Scientific Computing (2024)

Optimal Approximation Algorithms in High Dimensions

Akil Narayan
The increasing power of modern computational hardware has enabled computer-based simulation of sophisticated mathematical models that resolve important physical phenomena in great detail. With the advent of these computational abilities has come an increased demand to include more complex physical interactions in the models, and thus an increased strain on computational resources. Modern engineering design utilizes such models, and these design problems typically involve (1) numerous tunable parameters that affect reliability, cost, and failure, (2) uncertainty about external influences manifesting as randomness in the model, and (3) epistemic ignorance involving model form uncertainty. In realistic applications, the collection of these effects leads to predictions that depend on a cumulatively high-dimensional parameter. This project focuses on development and deployment of novel, near-optimal experimental design and sampling algorithms for the accurate and efficient simulation of physical models parameterized by high-dimensional inputs. The work of this project involves the application of recently developed approximation theory results in the computational arena, targeted advances that extend theoretical mathematics for computational purposes, and the development and implementation of algorithms for large-scale computations.

The technical aspects of this project are designed to provide feasible computational algorithms and concrete mathematical guarantees for tasks in high-dimensional approximation. The three major core components for the completion of this task involve the design, implementation, and analysis of algorithms that leverage optimality characteristics of (1) random and deterministic experimental and sampling design, (2) computational algorithms for identifying efficient sampling schemes, and (3) strategies and techniques for emerging approximation paradigms such as sparse approximation and dimension reduction. A crosscutting theme is application of these methods to problems of modern interest in scientific computing. This project involves fundamental contributions to the fields of applied approximation theory and computational approximation methods through the development of applications-oriented sampling designs with provable near-optimality. Theoretical investigations of this project connect classical techniques in approximation and linear algebra with emerging algorithms in data reduction and reduced order modeling. The implementation of these algorithms will significantly enhance theoretical understanding and computational feasibility for goal-oriented design, parameter study and reduction, sparse and compressive representations, model verification and calibration, and data-driven simulations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

Cyberinfrastructure Center of Excellence Pilot Study

Ewa Deelman, Valerio Pascucci, Anirban Mandal, Jaroslaw Nabrzyski, Robert Ricci
University of Southern California, Los Angeles, CA, United States

NSF's major multi-user research facilities (large facilities) are sophisticated research instruments and platforms - such as large telescopes, interferometers and distributed sensor arrays - that serve diverse scientific disciplines from astronomy and physics to geoscience and biological science. Large facilities are increasingly dependent on advanced cyberinfrastructure (CI) - computing, data and software systems, networking, and associated human capital - to enable broad delivery and analysis of facility-generated data. As a result of these cyber infrastructure tools, scientists and the public gain new insights into fundamental questions about the structure and history of the universe, the world we live in today, and how our plants and animals may change in the coming decades. The goal of this pilot project is to develop a model for a Cyberinfrastructure Center of Excellence (CI CoE) that facilitates community building and sharing and applies knowledge of best practices and innovative solutions for facility CI.

The pilot project will explore how such a center would facilitate CI improvements for existing facilities and for the design of new facilities that exploit advanced CI architecture designs and leverage establish tools and solutions. The pilot project will also catalyze a key function of an eventual CI CoE - to provide a forum for exchange of experience and knowledge among CI experts. The project will also gather best practices for large facilities, with the aim of enhancing individual facility CI efforts in the broader CI context. The discussion forum and planning effort for a future CI CoE will also address training and workforce development by expanding the pool of skilled facility CI experts and forging career paths for CI professionals. The result of this work will be a strategic plan for a CI CoE that will be evaluated and refined through community interactions: workshops and direct engagement with the facilities and the broader CI community.

This project is being supported by the Office of Advanced Cyberinfrastructure in the Directorate for Computer and Information Science and Engineering and the Division of Emerging Frontiers in the Directorate for Biological Sciences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

Efficiency and Productivity through Artificial Intelligence

Valerio Pascucci
Efficient cyberinfrastructure (advanced computing, data, software and networking infrastructure) is a critical component of the support that NSF provides for new discoveries in science and engineering. Cyberinfrastructure is complex and traditionally requires years of human hand-tuning to fully achieve maximal performance for scientific users. We propose to introduce Artificial Intelligence (AI) as a way to automatically and quickly optimize the performance and broadest use of recent NSF-supported advanced computing resources. Through this pilot effort our ultimate aim is to enable and accelerate scientific advances in widely diverse fields such as biology, chemistry, oceanography, materials science, climate modeling, and cosmology.

As the research cyberinfrastructure grows rapidly in scale and complexity, it is essential to integrate new technologies based on Machine Learning (ML) and AI to ensure that the investments in new hardware and software components result in proportional improvements in performance and capability. This project will undertake a transformative research activity targeting: (1) scaling ML algorithms to make them easily available to the scientific community; and (2) improving cyberinfrastructure efficiency through AI-based predictive models. This technical work will be complemented and informed by a community engagement effort to jointly catalog the state of the art and identify future challenges and opportunities in enabling a new smart cyberinfrastructure.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

Robust and Scalable Multi-Fidelity Algorithms for Model-Based Predictions

Akil Narayan
Modern computational models are complex in nature: accurate predictions of physics require detailed and intensive computational resources. As such, development of accurate scientific models has been the area of research emphasis in recent decades. Today’s scientific models involve largescale simulation tools, often with many interdependent components, and sometimes requiring days to complete a single simulation. Adding to this complexity is the presence of uncertainty, which is often encoded into models via parameters or random variables. Any direct approach to analyze the impact of parametric variation on such expensive models is infeasible.
One approach to circumvent this limitation is to utilize hierarchies of models, each with differing computational costs and predictive fidelities. Research in the past few years has demonstrated that intelligent allocation of resources across this ensemble of models can produce predictions with much greater accuracy than concentrating all resources in a single model. Such multi-fidelity procedures hold the potential to optimally utilize ensembles of models to make predictions.

The main components of this proposed project address optimal resource allocation and robust and scalable model reduction, generation, and learning via low-rank multi-fidelity and multilevel procedures. The overall goal is the construction of surrogate models with accuracy guarantees that can be used in design optimization, inference, and general uncertainty quantification scenarios. The tasks associated with this project involve fundamental mathematical and algorithmic advances in low-rank multi-fidelity methods. Error certificates to ensure accuracy will be developed when possible. Kernel learning techniques will be employed to explore problem-dependent low-rank structure and optimize allocation of resources. Algorithmic methods to handle heterogeneous models, data, and parameter spaces will be developed resulting in a comprehensive framework for utilizing low-rank multi-fidelity methods.

The multi-fidelity procedures devised in this project will also aid in developing novel strategies for model comparison, ranking, discrimination, and genesis. Model comparison and ranking will enable development of a comprehensive multi-fidelity pipeline to automatically learn and update model hierarchies and fidelities. Model generation using the simulation data from a multi-fidelity pipeline allows the automated construction of model emulators that can more easily be explored to detect and exploit low-rank structure.

This project will explore usage of low-rank multi-fidelity methods in two main application areas. The first area is in robust design under uncertainty, which requires robust, accurate, and efficient forward model evaluations. The second area of application is in statistical inference, requiring computationally expensive exploration of posterior distributions. This project will demonstrate the utility of low-rank multi-fidelity methods in acceleration of robust design and inferential tasks. Problems addressed by the work in this project include simulations in topology optimization, nonlocal/fractional differential equation models, modeling of multi-physics solar power receivers, and supersonic channel flow.

UINTAH + HEDGEHOG -- Hybrid Task Graph Execution Library Development for Generalized Work Loads

Martin Berzins
The Overall Objective is to develop a new Uintah runtime environment that demonstrates a flexible approach for accommodating different task execution and state management strategies consistent with a starting point:

1. Uintah uses an asynchronous manytask (AMT) approach that has been shown to strong and weak scale to 256K cores with 16K GPUs on Titan and 768K cores on Mira, through its asynchronous adaptive and over-decomposition based runtime scheduler. This scheduler works on many different and diverse architectures, from many DOE and NSF leadership class machines to Chinas Sunway Tiahulight. In addition this AMT approach when combined with mesh coarsening allows for an efficient approach to resilience.

2. HTGS/Hedgehog is a high performance single node multi-CPU/GPU tasked based system developed at NIST. Internal state management and execution strategies at the level of a single node is maintained within an explicit task graph representation. HTGS/Hedgehog has produced good competitive results on a single node.

The objective is to integrate the HTGS/Hedgehog Task Graph library into the Uintah Runtime. This new runtime would combine the global state management and multi-nodal execution characteristics of Uintah with the local single node execution facilities of HTGS/Hedgehog. This work would demonstrate and show how state management would be managed with these two different libraries. While the two libraries share many commonalities and architectural similarities, they are distinct in the underlying implementation. Understanding and developing a robust mechanism for sharing global and local state between the two libraries along with integrating the overall resource management strategies and task execution for multiple CPU/GPU architectures is the focus of this work.

The objectives will be carried out by first conducting feasibility studies between two different applications (3D structured grid application and an imaging analysis application) followed by the prototype implementation of new Uintah Scheduler that integrates the HTGS/Hedgehog library at the nodal level. The two different applications will be used demonstrate scalability and performance on both single node and multi-node systems. Finally, the proof-of-concept prototype Uintah Scheduler implementation will be transformed into a production level system in the third year of this effort.

Portable Applications Driven Approach to Scalability on Frontera and Future Exascale Systems

Martin Berzins
The present uncertainty in computer architectures requires software design to allow applications codes to both be able to scale across 20K to 100K nodes and to be able to run portably on a range of possible nodal architectures with a variety of processor technologies being involved, ranging from i86, ARM, GPU to possibly FPGAs. At the same time it isi important to use challenging applications to validate the software solutions and to ensure that they are realistic. This project led by Professor Martin Berzins will use the Frontera system to help address and demonstrate portability for an important class of engineering applications using the Uintah software.

Uintah software employs an asynchronous many task-based approach that has proved to be exceptionally robust at enabling complex engineering applications to run at scale on a broad range of architectures. As new and different architectures require not only the ability to execute tasks asynchronously but to deal with memory hierarchies and to execute efficiently on i86 architectures to GPUs and to a broad range of other possible architectures. Uintah use an approach based upon the Kokkos portability library that makes it possible to build a simple clean loop level interface that enables the loops themselves to execute efficiently on different architectures.

The work program will first port and evaluate existing Uintah architectures to Frontera and then consider new applications that apply the Uintah methodology to areas such as unstructured mesh calculations and particle methods applied to biomedical problems. The work program described here covers the application of these ideas to Frontera. The main effort will be through other funded projects, but any funding variability will be accomodated through an adaptive appropach to the applications space.

Collaborative Research: Detecting and Preventing Covid-19 with Privacy-Preserving Decentralized Machine Learning

Bao Wang
We are facing scientific challenges caused by the COVID-19, including detecting COVID-19 accurately and preventing its spread efficiently. Cutting-edge machine learning technologies, especially modern deep learning arts, provide feasible avenues to resolve these challenges. Deep learning-based computational imaging algorithms facilitate accurate and rapid COVID-19 diagnosis; sequential modeling with recurrent neural networks or transformers enables accurate and real-time COVID-19 spread prediction. However, most existing black-box deep learning research on the COVID-19 is the alchemy of turning unstructured data into gold and based on systematic trial and error. The current deep learning-based COVID-19 research raises many untrustworthy issues, including unreliable diagnosis, data privacy sacrifice, and lack of interpretability. Lacking interpretable and reliable predictions puts substantial strains on practitioners to leverage deep learning approaches to detect and prevent COVID-19. Data privacy constraints bring us many unraveling challenges. Thus, developing trustworthy machine learning algorithms while preserving data privacy is crucial to detect and prevent COVID-19.

We are a team of researchers with different expertise and common research interests, who jointly seek to develop theoretically principled decentralized machine learning algorithms that can provide reliable predictions. Furthermore, we focus on applying these machine learning algorithms to accurately and rapidly diagnose COVID-19 patients and predict the virus spread. We propose a challenging but walkable path towards developing privacy-preserving machine learning algorithms to detect and prevent COVID-19. We will integrate our expertise synergistically to develop privacy-preserving decentralized machine learning algorithms with performance guarantees and a high-throughput and low-latency software package to accurately and rapidly detect COVID-19 and effectively prevent its spread. As such, we propose three interconnected thrusts to develop novel neural network architectures based on mathematical principles, efficient privacy-preserving decentralized optimization algorithms, algorithms for spatiotemporal data forecasting and medical image processing and analysis, and an integrated software package to assist fighting against the coronavirus. Each thrust contains multiple theoretical explorations and numerical validation.

Intellectual Merit:
The proposal's intellectual merit include: (i) development of robust and mathematically principled recurrent neural networks for accurate real-time spatio-temporal forecasting, (ii) development of novel efficient federated and decentralized machine learning algorithms with a performance guarantee, (iii) leveraging the stochastic differential equations theory to develop new privacy-preserving machine learning mechanisms, (iv) construction of new epidemiology models-principled recurrent neural networks with accurate and interpretable predictions, (v) development of trustworthy deep learning-based frameworks for COVID-19 diagnosis from multi-modal medical measurements.

Broader Impacts:
The broader impacts of this project are in applying the proposed algorithms and their analysis over a wide range of science and engineering disciplines, such as scientific and medical image analysis, epidemic forecasting, patient monitoring, and microscopic imaging. The projects shall train a diverse body of the graduate and undergraduate students at Michigan State University, the University of Kentucky, and the University of Utah through collaborative education and research activities in applied mathematics, statistics, computer science, data science, physics, and social science. The project also plans to have research activities involving under-represented students in three universities located in three states. Besides the interdisciplinary collaboration across other institutions, we also aim to establish industrial partnerships to extend the proposed project's impact. The developed software will be shared with the general public through Github.

Sub-Pilot-Scale Production of High-Value Products for U.S. Coals

Chris Johnson
The primary objectives of this project are to: 1) provide sub-pilot scale verification of lab-scale developments on the production of isotropic and mesophase coal-tar pitch (CTP) for carbon fiber production, using coals from five U.S. coal-producing regions (UT, WY, WV, AK, IL); 2) investigate the production of a high-value b-SiC byproduct using residual coal char from the tar production process, and 3) develop an extensive database and suite of tools for data analysis and economic modeling, to relate process conditions to product quality, to assess the economic viability of coals from different regions for producing specific high-value products.

The University of Utah will use a 0.5 ton/day rotary reactor to pyrolyze coals to produce tars suitable for upgrading to coal tar pitch. The same reactor technology will be used in a second stage to perform the tar upgrading to either mesophase or isotropic pitch, depending on the properties of the original coal. The University of Wyoming will spin the product pitch into carbon fiber, to assess fiber quality arising from different coals and from different processing conditions. The solid char byproduct from coal pyrolysis will be used by the University of Wyoming to produce b-SiC. The University of Utah will work with Marshall University to develop a novel database, coupled with detailed economic models and analysis tools, to provide a means for understanding correlations between coal properties, process conditions and product quality, to allow assessment of the potential economic viability of coals from different regions for producing specific high-value products. Access to these some of these computational tools will become available to the public through a web-based community portal.

This effort is a major step towards providing a low-cost carbon fiber product from coal for potential use in automotive and other important markets, and will also lead to new economic development opportunities for communities with coal-based economies.

Experimental Characterization and Modeling of Failure in Post-Buckled Composite Stiffened Panels with a Scarf Repair

Mike Kirby

Alliance for Multiscale Modeling of Electronic Materials for an Energy Efficient Army

Mike Kirby
The objective of this Alliance is to conduct fundamental research to create MSME to support development of future electronic materials and devices for the Army. The U.S. Army Research Laboratory (ARL) envisions the MultiScale multidisciplinary Modeling of Electronic materials (MSME) Collaborative Research Alliance (CRA) which will bring together government, industrial, and academic institutions to undertake the fundamental research necessary to enable the quantitative understanding of electronic materials from the smallest to the largest relevant scales.

Augmented Design Through Analysis and Visualization Facilitating Better Designs and Enhanced Designers

Mike Kirby
The objective is to design analysis and visualization tools that help the designer to analyze ensembles of design/output pairs.

In Situ Feature Extraction and Visualization from Discontinuous Galerkin Based High-Order Methods

Mike Kirby
The use of simulation science as a means of scientific inquiry is increasing at a tremendous rate. The process of mathematically modeling physical phenomena, estimating key modeling parameters, numerically approximating the solution, and computationally solving the resulting algorithm has inundated the scientific and engineering worlds, allowing for rapid advances in our understanding and utilization of the world around us. The efficacy of simulation science has been, in part, due to two critical components: (1) the identification and minimization of the error budget (e.g. modeling, discretization and uncertainty errors), and equally importantly, (2) evaluation mechanisms (such as visualization) by which the investigator assimilates the data produced through simulation. The latter allows for further refinement of the simulation science process (through model correction, increased numerical resolution, or algorithm debugging, etc.) and makes possible scientific statements about the physical phenomena being investigated.

Tremendous effort has been exerted over many decades in the pursuit of numerical methods that are both flexible and accurate, hence providing sufficient fidelity to be employed in the numerical solution of a large number of models, and sufficient analysis of accuracy to allow researchers to focus their attention on model refinement and uncertainty quantification. High-order finite element methods (also known as spectral/hp element methods), using either the continuous Galerkin or discontinuous Galerkin formulation, have reached a level of sophistication that allows them to be commonly applied to a diverse set of real-life engineering problems in computational solid mechanics, fluid dynamics, acoustics and electromagnetics. Many of the physical problems of interest are, unfortunately, not steady-state --- leading to simulations that must run for a long time (days, weeks and in some cases months). Thus, in the absence of creative solutions, datasets can easily consume all available storage and networking resources. Examples of such simulations within fluid dynamics include all simulations in which the fluid is in transition or fully turbulent. With regards to ARO interests, problems in turbo-machinery and rotorcraft, where aspects of the geometry are rotating and/or sliding past one other, fall into this category. High-order finite element methods are now beginning to be used to simulate these physical systems due to their inherent ability to capture complex structures (such as vortices) with little numerical dissipation and dispersion. The transient nature of these simulations complicates the data handling (post processing requires the time history) and renders single snap-shots of the solution insufficient to understand the time-varying nature of the physics.

Objective
Our research objectives are two-fold: (1) We will generate "high-order FEM" appropriate dimensionality reduction feature extraction methods such as vortex cores which can be accomplished as part of an in situ data processing pipeline. (2) Given the exploratory nature inherent in analyzing and visualizing transient phenomena, we may specify regions of interest in an in situ fashion within a simulation field based upon the visualization objective, extract and transmit the result of working on relevant high-order FEM information to our visualization system, and then reconstruct the visualization features of interest with the cognizance of V&V.