution), 4 (solidification cracking), and 5 (cost). However, an unmodeled mechanism of thermal stress cracking was identified in the WAAM produced materials, perhaps exacerbated by the lack of grain boundary strengthening elements (B, C). Conclusions & Recommendations: A high-throughput (rapid) alloy design technique was applied to designing and manufacturing new high entropy alloys (HEAs) for extreme environments utilizing MOBO and mWAAM. The developed process was rapid and effective in addressing the mechanisms included in the model. The lack of grain boundary strengthening element additions (e.g., B, C) was a simplification that likely produced thermal stress cracking that turned into a large part of the investigation. Additions on the order of 0.005 wt% B and 0.05 wt% C likely would have minimized thermal stress grain boundary cracking. Overall, the high throughput design strategy is promising for rapid design of metrics-driven alloys for advanced ultra supercritical (A-USC) steam cycles for power generation. The MOBO and mWAAM process could be commercialized to accelerate metrics-driven alloy design. In addition, the cored-wire process utilized for scale-up is a promising high-volume process for WAAM alloy development and scale-up.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Zero-Field Splitting Calculations by Multiconfiguration Pair-Density Functional Theory

Zero-field splitting (ZFS) is a fundamental molecular property that is especially relevant for single-molecule magnets (SMMs), electron paramagnetic resonance spectra, and quantum computing. Developing a method that can accurately predict ZFS parameters can be very powerful for designing new SMMs. One of the challenges is to include external correlation in an inherently multiconfigurational open-shell species for the accurate prediction of magnetic properties. Previously available methods depend on expensive multireference perturbation theory calculations to include external correlation. In this paper, we present spin-orbit-inclusive multiconfiguration and multistate pair-density functional theory (MC-PDFT) calculations of ZFSs; these calculations have a cost comparable to complete-active-space self-consistent field (CASSCF) theory, but they include correlation external to the active space. We found that combining a multistate formulation of MC-PDFT, namely, compressed-state multistate pair-density functional theory, with orbitals optimized by weighted-state-averaged CASSCF, yields reasonably accurate ZFS results

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Silicon nitride stress-optic microresonator modulator for optical control applications

Modulation-based control and locking of lasers, filters and other photonic components is a ubiquitous function across many applications that span the visible to infrared (IR), including atomic, molecular and optical (AMO), quantum sciences, fiber communications, metrology, and microwave photonics. Today, modulators used to realize these control functions consist of high-power bulk-optic components for tuning, sideband modulation, and phase and frequency shifting, while providing low optical insertion loss and operation from DC to 10s of MHz. In order to reduce the size, weight and cost of these applications and improve their scalability and reliability, modulation control functions need to be implemented in a low loss, wafer-scale CMOS-compatible photonic integration platform. The silicon nitride integration platform has been successful at realizing extremely low waveguide losses across the visible to infrared and components including high performance lasers, filters, resonators, stabilization cavities, and optical frequency combs. Yet, progress towards implementing low loss, low power modulators in the silicon nitride platform, while maintaining wafer-scale process compatibility has been limited. Here we report a significant advance in integration of a piezo-electric (PZT, lead zirconate titanate) actuated micro-ring modulation in a fully-planar, wafer-scale silicon nitride platform, that maintains low optical loss (0.03 dB/cm in a 625 µm resonator) at 1550 nm, with an order of magnitude increase in bandwidth (DC - 15 MHz 3-dB and DC - 25 MHz 6-dB) and order of magnitude lower power consumption of 20 nW improvement over prior PZT modulators. The modulator provides a >14 dB extinction ratio (ER) and 7.1 million quality-factor (Q) over the entire 4 GHz tuning range, a tuning efficiency of 162 MHz/V, and delivers the linearity required for control applications with 65.1 dB·Hz 2/3 and 73.8 dB·Hz 2/3 third-order intermodulation distortion (IMD3) spurious free dynamic range (SFDR) at 1 MHz and 10 MHz respectively. We demonstrate two control applications, laser stabilization in a Pound-Drever Hall (PDH) lock loop, reducing laser frequency noise by 40 dB, and as a laser carrier tracking filter. This PZT modulator design can be extended to the visible in the ultra-low loss silicon nitride platform with minor waveguide design changes. This integration of PZT modulation in the ultra-low loss silicon nitride waveguide platform enables modulator control functions in a wide range of visible to IR applications such as atomic and molecular transition locking for cooling, trapping and probing, controllable optical frequency combs, low-power external cavity tunable lasers, quantum computers, sensors and communications, atomic clocks, and tunable ultra-low linewidth lasers and ultra-low phase noise microwave synthesizers.

Wang, Jiawei (ORCID:0000000257965220)↗
DOE OSTI2024

Lignin valorization reshapes sustainable biomass refining

As the largest natural reservoir of aromatics, lignin offers significant potential for bioproduct manufacturing through advances in valorization technologies. However, the intrinsically complex structures of lignin pose significant challenges for its fractionization and downstream valorization. Overcoming challenges in lignin chemistry modification is crucial for achieving effective lignin valorization and establishing sustainable biorefinery industries. This review explores the potential of tailoring lignin reactivity to enable functional bioproduct manufacturing thereby contributing to profitable biorefining. The intrinsic characteristics of lignin are first summarized, highlighting their roles in both fractionization and valorization. The latest progress in lignin fractionation is then presented, emphasizing their potential to tailor lignin chemistry, reactivity, and processibility. Furthermore, advancements in lignin valorization are covered, recognizing that tailored lignin reactivity is key to defining bioproduct functionality. By examining these chemical mechanisms, this review sheds on the structure-function relationships between lignin and its derived products. To address the dilemma of lignin valorization and biorefineries, a promising synergistic biorefinery is proposed. This involves redesigning biomass fractionation strategies, tailoring lignin chemistry, and upgrading both carbohydrate and lignin streams across the entire biorefinery chain—from feedstock to application. Altogether, a deeper understanding of tailored lignin chemistry is crucial for decoding the reaction mechanisms in biomass processing. A synergistic biorefinery could harness lignin's intrinsic properties to improve product functionality and address key challenges, paving the way for cost-effective, sustainable biorefinery solutions.

09 BIOMASS FUELS↗
DOE OSTI2024

Field Performance of Commercial Building Load Flexibility Using Model Predictive Control

Model Predictive Control (MPC) applied to buildings is starting to see some commercial adoption by companies. However, it is hard to estimate if relative energy cost savings are enough to justify the cost of MPC implementation with few reported demonstrations. In small commercial and residential buildings, a one size-fits-all solution can help reduce implementation costs, while in very large buildings or districts the potential energy cost savings magnitude can cover more tailored solutions. This estimation becomes harder for medium to large commercial buildings, where a one-size-fits-all solution cannot be adopted and potential energy cost savings might not be sufficient to cover a tailored solution. Therefore, value propositions in addition to energy efficiency alone can make MPC technology more attractive through additional energy cost savings. One such value proposition is load shifting in response to dynamic electricity prices. On this aspect, MPC is a key technology to unlock building thermal mass for energy flexibility in response to electric grid conditions. This study shows the experimental results of MPC control of an office building in Berkeley, where different dynamic electricity price profiles were used in the MPC objective function to shift the building load and to calculate hypothetical electricity costs. Results show potential 50% cost savings with respect to the existing controller with the dynamic price scenario.

Zanetti, Ettore↗
DOE OSTI2023

Scrambling and quantum chaos indicators from long-time properties of operator distributions

Scrambling is a key concept in the analysis of nonequilibrium properties of quantum many-body systems. Most studies focus on its characterization via out-of-time-ordered correlation (OTOC) functions, particularly through the early-time decay of the OTOC. However, scrambling is a complex process which involves operator spreading and operator entanglement, and a full characterization requires one to access more refined information on the operator dynamics at several timescales. In this work we analyze operator scrambling by expanding the target operator in a complete basis and studying the structure of the expansion coefficients treated as a coarse-grained probability distribution in the space of operators. Here we study different features of this distribution, such as its mean, variance, and participation ratio, for the Ising model with longitudinal and transverse fields, kicked collective spin models, and random circuit models. We show that the long-time properties of the operator distribution display common features across these cases and discuss how these properties can be used as a proxy for the onset of quantum chaos. Finally, we discuss the connection with OTOCs and analyze the cost of probing the operator distribution experimentally using these correlation functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

Here, in this paper, we design efficient quadrature rules for finite element (FE) discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work, we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first show that the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient FE assembly.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first showthat the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient finite element assembly.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Enhanced Data Efficiency Using Deep Neural Networks and Gaussian Processes for Aerodynamic Design Optimization

Adjoint-based optimization methods are attractive for aerodynamic shape design primarily due to their computational costs being independent of the dimensionality of the input space and their ability to generate high-fidelity gradients that can then be used in a gradient-based optimizer. This makes them very well suited for high-fidelity simulation based aerodynamic shape optimization of highly parametrized geometries such as aircraft wings. However, the development of adjoint-based solvers involve careful mathematical treatment and their implementation require detailed software development. Furthermore, they can become prohibitively expensive when multiple optimization problems are being solved, each requiring multiple restarts to circumvent local optima. In this work, we propose a machine learning enabled, surrogate-based framework that replaces the expensive adjoint solver, without compromising on predicting predictive accuracy. Specifically, we first train a deep neural network (DNN) from training data generated from evaluating the high-fidelity simulation model on a model-agnostic design of experiments on the geometry shape parameters. The optimum shape may then be computed by using a gradient-based optimizer coupled with the trained DNN. Subsequently, we also perform a gradient-free Bayesian optimization, where the trained DNN is used as the prior mean. We observe that the latter framework (DNN-BO) improves upon the DNN-only based optimization strategy for the same computational cost. Overall, this framework predicts the true optimum with very high accuracy, while requiring far fewer high-fidelity function calls compared to the adjoint-based method. Furthermore, we show that multiple optimization problems can be solved with the same machine learning model with high accuracy, to amortize the offline costs associated with constructing our models. Our methodology finds applications in the early stages of aerospace design. (C) 2021 Published by Elsevier Masson SAS.

Renganathan, S. Ashwin↗