SEARCH · Search NASA

Results for “adaptive robust optimization”

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.

SourceResearch connectionFrom yearThrough year

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

At least 253 records · Page 14

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Sequential Decision Making (SDM) for Mesh Refinement and Model Selection in Multiscale, Multi-Physics Applications

Intelligent automation and decision support are needed to enhance computational efficiency and robustness in multiscale and multi-physics problems, including materials science, manufacturing, and climate and weather modeling. Current scientific computing approaches for enabling decisions by scientists fail to explore the role of learning, reasoning, and probabilistic planning. Often these decisions are not performed in real-time during the computation but are made prior to the start of the computation, which must be interrupted in order to make changes to the prior choices. Such interruptions at different stages of the computation increase the total computing time and the need for a human expert to frequently monitor the results. State of art scientific computing methods consist of rule-based algorithms that cannot automatically adapt to a dynamically changing computing environment. The development of a Sequential Decision Making (SDM) framework will automate scientific computing by optimizing the policies for mesh refinement, time-stepping, model and algorithm selection, resource allocation, and pre and post-processing. Our agent SDM framework for scientific computing will consist of data-driven learning (Classifier), automated reasoning (contextual knowledge), and probabilistic planning (Reinforcement Learning). In this project, we focused on three problems to demonstrate our SDM framework on a set of ordinary and partial differential equations. Classification of Lorenz system regions using Feed-Forward Neural Networks examined learning in the SDM framework. On the other hand, reasoning and planning in the SDM framework were used in two problems: adaptive time-stepping for nonlinear ODEs using on-policy RL algorithms, and adaptive mesh refinement for 2-D PDEs using off-policy RL algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Mid-IR UAV-based sensing platform with deep learning to Identify and Quantify Gaseous Emission in Gas Flares

This report details the development and evaluation of a Mid-Infrared (Mid-IR) Unmanned Aerial Vehicle (UAV)-based sensing platform integrated with deep learning algorithms for the identification and quantification of gaseous emissions in gas flares. The project, spearheaded by Omega Optics, Inc., aimed to address environmental monitoring challenges by leveraging advanced photonic technologies and autonomous UAV operations. The research focused on designing, optimizing, and fabricating photonic crystal waveguides and grating couplers to enhance the sensitivity and accuracy of gas detection. A comprehensive drone-based system was developed, featuring a miniaturized sensor, GPS module, and microcontroller communication network for real-time gas concentration monitoring. The system's adaptive sampling algorithm, implemented using the Robot Operating System (ROS), enables autonomous detection and localization of gas emission sources. Preliminary results demonstrate the platform's capability to detect and monitor gas emissions with high precision, cost-effectiveness, and scalability. Future work will expand upon this foundation by introducing 3D wind model-based learning for dynamic environmental conditions and further enhancing the user interface and data processing algorithms to support broader environmental monitoring applications. Overall, this project represents a significant step forward in UAV-based environmental sensing technologies, offering robust solutions for detecting and mitigating the impacts of gaseous emissions on public health and safety.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Engineering and evolution of Yarrowia lipolytica for producing lipids from lignocellulosic hydrolysates

Yarrowia lipolytica, an oleaginous yeast, shows promise for industrial fermentation due to its robust acetyl-CoA flux and well-developed genetic engineering tools. However, its lack of an active xylose metabolism restricts the conversion of cellulosic sugars to valuable products. To address this, metabolic engineering, and adaptive laboratory evolution (ALE) were applied to the Y. lipolytica PO1f strain, resulting in an efficient xylose-assimilating strain (XEV). Whole-genome sequencing (WGS) of the XEV followed by reverse engineering revealed that the amplification of the heterologous oxidoreductase pathway and a mutation in the GTPase-activating protein gene (YALI0B12100g) might be the primary reasons for improved xylose assimilation in the XEV strain. When a sorghum hydrolysate was used, the XEV strain showed superior xylose consumption and lipid production compared to its parental strain (X123). This study advances our understanding of xylose metabolism in Y. lipolytica and proposes effective metabolic engineering strategies for optimizing lignocellulosic hydrolysates.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2024

raogroupuiuc/yl_variantcalling

NGS analysis for mutation analysis in Yarrowia lipolytica evolved strains. Yarrowia lipolytica, an oleaginous yeast, shows promise for industrial fermentation due to its robust acetyl-CoA flux and well-developed genetic engineering tools. However, its lack of an active xylose metabolism restricts the conversion of cellulosic sugars to valuable products. To address this, metabolic engineering, and adaptive laboratory evolution (ALE) were applied to the Y. lipolytica PO1f strain, resulting in an efficient xylose-assimilating strain (XEV). Whole-genome sequencing (WGS) of the XEV followed by reverse engineering revealed that the amplification of the heterologous oxidoreductase pathway and a mutation in the GTPase-activating protein gene (YALI0B12100g) might be the primary reasons for improved xylose assimilation in the XEV strain. When a sorghum hydrolysate was used, the XEV strain showed superior xylose consumption and lipid production compared to its parental strain (X123). This study advances our understanding of xylose metabolism in Y. lipolytica and proposes effective metabolic engineering strategies for optimizing lignocellulosic hydrolysates.

Deewan, Anshu↗

DOE OSTI2025

Efficient near-field ptychography reconstruction using the Hessian operator

X-ray ptychography is a powerful and robust coherent imaging method providing access to the complex object and probe (illumination). Ptychography reconstruction is typically performed using first-order methods due to their computational efficiency. Higher-order methods, while potentially more accurate, are often prohibitively expensive in terms of computation. In this study, we present a mathematical framework for reconstruction using second-order information derived from an efficient computation of the bilinear Hessian and Hessian operator. The formulation is provided for Gaussian-based models, enabling the simultaneous reconstruction of the object, probe, and object positions. Synthetic data tests, along with experimental near-field ptychography data processing, demonstrate a ten-fold reduction in computation time compared to first-order methods. The derived formulas for computing the Hessians, along with the strategies for incorporating them into optimization schemes, are well-structured and easily adaptable to various ptychography problem formulations.

Carlsson, Marcus [Lund Univ. (Sweden)] (ORCID:0000↗

NASA NTRS2011

Simple, Robust Cryogenic Propellant Depot for Near Term Applications

The ability to refuel cryogenic propulsion stages on-orbit provides an innovative paradigm shift for space transportation supporting National Aeronautics and Space Administration s (NASA) Exploration program as well as deep space robotic, national security and commercial missions. Refueling enables large beyond low Earth orbit (LEO) missions without requiring super heavy lift vehicles that must continuously grow to support increasing mission demands as America s exploration transitions from early Lagrange point missions to near Earth objects (NEO), the lunar surface and eventually Mars. Earth-to-orbit launch can be optimized to provide competitive, cost-effective solutions that allow sustained exploration. This paper describes an experimental platform developed to demonstrate the major technologies required for fuel depot technology. This test bed is capable of transferring residual liquid hydrogen (LH2) or liquid oxygen (LO2) from a Centaur upper stage, and storage in a secondary tank for up to one year on-orbit. A dedicated, flight heritage spacecraft bus is attached to an Evolved Expendable Launch Vehicle (EELV) Secondary Payload Adapter (ESPA) ring supporting experiments and data collection. This platform can be deployed as early as Q1 2013. The propellant depot design described in this paper can be deployed affordably this decade supporting missions to Earth-Moon Lagrange points and lunar fly by. The same depot concept can be scaled up to support more demanding missions and launch capabilities. The enabling depot design features, technologies and concept of operations are described.

McLean, Christopher↗

DOE OSTI2021

Beyond optimization—supervised learning applications in relativistic laser-plasma experiments

We explore the applications of machine learning techniques in relativistic laser-plasma experiments beyond optimization purposes. We predict the beam charge of electrons produced in a laser wakefield accelerator given the laser wavefront change caused by a deformable mirror. Machine learning enables feature analysis beyond merely searching for an optimal beam charge, showing that specific aberrations in the laser wavefront are favored in generating higher beam charges. Supervised learning models allow characterizing the measured data quality as well as recognizing irreproducible data and potential outliers. Furthermore, we also include virtual measurement errors in the experimental data to examine the model robustness under these conditions. This work demonstrates how machine learning methods can benefit data analysis and physics interpretation in a highly nonlinear problem of relativistic laser-plasma interaction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRSDate not supplied

Lessons Learned from Astrobee Operations on the International Space Station

Since its launch in 2019, NASA has been operating three Astrobee free-flying robots providing an autonomous and adaptable research platform aboard the International Space Station (ISS). These robots have not only facilitated a myriad of national and international research endeavors in microgravity but have also served as a STEM outreach platform for student competitions aboard the ISS. Amidst its extensive operational tenure, spanning over five years and exceeding 1200 hours of cumulative free-flyer operation as of April 2024, the Astrobee robots have encountered software and hardware anomalies. Despite its inherent design for on-orbit repair or replacement, certain anomalies have proven to be complex, necessitating remote resolution via software and firmware updates or, in extreme cases, hardware replacements or the return of faulty units to NASA's ground facilities for repair. Such challenges underscore the delicate balance between the autonomous functionality of Astrobee and the occasional need for human intervention to maintain optimal performance. One recurring point of failure identified during Astrobee's operational lifespan has been the SD card, a critical component utilized by the different Astrobee processors and the Dock Station. The occurrence of SD card anomalies, both on orbit and within ground units, has provided invaluable insights into the improvement of Astrobee's systems and mitigation to future faults. This presentation will focus on four key areas: 1. Overview of Faults and Anomalies: A comprehensive examination of the diverse array of faults and anomalies encountered by Astrobee and its associated systems both in orbit and on the ground. From software glitches to hardware malfunctions, this section provides insights into the challenges faced during Astrobee's operational tenure. 2. Resolution Processes and Procedures: An in-depth discussion of the methodologies and procedures implemented to resolve the encountered anomalies. This includes remote troubleshooting, software patches, firmware updates, and, when necessary, the logistics involved in hardware replacements or down-massing for repair. 3. Implementation of Software Updates and Hardware Upgrades: A detailed exploration of the strategies employed to mitigate the risk of recurring anomalies through the implementation of software updates and hardware upgrades. This section highlights the iterative nature of Astrobee's development, emphasizing the continuous pursuit of robustness and reliability. 4. Lessons Learned and Future Directions: Reflecting on the insights gained from addressing anomalies, this section examines the lessons learned and outlines future directions for enhancing Astrobee's robustness and resilience. It underscores the iterative nature of space exploration and the importance of adaptability and continuous improvement in the pursuit of scientific discovery. Through a nuanced examination of Astrobee's operational challenges and the strategies employed to overcome them, this presentation sheds light on the complexities of operating autonomous robotic systems in the ISS environment. It underscores NASA's commitment to pushing the boundaries of exploration and innovation while navigating the inherent challenges of space exploration.

Astrobee↗

NASA NTRSDate not supplied

Lessons Learned from Astrobee Operations on the International Space Station

Astrobee↗

DOE OSTI2026

Biorefinery siting and sizing to achieve the US Billion‐Ton Bioeconomy vision: A case study using a gasification–Fischer–Tropsch process

Achieving a secure, abundant, and affordable energy future requires a robust and adaptable energy strategy, with bioenergy playing a pivotal role. Biomass-based energy presents a promising pathway to use domestic resources while fostering economic opportunities in rural areas. Despite the potential to source more than 1 billion dry short tons of biomass annually in the US, significant infrastructure and economic barriers hinder full utilization for energy production. This study used the Biofuel Infrastructure, Logistics, and Transportation (BILT) model to assess biorefinery siting and scale and determine the number and size of facilities required to maximize use of the US biomass potential. A spatially agnostic approach first assessed the effects of facility capacity and transportation constraints on biomass use. Then, a spatially explicit analysis integrated county-level biomass availability from the US Department of Energy's 2023 Billion-Ton Report and technoeconomic assessments to evaluate different biorefinery deployment scenarios. The results indicate that an optimized mix of facility sizes is essential to leverage biomass resources fully across varying regional production densities to maximize use of the US biomass potential. Larger biorefineries or co-located smaller facilities significantly enhance biomass use while reducing costs through economies of scale. These findings underscore the importance of strategically balancing facility capacity and spatial distribution to optimize the bioenergy supply chain. In conclusion, this study provides critical insights for advancing the US bioenergy economy by aligning biorefinery deployment with biomass resource availability and economic viability.

BILT Model↗

DOE OSTI2020

MimicGAN: Robust Projection onto Image Manifolds with Corruption Mimicking

In the past few years, Generative Adversarial Networks (GANs) have dramatically advanced our ability to represent and parameterize high-dimensional, non-linear image manifolds. As a result, they have been widely adopted across a variety of applications, ranging from challenging inverse problems like image completion, to problems such as anomaly detection and adversarial defense. A recurring theme in many of these applications is the notion of projecting an image observation onto the manifold that is inferred by the generator. In this context, Projected Gradient Descent (PGD) has been the most popular approach, which essentially optimizes for a latent vector that minimizes the discrepancy between a generated image and the given observation. However, PGD is a brittle optimization technique that fails to identify the right projection (or latent vector) when the observation is corrupted, or perturbed even by a small amount. Such corruptions are common in the real world, for example images in the wild come with unknown crops, rotations, missing pixels, or other kinds of non-linear distributional shifts which break current encoding methods, rendering downstream applications unusable. To address this, we propose corruption mimicking—a new robust projection technique, that utilizes a surrogate network to approximate the unknown corruption directly at test time, without the need for additional supervision or data augmentation. The proposed method is significantly more robust than PGD and other competing methods under a wide variety of corruptions, thereby enabling a more effective use of GANs in real-world applications. Finally, more importantly, we show that our approach produces state-of-the-art performance in several GAN-based applications—anomaly detection, domain adaptation, and adversarial defense, that benefit from an accurate projection.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2013

Orion MPCV Touchdown Detection Threshold Development and Testing

A robust method of detecting Orion Multi-Purpose Crew Vehicle (MPCV) splashdown is necessary to ensure crew and hardware safety during descent and after touchdown. The proposed method uses a triple redundant system to inhibit Reaction Control System (RCS) thruster firings, detach parachute risers from the vehicle, and transition to the post-landing segment of the Flight Software (FSW). An in-depth trade study was completed to determine optimal characteristics of the touchdown detection method resulting in an algorithm monitoring filtered, lever-arm corrected, 200 Hz Inertial Measurement Unit (IMU) vehicle acceleration magnitude data against a tunable threshold using persistence counter logic. Following the design of the algorithm, high fidelity environment and vehicle simulations, coupled with the actual vehicle FSW, were used to tune the acceleration threshold and persistence counter value to result in adequate performance in detecting touchdown and sufficient safety margin against early detection while descending under parachutes. An analytical approach including Kriging and adaptive sampling allowed for a sufficient number of finite element analysis (FEA) impact simulations to be completed using minimal computation time. The combination of a persistence counter of 10 and an acceleration threshold of approximately 57.3 ft/s2 resulted in an impact performance factor of safety (FOS) of 1.0 and a safety FOS of approximately 2.6 for touchdown declaration. An RCS termination acceleration threshold of approximately 53.1 ft/s(exp)2 with a persistence counter of 10 resulted in an increased impact performance FOS of 1.2 at the expense of a lowered under-parachutes safety factor of 2.2. The resulting tuned algorithm was then tested on data from eight Capsule Parachute Assembly System (CPAS) flight tests, showing an experimental minimum safety FOS of 6.1. The formulated touchdown detection algorithm will be flown on the Orion MPCV FSW during the Exploration Flight Test 1 (EFT-1) mission in the second half of 2014.

Daum, Jared↗

DOE OSTI2021

Sensor enabled data-driven predictive analytics for modeling and control with high penetration of DERs in distribution systems

The electric power grid is undergoing a tremendous transformation due to the increasing penetration of renewable energy resources beginning with wind and more recently with the distributed energy resources (DERs) such as solar and battery storage. DERs have dramatically changed the role of the distribution systems in the overall power grid, and they are expected to contribute a significant portion of power generation in the future. If current trends for DERs continue, system operation and control will need to change dramatically for improved grid reliability and resiliency. As renewable resources increase in penetration, new and challenging operational, planning, and design problems are expected to emerge. Some of the key challenges that arise in the planning and operation of the future grid are: 1) Quantifying the impact of high DER penetration in distribution systems on bulk grid behavior over multiple time scales. 2) Identifying whether a particular DER configuration/settings have a large impact on the overall grid behavior. These challenges can be addressed in an offline manner using detailed T&D grid models and they can also be addressed in an online manner using sensor measurements. In particular, the advancement and planned growth in sensor technology in power grid over various voltage levels provide us with a unique opportunity to tackle these challenges from a data analytic perspective without needing detailed T&D grid models. A few questions that naturally arise when addressing the challenges from DERs using sensor data are: 1) How can we use limited sensor measurements to monitor & control voltage stability and small signal stability of the bulk system? 2) How can we ensure that the developed data analytic methods are robust to data availability and quality issues? 3) How can we compute the developed analytics in a scalable manner using streaming measurements? In this project, we addressed the aforementioned challenges arising from DERs and answered the questions raised above on how to effectively use the sensor measurements to enhance the reliability and performance of the electric grid. Thus, the overarching goal of this project is to develop effective reduced/representative system models from data that make the computational complexity sufficiently manageable so as to be useful to simulate, analyze, and even control complex non-linear power systems dynamics with large penetrations of DERs. In order to achieve the objective, the project team established a four-fold technical approach 1) Formulated a combined transmission-distribution co-simulation framework for data generation and validation, 2) Derived reduced/representative models of power systems based on data-driven methods for efficient computation and appropriate representation of system behavior, 3) Developed data driven characterization of power system behavior based on transfer operator theory, machine learning and optimization for model estimation, 4) Incorporated a scalable data management and processing architecture using distributed Kafka streaming applications that coordinate input data streams to the developed data analytics. The key accomplishments of the project are: 1) Development of a scalable multi-timescale T&D co-simulation framework (both for steady state and for dynamic co-simulation) using commercial solvers (PSSE and GridLAB-D). The steady-state T&D co-simulation interface is shared with our industry partner (PJM). 2) A structured reduced order dynamic model of distribution systems that can represent partial motor stalling along with a systematic procedure to derive the model parameters. 3) A PMU based online method to monitor, localize and mitigate fault-induced delayed voltage recovery using DER reactive support and load control in distribution systems. 4) Development of linear operator based robust methodologies for dynamic state estimation, uncertainty quantification, system identification and trajectory prediction for power system dynamics. 5) An adaptive damping control for utilizing wind energy resources to provide oscillation damping and system stability. 6) Implementation of Kafka-based framework for efficient processing of streaming data using Linux-based local virtual environment.

DER integration↗

DOE OSTI2021

Revisiting the ODE Method for Recursive Algorithms: Fast Convergence Using Quasi Stochastic Approximation

Several decades ago, Profs. Sean Meyn and Lei Guo were postdoctoral fellows at ANU, where they shared interest in recursive algorithms. It seems fitting to celebrate Lei Guo's 60th birthday with a review of the ODE Method and its recent evolution. The method has been regarded as a technique for algorithm analysis. It is argued that this viewpoint is backwards: The original stochastic approximation method was surely motivated by an ODE, and tools for analysis came much later (based on establishing robustness of Euler approximations). The paper presents a brief survey of recent research in machine learning that shows the power of algorithm design in continuous time, following by careful approximation to obtain a practical recursive algorithm. While these methods are usually presented in a stochastic setting, this is not a prerequisite. In fact, recent theory shows that rates of convergence can be dramatically accelerated by applying techniques inspired by quasi Monte-Carlo. Subject to conditions, the optimal rate of convergence can be obtained by applying the averaging technique of Polyak and Ruppert. The conditions are not universal, but theory suggests alternatives to achieve acceleration. The theory is illustrated with applications to gradient-free optimization, and policy gradient algorithms for reinforcement learning.

learning and adaptive systems in artificial intell↗

NASA NTRS2017

Genetic Algorithm-Guided, Adaptive Model Order Reduction of Flexible Aircrafts

This paper presents a methodology for automated model order reduction (MOR) of flexible aircrafts to construct linear parameter-varying (LPV) reduced order models (ROM) for aeroservoelasticity (ASE) analysis and control synthesis in broad flight parameter space. The novelty includes utilization of genetic algorithms (GAs) to automatically determine the states for reduction while minimizing the trial-and-error process and heuristics requirement to perform MOR; balanced truncation for unstable systems to achieve locally optimal realization of the full model; congruence transformation for "weak" fulfillment of state consistency across the entire flight parameter space; and ROM interpolation based on adaptive grid refinement to generate a globally functional LPV ASE ROM. The methodology is applied to the X-56A MUTT model currently being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies indicate that X-56A ROM with less than one-seventh the number of states relative to the original model is able to accurately predict system response among all input-output channels for pitch, roll, and ASE control at various flight conditions. The GA-guided approach exceeds manual and empirical state selection in terms of efficiency and accuracy. The adaptive refinement allows selective addition of the grid points in the parameter space where flight dynamics varies dramatically to enhance interpolation accuracy without over-burdening controller synthesis and onboard memory efforts downstream. The present MOR framework can be used by control engineers for robust ASE controller synthesis and novel vehicle design.

Numerical Analysi↗

DOE OSTI2024

Collaborative Design of Robust Adaptation Pathways for Urban Flooding Resilience in Baltimore

Urban pluvial flooding poses a growing threat to the city of Baltimore, driven by changes in climate and rainfall, increased impervious area, aging infrastructure, and severe social inequity. Adaptations to urban flooding should strengthen community-scale resilience while navigating the uncertainties associated with future actions. However, the highly uncertain future climate and conflicting stakeholder objectives complicate the selection of effective and socially acceptable strategies. This study addresses these challenges through a community-informed Multi Objective Robust Decision Making (MORDM) process, coupled with Dynamic Adaptation Policy Pathways (DAPP). Community stakeholders are engaged on a large scale through community partnerships, including priority identification sessions, focus groups, and metric identification workshops. The combination of community partnership, MORDM, and DAPP will create an original set of adaptation pathways which are aligned with community goals and values, and furthermore are adjustable under changing future constraints and conditions. This framework will enhance the city's capacity to respond to evolving pluvial flood conditions while accounting for diverse stakeholder interests and will provide guidance for addressing both the immediate and long-term challenges of urban flooding in Baltimore.

BSEC↗

NASA NTRS1993

Structured adaptive grid generation using algebraic methods

The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration of points to the grid redistribution scheme. The evaluation of the weighting mesh is accomplished by utilizing the weight function representing the solution variation and the equidistribution law. The selection of the weight function plays a key role in grid adaptation. A new weight function utilizing a properly weighted boolean sum of various flowfield characteristics is defined. The redistribution scheme is developed utilizing Non-Uniform Rational B-Splines (NURBS) representation. The application of NURBS representation results in a well distributed smooth grid by maintaining the fidelity of the geometry associated with boundary curves. Several algebraic methods are applied to smooth and/or nearly orthogonalize the grid lines. An elliptic solver is utilized to smooth the grid lines if there are grid crossings. Various computational examples of practical interest are presented to demonstrate the success of these methods.

Yang, Jiann-Cherng↗

DOE OSTI2023

Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures

Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach. In this work, we propose a learning framework to extract a peridynamics model as a mesoscale continuum surrogate from MD simulated material fracture data sets. Firstly, we develop a novel coarse-graining method, to automatically handle the material fracture and its corresponding discontinuities in the MD displacement data sets. Inspired by the weighted essentially non-oscillatory (WENO) scheme, the key idea lies at an adaptive procedure to automatically choose the locally smoothest stencil, then reconstruct the coarse-grained material displacement field as the piecewise smooth solutions containing discontinuities. Then, based on the coarse-grained MD data, a two-phase optimization-based learning approach is proposed to infer the optimal peridynamics model with damage criterion. In the first phase, we identify the optimal nonlocal kernel function from the data sets without material damage to capture the material stiffness properties. Then, in the second phase, the material damage criterion is learnt as a smoothed step function from the data with fractures. As a result, a peridynamics surrogate is obtained. As a continuum model, our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training, and hence allows for substantial reductions in computational cost compared with MD. We illustrate the efficacy of the proposed approach with several numerical tests for the dynamic crack propagation problem in a single-layer graphene. Our tests show that the proposed data-driven model is robust and generalizable, in the sense that it is capable of modeling the initialization and growth of fractures under discretization and loading settings that are different from the ones used during training.

97 MATHEMATICS AND COMPUTING↗