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All sources NASA NTRS DOE OSTI

DOE OSTI2021

A multiresolution adaptive wavelet method for nonlinear partial differential equations

We report the multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to solve partial differential equations (PDEs) with features evolving on a wide range of spatial and temporal scales. To meet these challenges, we present a multiresolution wavelet algorithm to solve PDEs with significant data compression and explicit error control. We discretize in space by projecting fields and spatial derivative operators onto wavelet basis functions. We provide error estimates for the wavelet representation of fields and their derivatives. Then, our estimates are used to construct a sparse multiresolution discretization which guarantees the prescribed accuracy. Additionally, we embed a predictor-corrector procedure within the temporal integration to dynamically adapt the computational grid and maintain the accuracy of the solution of the PDE as it evolves. We present examples to highlight the accuracy and adaptivity of our approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Digital Twin: Visualizing the Future of the Power Grid [Slides]

The energy systems are generating data at a scale and complexity that increasingly outpaces our ability to analyze it. This talk argues that rigorous, large-scale visualization is a critical tool for meeting that challenge. Drawing on recent work in the Computational Science Center at the National Laboratory of the Rockies, we trace a progression of visualization research culminating in an immersive digital twin of a real campus power grid. Along the way, we examine why visualization matters at all, where widely-used techniques quietly fail, and what becomes analytically possible when you match the display environment to the scale of the problem.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1994

Merging Intelligent Systems Technologies with CFD Analysis Strategies: Prototype Development at NASA Ames

A collaborative team of researchers from fields of Computational Fluid Dynamics (CFD), fluid physics, computer architectures, and computer science and knowledge engineering have begun work on a prototype system that addresses several of industry's concerns in using NASA-developed CFD codes as part of the design cycle. A major problem exists in the application of CFD technologies within the aeronautics design cycle due primarily to misunderstandings in the ranges of applicability of the various solver codes or turbulence models. Features that arise during the CFD solution process need to be discriminated and recognized as actual flow features with physical support in the geometry and flow conditions of the problem being solved, or as numerical or non-physical errors arising from mis-application of solver code and its parameters, gridding strategies, or discretization. interpolations. The fundamental concept is to develop an intelligent computational system that can accept the engineer's definition of the problem and construct an optimal CFD solution. To do this requires capturing both the knowledge of how to apply the various CFD tools and how to adapt the application of those tools to flow structures as they evolve during the flow simulation. Embedded within this adaptive system approach is the additional desire to automatically identify and quantify the quality of resolution of the pertinent flow structures, be they genuine or error-induced, and then to adjust the solution strategy accordingly. This paper discusses the status of that prototyping effort.

Thompson, David E.↗

DOE OSTI2024

MFANS 2024 - Formally Proving Characteristics of Cyber-Physical Systems

Cyber-physical systems (CPS) are engineered systems that rely on the smooth integration of computational algorithms and physical elements. This integration presents new challenges for verifying that systems will behave as expected. The goal of this presentation is to present current challenges and potential solutions for the formal verification of cyber-physical systems. For cyber systems, formal methods refer to systematically rigorous mathematical techniques employed in the specification, development, analysis, and verification of both software and hardware systems. Recent advancements in computer science have yielded sophisticated tools specifically designed to address challenges associated with formal methods in complex systems. These tools leverage various foundational concepts such as logic, formal languages, program semantics, type systems, type theory, and automata theory. A notable achievement in the application of formal methods is the seL4 microkernel, claimed to be the first general-purpose operating-system kernel to be verified. Its proof implies the absence of bugs and guarantees that the kernel meets specifications. For physical systems, dynamic and control theory has a history of using rigorous analytic techniques to prove functional correctness. Lyapunov, optimal, classical, modern, and robust control theories all provide rigorous mathematical methods both to analyze system performance and to design controller that can be guaranteed to meet certain objectives. Recent computational techniques like level set theory and reachability analysis provide assertions that a system's state will avoid unsafe regions. Even though success has been independently achieved for cyber systems and physical systems, the integration of such systems creates new challenges. In particular, there is an obvious discrepancy between finite-state machines and infinite-state systems, resulting in different approaches for modeling and analyzing these system. While it is possible to simulate hybrid systems, this provides only a demonstration of a performance and not proof. For hybrid systems, current formal methods and system analysis approaches typically require a workarounds to work on hybrid systems like CPS. This paper will outline the state of the art and limits of current practice for formally verifying CPS and will identify possible research directions that require attention.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Cabana: A Performance Portable Library for Particle-Based Simulations

Particle-based simulations are ubiquitous throughout many fields of computational science and engineering, spanning the atomistic level with molecular dynamics (MD), to mesoscale particle-in-cell (PIC) simulations for solid mechanics, device-scale modeling with PIC methods for plasma physics, and massive N-body cosmology simulations of galaxy structures, with many other methods in between (Hockney & Eastwood, 1989). While these methods use particles to represent significantly different entities with completely different physical models, many low-level details are shared including performant algorithms for short- and/or long-range particle interactions, multi-node particle communication patterns, and other data management tasks such as particle sorting and neighbor list construction. Cabana is a performance portable library for particle-based simulations, developed as part of the Co-Design Center for Particle Applications (CoPA) within the Exascale Computing Project (ECP) (Alexander et al., 2020). The CoPA project and its full development scope, including ECP partner applications, algorithm development, and similar software libraries for quantum MD, is described in (Mniszewski et al., 2021). Cabana uses the Kokkos library for on-node parallelism (Edwards et al., 2014; Trott et al., 2022), enabling simulation on multi-core CPU and GPU architectures, and MPI for GPU-aware, multi-node communication. Cabana provides particle simulation capabilities on almost all current Kokkos backends, including serial execution, OpenMP (including OpenMP-Target for GPUs), CUDA (NVIDIA GPUs), HIP (AMD GPUs), and SYCL (Intel GPUs), providing a clear path for the coming generation of accelerator-based exascale hardware. Cabana builds on Kokkos by providing new particle data structures and particle algorithms resulting in a similar execution policy-based, node-level programming model that is intended to be used in addition to the core Kokkos library within an application. Cabana is designed as an application and physics agnostic, but particle-specific toolkit which can either be used to generate a new application, or to be used as needed in existing applications at various levels of invasiveness including through interfaces that wrap user memory in existing data structures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Comparison of Radiation Models for a Turbulent Piloted Methane/Air Jet Flame: A Frozen-Field Study

Numerical modeling of radiative transfer in nongray reacting media is a challenging problem in computational science and engineering. The choice of radiation models is important for accurate and efficient high-fidelity combustion simulations. Different applications usually involve different degrees of complexity, so there is yet no consensus in the community. In this paper, the performance of different radiative transfer equation (RTE) solvers and spectral models for a turbulent piloted methane/air jet flame are studied. The flame is scaled from the Sandia Flame D with a Reynolds number of 22,400. Three classes of RTE solvers, namely the discrete ordinates method, spherical harmonics method, and Monte Carlo method, are examined. The spectral models include the Planck-mean model, the full-spectrum k-distribution (FSK) method, and the line-by-line (LBL) calculation. The performances of different radiation models in terms of accuracy and computational cost are benchmarked. The results have shown that both RTE solvers and spectral models are critical in the prediction of radiative heat source terms for this jet flame. The trade-offs between the accuracy, the computational cost, and the implementation difficulty are discussed in detail. The results can be used as a reference for radiation model selection in combustor simulations.

David, Chloe↗

NASA NTRS2004

College Bound with the Office of Educational Programs

The Educational Programs Office at NASA Glenn Research Center hosts a variety of programs that takes on the hard task of getting students of all ages interested in pursuing careers in science, mathematics, and engineering. To help assist students along the way there are many programs to participate in such as: the explorers, shadowing opportunities, and paid internships. The Educational Programs Office not only creates learning opportunities for students, they also host workshops to help educators enhance their knowledge these fields. This summer I assisted Marie Borowski in the Educational Programs Office with the Tennessee State University College Bound Program. The Tennessee state University College Bound Program is an intensive two-week summer academic workshop designed to introduce minority students to the profession of engineering. NASA Glenn Research Center sent forty dedicated students on a bus to Nashville, Tennessee to experience college life as a whole. At the college the students day consisted of a math class, aeronautics, ACT/SAT preparation, writing and research, African American Culture, computer science, and study sessions. The students also went on educational field trips to the Fisk Museum, the Space and Rocket Center, and the Parthenon Museum. On the last day of the program the students competed in an oratorical contest where the students made a Powerpoint presentation on the class that they enjoyed the most. There were many processes that had to be put into action for the college bound program to run smoothly. The process started in early January with the preparation of applications. Once prepared, the applications were then sent to schools and past participants in hopes of receiving a well-qualified pool of applicants. Once the applications were received, a prescreening is done which ensures all of the information is complete. Then, they are reviewed by a panel, using a rubric to evaluate them, and the semifinalists are then selected. Interviews are held with the students and their parents had to be interviewed by a panel of judges and graded on a rubric. The scores were added up and the forty students were selected. My job this summer was getting the students ready to leave for Tennessee. My job consisted of working very closely with my mentor, Marie Borowski, compile the student data to provide it to the chaperones, TSU records, and NASA records. I learned about the vital communication between the NASA and the TSU program managers. After all the planning was done and the program had begun I had a chance to fly to Tennessee for six days to observe the students daily activities. The students had adjusted very well to the intense schedule, and seemed very enthusiastic about the activities to follow. The whole group was very attentive and enthusiastic program be longer. My goals for the summer were all met. I wanted to learn and retain all the information I possibly could on the job I was given. I was very happy with the end result.

Neal, Brittany D.↗

DOE OSTI2023

Tensor Decompositions for Count Data that Leverage Stochastic and Deterministic Optimization

There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank, nonnegative CPD model to Poisson-distributed count data is of particular interest. Several popular algorithms use local search methods to approximate the global maximum likelihood estimator from local minima. Simultaneously, a recent trend in theoretical computer science and numerical linear algebra leverages randomization to solve very large, hard problems. The typical approach is to use randomization for a fast approximation and determinism for refinement to yield effective algorithms with theoretical guarantees. Two popular algorithms for Poisson CPD reflect that emergent dichotomy: CP Alternating Poisson Regression is a deterministic algorithm and Generalized Canonical Polyadic decomposition makes use of stochastic algorithms in several variants. This work extends recent work to develop two new methods that leverage randomized and deterministic algorithms for improved accuracy and performance.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Exabiome: Advancing Microbial Science through Exascale Computing

The Exabiome project seeks to improve the understanding of microbiomes through the development of methods for accelerating metagenomic science using exascale computing. This article gives an overview of scientific impact of the three components of the project: metagenome assembly, protein family detection, and comparative analysis of metagenomes. Exabiome developed MetaHipMer, the only metagenome assembler capable of scaling to full exascale systems. MetaHipMer has enabled ground-breaking assemblies on the Frontier supercomputer, with many scientific benefits, such as the discovery of rare species and viral genomes. To investigate protein families, Exabiome developed two exascale tools, PASTIS and HipMCL. Together, these can utilize exascale resources to understand the functional diversity of billions of dark matter proteins and novel protein families. For comparative analysis, Exabiome developed kmerprof, a tool that can be used to compare huge metagenomes for many different scientific purposes, for example, grouping human microbiomes according to body location.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Roadmap on electronic structure codes in the exascale era

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing.

36 MATERIALS SCIENCE↗

NASA NTRS2003

Scientific Visualization & Modeling for Earth Systems Science Education

Providing research experiences for undergraduate students in Earth Systems Science (ESS) poses several challenges at smaller academic institutions that might lack dedicated resources for this area of study. This paper describes the development of an innovative model that involves students with majors in diverse scientific disciplines in authentic ESS research. In studying global climate change, experts typically use scientific visualization techniques applied to remote sensing data collected by satellites. In particular, many problems related to environmental phenomena can be quantitatively addressed by investigations based on datasets related to the scientific endeavours such as the Earth Radiation Budget Experiment (ERBE). Working with data products stored at NASA's Distributed Active Archive Centers, visualization software specifically designed for students and an advanced, immersive Virtual Reality (VR) environment, students engage in guided research projects during a structured 6-week summer program. Over the 5-year span, this program has afforded the opportunity for students majoring in biology, chemistry, mathematics, computer science, physics, engineering and science education to work collaboratively in teams on research projects that emphasize the use of scientific visualization in studying the environment. Recently, a hands-on component has been added through science student partnerships with school-teachers in data collection and reporting for the GLOBE Program (GLobal Observations to Benefit the Environment).

Chaudhury, S. Raj↗

DOE OSTI2021

Outlook for artificial intelligence and machine learning at the NSLS-II

Abstract We describe the current and future plans for using artificial intelligence and machine learning (AI/ML) methods at the National Synchrotron Light Source II (NSLS-II), a scientific user facility at the Brookhaven National Laboratory. We discuss the opportunity for using the AI/ML tools and techniques developed in the data and computational science areas to greatly improve the scientific output of large scale experimental user facilities. We describe our current and future plans in areas including from detecting and recovering from faults, optimizing the source and instrument configurations, streamlining the pipeline from measurement to insight, through data acquisition, processing, analysis. The overall strategy and direction of the NSLS-II facility in relation to AI/ML is presented.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Holistic Measurement Driven Resilience: Combining Operational Fault and Failure Measurements and Fault Injection for Quantifying Fault Detection, Propagation and Impact. Final report

For HPC systems to date, application resilience to faults and failures has been accomplished by the brute- force method of checkpoint/restart, which allows an application to make forward progress in the face of system and application faults, errors, and failures independent of root cause or end result. It has remained the primary resilience mechanism because we lack a way to identify faults and anticipate consequences early enough to take meaningful mitigating action. However, checkpoint/restart implementations put a tremendous burden on system resources and on the applications themselves and is becoming less feasible at scale. Because we have not yet operated at scales at which checkpoint/restart fails to provide forward progress, despite increasing costs, vendors have had little motivation to provide the instrumentation necessary for early identification of faults and failures. However, as we move from petascale to exascale, component mean time to failure (MTTF) will render the existing techniques ineffectual and/or too expensive. Furthermore, fault recovery mechanisms such as failover and/or error correction introduce performance inconsistency. Instrumentation allowing early indication of problems and tools to enable use of such information by systems, operating systems, and applications offer an alternative, more scalable and less costly solution. In the HMDR project, we built on our experience and expertise developed and accumulated over years of research on design, monitoring, measurement, and assessment of resilient computing systems. Analysis of field data on the current and past generations of extreme-scale systems revealed several challenges that, if not addressed in increasingly larger and more complex systems, may hinder the effectiveness of future exascale computing systems. Specifically, i) file systems and interconnects in current-generation large-scale systems already operate at the margins of resiliency, including consistent performance, and may not scale to larger deployments; ii) automated, software-based failover mechanisms are frequently inadequate and can introduce wider failures, such that failures during recovery may lead to system/application failures, including system-wide outages; and iii) silent data corruption represents a critical fault mode and will require efficient detection mechanisms if next-generation applications are to take full advantage of exascale hardware. To address the above challenges, we assembled a team of world-renowned experts in resilient extreme- scale computing from the University of Illinois (Electrical and Computer Engineering, Computer Science, and NCSA), SNL, LANL, NERSC, and Cray. Our team includes representatives from centers that house many of the largest HPC resources in the world, both today and over the coming years. The team has a unique track record of research in i) system and application failure characterization based on the analysis of field data, ii) data-driven design of fault/error detection mechanisms, and iii) experimental characterization of system/application resiliency. The team includes system owners/operators who provide continuous data collection and access and ensure installation of appropriate analysis tools.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1997

The HSCaRS Summer Enrichment Program; Research Opportunities for Minority and Women Undergraduates in Global Change Science

The primary objective of the HSCaRS Summer Enrichment Program (SEP) is to make significant contributions to the NASA Mission to Planet Earth (MTPE) and the Alabama A&M University (AAMU) Center for Hydrology, Soil Climatology and Remote Sensing (HSCaRS) research missions by providing undergraduate student research internships with an emphasis on minority and women students. Additional objectives are to encourage more minority and women students to pursue advanced degrees in Earth system and global change science and to increase the participation of minority institutions in the U.S. Global Change Research Program. Also, the SEP strives to make students in the traditional science disciplines more aware of the opportunities in Earth System Science. In designing the SEP, it was acknowledged that HSCaRS was a new research effort and Center. Consequently, students were not expected to immediately recognize the Center as one would older, more established research laboratories with national reputations, such as Los Alamos, Battelle, National Consortium for Atmospheric Research (NCAR), etc. Yet we still wanted to compete nationally for the best students. Therefore, we designed the program with a competitive financial package that includes a stipend of $400 per week, round-trip transportation from home to the summer research site, and free campus housing and meal plans provided by Alabama A&M University. Students also received a modest living allowance of approximately $25 per week. The internship program was 10 weeks in residence at Alabama A&M University or IGCRE, and gave students the opportunity to select from six general research areas: micro-meteorology, soil data analysis, soil moisture modeling, instrumentation, geographic information systems, and computer science. Student participants also enrolled in an introductory global change science course as part of the summer program (a copy of the course outline is in the appendix). The program included participation in a field program for approximately two weeks. All students were required to participate in the field program as a learning experience, regardless of the relationship of the field program to their majors or particular research project.

Estes, Jr., Maurice G.↗

DOE OSTI2020

On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encountered in computational science and engineering. Guided by data and physical laws, PINNs find a neural network that approximates the solution to a system of PDEs. Such a neural network is obtained by minimizing a loss function in which any prior knowledge of PDEs and data are encoded. Despite its remarkable empirical success in one, two or three dimensional problems, there is little theoretical justification for PINNs. As the number of data grows, PINNs generate a sequence of minimizers which correspond to a sequence of neural networks. We want to answer the question: Does the sequence of minimizers converge to the solution to the PDE? We consider two classes of PDEs: linear second-order elliptic and parabolic. By adapting the Schauder approach and the maximum principle, we show that the sequence of minimizers strongly converges to the PDE solution in C 0 . Furthermore, we show that if each minimizer satisfies the initial/boundary conditions, the convergence mode becomes H 1 . Computational examples are provided to illustrate our theoretical findings. To the best of our knowledge, this is the first theoretical work that shows the consistency of PINNs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

PETSc Users Manual (Rev. 3.13)

This manual describes the use of PETSc for the numerical solution of partial differential equations and related problems on high-performance computers. The Portable, Extensible Toolkit for Scientific Computation (PETSc) is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all message-passing communication. PETSc includes an expanding suite of parallel linear solvers, nonlinear solvers, and time integrators that may be used in application codes written in Fortran, C, C++, and Python. PETSc provides many of the mechanisms needed within parallel application codes, such as parallel matrix and vector assembly routines. The library is organized hierarchically, enabling users to employ the level of abstraction that is most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users. PETSc is a sophisticated set of software tools; as such, for some users it initially has a much steeper learning curve than a simple subroutine library. In particular, for individuals without some computer science background, experience programming in C, C++, python, or Fortran and experience using a debugger such as gdb or dbx, it may require a significant amount of time to take full advantage of the features that enable efficient software use. However, the power of the PETSc design and the algorithms it incorporates may make the efficient implementation of many application codes simpler than \rolling them" yourself.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Chapter Nine - Automated Optimal Control in Energy Systems: The Reinforcement Learning Approach

With the development of smart grid technologies an increasing number of new devices and participants have joined modern energy systems and are inevitably making them more complicated and interdependent than ever. Optimally controlling such a complex energy system and maintaining its operation in a high-efficient, secure, and resilient manner are challenging tasks to the system operators. Fortunately, the revolution in deep learning and artificial intelligence (AI), both from hardware and algorithms perspectives, has provided new ideas and solutions to many previously intractable problems. As a result, this advance in computer science also sparked great research interests in utilizing AI in solving engineering problems related to the modern energy systems. Among many AI techniques, deep reinforcement learning (DRL) has demonstrated great potential for solving sequential optimization problems, which are very common in the engineering domains. Its ability to handle nonlinearity and stochasticity in controlled systems has out-competed many traditional optimal control algorithms. Therefore in this chapter, we focus on the state-of-the-art of DRL concepts and related algorithms, compare their pros and cons with traditional optimal control approaches and discuss the typical workflow for leveraging RL in solving complex problems in modern energy systems.

artificial intelligence↗

DOE OSTI2026

Report of the 2026 Workshop on Next-Generation Ecosystems for Scientific Computing: Harnessing Community, Software, and AI for Cross-Disciplinary Team Science

Scientific computing is undergoing rapid transformation as advances in artificial intelligence, heterogeneous computing, automation, and data-intensive research reshape not only computational tools but also the institutions, workforce models, and collaborative practices that support scientific discovery. This report synthesizes insights from the 2026 Workshop on Next-Generation Ecosystems for Scientific Computing, the second in a three-year series focused on strengthening scientific computing ecosystems through socio-technical co-design. Workshop discussions identified four interdependent strategic themes: software ecosystems for AI-enabled scientific discovery; trust, validation, and traceability; human-AI teaming and paradigm shifts; and workforce, pedagogy, and governance. The report translates these themes into eight priorities for community action spanning shared research infrastructure, trust and traceability, user experience, human-AI teaming, workforce development, cross-sector coordination, stewardship and sustainability, and evaluation of scientific value. Together, these priorities outline directions for building scientific computing ecosystems that remain trustworthy, sustainable, innovative, and resilient as AI assumes a growing role in scientific work.

AI↗