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In this paper, we show how methods developed for solving a theoretical computer problem of graph isomorphism are used in structural chemistry. We also discuss potential applications of these methods to exobiology: the search for life outside Earth.
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.
Agnew National Security Postdoc Fellows pursue cutting-edge experimental, theoretical, computational science, and engineering research aligned with the national security mission. Metropolis Postdoc Fellows pursue cutting-edge research in the areas of computational and computer science, physics, and engineering. Computer simulation capabilities are developed in support of the stockpile stewardship program together with broader national nuclear security needs. Fellows have access to some of the most powerful supercomputers in the world to perform pioneering research.
Sampling from known probability distributions is a ubiquitous task in computational science, underlying calculations in domains from linguistics to biology and physics. Generative machine-learning (ML) models have emerged as a promising tool in this space, building on the success of this approach in applications such as image, text, and audio generation. Often, however, generative tasks in scientific domains have unique structures and features—such as complex symmetries and the requirement of exactness guarantees—that present both challenges and opportunities for ML. This Perspective outlines the advances in ML-based sampling motivated by lattice quantum field theory, in particular for the theory of quantum chromodynamics. Enabling calculations of the structure and interactions of matter from our most fundamental understanding of particle physics, lattice quantum chromodynamics is one of the main consumers of open-science supercomputing worldwide. Here, the design of ML algorithms for this application faces profound challenges, including the necessity of scaling custom ML architectures to the largest supercomputers, but also promises immense benefits, and is spurring a wave of development in ML-based sampling more broadly. In lattice field theory, if this approach can realize its early promise it will be a transformative step towards first-principles physics calculations in particle, nuclear and condensed matter physics that are intractable with traditional approaches.
Here we examine the utility of the quadratic pseudospectrum for understanding and detecting states that are somewhat localized in position and energy, in particular, in the context of condensed matter physics. Specifically, the quadratic pseudospectrum represents a method for approaching systems with incompatible observables {A j |1 ≤ j ≤ d} as it minimizes collectively the errors $\parallel$A j v - λ j v$\parallel$ while defining a joint approximate spectrum of incompatible observables. Moreover, we derive an important estimate relating the Clifford and quadratic pseudospectra. Finally, we prove that the quadratic pseudospectrum is local and derive the bounds on the errors that are incurred by truncating the system in the vicinity of where the pseudospectrum is being calculated.
We report, in fluid physics, data-driven models to enhance or accelerate time to solution are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In the context of reduced order models of high-dimensional time-dependent fluid systems, machine learning methods grant the benefit of automated learning from data, but the burden of a model lies on its reduced-order representation of both the fluid state and physical dynamics. In this work, we build a physics-constrained, data-driven reduced order model for Navier–Stokes equations to approximate spatiotemporal fluid dynamics in the canonical case of isotropic turbulence in a triply periodic box. The model design choices mimic numerical and physical constraints by, for example, implicitly enforcing the incompressibility constraint and utilizing continuous neural ordinary differential equations for tracking the evolution of the governing differential equation. We demonstrate this technique on a three-dimensional, moderate Reynolds number turbulent fluid flow. In assessing the statistical quality and characteristics of the machine-learned model through rigorous diagnostic tests, we find that our model is capable of reconstructing the dynamics of the flow over large integral timescales, favoring accuracy at the larger length scales. More significantly, comprehensive diagnostics suggest that physically interpretable model parameters, corresponding to the representations of the fluid state and dynamics, have attributable and quantifiable impact on the quality of the model predictions and computational complexity.
We compare and contrast the traditionally used method of solving the pressure–temperature equilibration problem in hydrodynamics, where specific internal energy and density are considered independent variables, with a different method where pressure and temperature are independent variables. With the goal of examining the robustness of the two methods as the number of components increases, we examine 2-, 4-, 6-, and 8-component systems. After equilibrating more than 10 4 initial conditions for each system using both methods, we demonstrate that the latter method constrains the search space by lowering its dimensionality and forces a better initial guess, resulting in a higher probability of convergence to solution with fewer, cheaper iterations.
There is a growing desire for inter-package modularity within the chemistry software community to reuse encapsulated code units across a variety of software packages. Most comprehensive efforts at achieving inter-package modularity will quickly run afoul of a very practical problem, being able to cohesively build the modules. Writing and maintaining build systems has long been an issue for many scientific software packages that rely on compiled languages such as C/C++. The push for inter-package modularity compounds this issue by additionally requiring binary artifacts from disparate developers to interoperate at a binary level. Thankfully, the de facto build tool for C/C++, CMake, is more than capable of supporting the myriad of edge cases that complicate writing robust build systems. Unfortunately, writing and maintaining a robust CMake build system can be a laborious endeavor because CMake provides few abstractions to aid the developer. Further, the need to significantly simplify the process of writing robust CMake-based build systems, especially in inter-package builds, motivated us to write CMaize. In addition to describing the architecture and design of CMaize, the article also demonstrates how CMaize is used in production-level software.
In this work, we propose a polynomial-time algorithm for preparing the Gibbs state of the two-dimensional toric code Hamiltonian at any temperature, starting from any initial state, significantly improving upon prior estimates that suggested exponential scaling with inverse temperature. We prove that fast mixing at low temperature for the two-dimensional toric code can be achieved by augmenting local jump operators with simple global jump operators, which enable efficient transitions between logical sectors. To establish tight lower bounds on the spectral gap, we introduce a new reduction method that eventually maps the problem to estimating the spectral gap of a perturbed graph Laplacian on a stair graph. Our proof also shows that the Lindblad dynamics with a digitally implemented low-temperature local Davies generator is able to efficiently drive the quantum state toward the ground state manifold.
The search for room-temperature superconductors is a major challenge in modern physics. The discovery of copper-oxide superconductors in 1986 brought hope but also revealed complex mechanisms that are difficult to analyze and compute. In contrast, the traditional electron–phonon coupling (EPC) mechanism facilitated the practical realization of superconductivity (SC) in metallic hydrogen. Since 2015, the discovery of new hydrogen compounds has shown that EPC can enable room-temperature SC under high pressures, driving extensive research. Advances in computational capabilities, especially exascale computing, now allow for the exploration of millions of materials. This paper reviews newly predicted superconducting systems in 2023–2024, focusing on hydrides, boron–carbon systems, and compounds with nitrogen, carbon, and pure metals. Although many computationally predicted high-T c superconductors were not experimentally confirmed, some low-temperature superconductors were successfully synthesized. This paper provides a review of these developments and future research directions.
In recent years, kinetic simulations have been crucial to further our understanding of pulsar electrodynamics. Yet, due to the large-scale separation between the gyro-period and the stellar rotation period, resolving the particle gyration has been computationally unfeasible for realistic pulsar parameters. The main aim of this work is comparing our gyro-phase-resolved model with a gyro-centric pulsar model, where our model solves the general equations of motion with included radiation reaction using a higher order numerical solver with adaptive time-steps. Specifically, we aim to (i) reproduce a pulsar’s high-energy emission maps, namely one with 10 per cent of the surface B-field strength of Vela, and the spectra produced by an independent gyro-centric pulsar emission model; and (ii) test convergence of these results to the radiation-reaction limit of Aristotelian electrodynamics. (iii) Additionally, we identify the effect that a large $E_{\parallel }$-field has on the trajectories and radiation calculations. We find that we can reproduce the curvature radiation emission maps and spectra well, using 10 per cent field strengths of the Vela pulsar and injecting our particles at a higher altitude in the magnetosphere. Using sufficiently large $E_{\parallel }$-fields, our numeric results converge to the analytic radiation-reaction limit trajectories. Additionally, we illustrate the importance of accounting for the $\mathbf {E}\times \mathbf {B}$-drift in the particle trajectories and radiation calculations, validating the Harding and collaborators’ model approach. Lastly, we found that our model deals very well with the high-radiation-reaction and high-field regimes present in pulsars.
Rapid progress in quantum technology has transformed quantum computing and quantum information science from theoretical possibilities into tangible engineering challenges. Breakthroughs in quantum algorithms, quantum simulations, and quantum error correction are bringing useful quantum computation closer to fruition. These remarkable achievements have been facilitated by advances in quantum characterization, verification, and validation (QCVV). QCVV methods and protocols enable scientists and engineers to scrutinize, understand, and enhance the performance of quantum information-processing devices. In this tutorial, we review the fundamental principles underpinning QCVV, and introduce a diverse array of QCVV tools used by quantum researchers. We define and explain QCVV’s core models and concepts—quantum states, measurements, and processes—and illustrate how these building blocks are leveraged to examine a target system or operation. We survey and introduce protocols ranging from simple qubit characterization to advanced benchmarking methods. Along the way, we provide illustrated examples and detailed descriptions of the protocols, highlight the advantages and disadvantages of each, and discuss their potential scalability to future large-scale quantum computers. This tutorial serves as a guidebook for researchers unfamiliar with the benchmarking and characterization of quantum computers, and also as a detailed reference for experienced practitioners.
The opening of the NASA Pan American Center for Environmental and Earth Sciences (PACES) at the University of Texas at El Paso made it possible to organize the student Center for Theoretical Research and its Applications in Computer Science (TRACS). In this abstract, we briefly describe the main NASA-related research directions of the TRACS center, and give an overview of the preliminary results of student research.
This paper discusses planned velocity measurements in microgravity laminar jet diffusion flames. These measurements will be conducted using Particle-Image Velocimetry (PIV) in the NASA Glenn 2.2-second drop tower. The observations are of fundamental interest and may ultimately lead to improved efficiency and decreased emissions from practical combustors. The velocity measurements will support the evaluation of analytical and numerical combustion models. There is strong motivation for the proposed microgravity flame configuration. Laminar jet flames are fundamental to combustion and their study has contributed to myriad advances in combustion science, including the development of theoretical, computational and diagnostic combustion tools. Nonbuoyant laminar jet flames are pertinent to the turbulent flames of more practical interest via the laminar flamelet concept. The influence of gravity on these flames is deleterious: it complicates theoretical and numerical modeling, introduces hydrodynamic instabilities, decreases length scales and spatial resolution, and limits the variability of residence time. Whereas many normal-gravity laminar jet diffusion flames have been thoroughly examined (including measurements of velocities, temperatures, compositions, sooting behavior and emissive and absorptive properties), measurements in microgravity gas-jet flames have been less complete and, notably, have included only cursory velocity measurements. It is envisioned that our velocity measurements will fill an important gap in the understanding of nonbuoyant laminar jet flames.
Over the three years of this project, we made significant progress on critical theoretical and computational issues in nanoscale science and technology, particularly in:(1) Fullerenes and nanotubes, (2) Characterization of surfaces of diamond and silicon for NEMS applications, (3) Nanoscale machine and assemblies, (4) Organic nanostructures and dendrimers, (5) Nanoscale confinement and nanotribology, (6) Dynamic response of nanoscale structures nanowires (metals, tubes, fullerenes), (7) Thermal transport in nanostructures.
Organic semiconductors based on conjugated donor-acceptor (D–A) polymers are a unique platform for electronic, spintronic, and energy-harvesting devices. Understanding the electronic structure of D–A polymers with a small band gap is essential for developing next-generation technologies. Here, we investigate the electronic structure and optical spectra of cyclopentadithiophene-based closed/open-shell D–A polymers using density functional theory and the Bethe–Salpeter equation based on G 0 W 0 approximation. We explored the role of different acceptor units and chemical substitutions on the structural changes and, more importantly, electronic, optical, and dielectric behavior. We found that the computed first exciton peak of the polymers agreed well with the available experimentally measured optical gap. Furthermore, D–A polymers with open-shell character display higher dielectric constant than the closed-shell polymers. We show that the exceptional performance of polycyclopentadithiophene-thiophenylthiadiazoloquinoxaline (PCPDT-TTQ) as a scalable n-type material for Faradaic supercapacitors can be partly ascribed to its elevated dielectric constant. Consequently, these D–A polymers, characterized by their high dielectric constants, exhibit significant potential for various applications, including energy storage, organic electronics, and the production of dielectric films.
Accurate and efficient prediction of polymer properties is of great significance in polymer design. Conventionally, expensive and time-consuming experiments or simulations are required to evaluate polymer functions. Recently, Transformer models, equipped with self-attention mechanisms, have exhibited superior performance in natural language processing. However, such methods have not been investigated in polymer sciences. Herein, we report TransPolymer, a Transformer-based language model for polymer property prediction. Our proposed polymer tokenizer with chemical awareness enables learning representations from polymer sequences. Rigorous experiments on ten polymer property prediction benchmarks demonstrate the superior performance of TransPolymer. Moreover, we show that TransPolymer benefits from pretraining on large unlabeled dataset via Masked Language Modeling. Experimental results further manifest the important role of self-attention in modeling polymer sequences. We highlight this model as a promising computational tool for promoting rational polymer design and understanding structure-property relationships from a data science view.
Computational mechanics is that discipline of applied science and engineering devoted to the study of physical phenomena by means of computational methods based on mathematical modeling and simulation, utilizing digital computers. The discipline combines theoretical and applied mechanics, approximation theory, numerical analysis, and computer science. Computational mechanics has had a major impact on engineering analysis and design. When applied to structural mechanics, the discipline is referred to herein as computational structural mechanics. Complex structures being considered by NASA for the 1990's include composite primary aircraft structures and the space station. These structures will be much more difficult to analyze than today's structures and necessitate a major upgrade in computerized structural analysis technology. NASA has initiated a research activity in structural analysis called Computational Structural Mechanics (CSM). The broad objective of the CSM activity is to develop advanced structural analysis technology that will exploit modern and emerging computers, such as those with vector and/or parallel processing capabilities. Here, the current research directions for the Methods and Application Studies Team of the Langley CSM activity are described.