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At least 19 records

Enriched immersed finite element and isogeometric analysis: algorithms and data structures

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their implementation remains a major challenge due to, among other things, the need to apply nontrivial stabilization schemes and generate custom quadrature rules. This article introduces the robust and computationally efficient algorithms and data structures comprising an immersed finite element preprocessing framework. The input to the preprocessor consists of a background mesh and one or more geometries defined on its domain. The output is structured into groups of elements with custom quadrature rules formatted such that common finite element assembly routines may be used without or with only minimal modifications. The key to the preprocessing framework is the construction of material topology information, concurrently with the generation of a quadrature rule, which is then used to perform enrichment and generate stabilization rules. While the algorithmic framework applies to a wide range of immersed finite element methods using different types of meshes, integration, and stabilization schemes, the preprocessor is presented within the context of the extended isogeometric analysis. This method utilizes a structured B-spline mesh, a generalized Heaviside enrichment strategy considering the material layout within individual basis functions’ supports, and face-oriented ghost stabilization. Using a set of examples, the effectiveness of the enrichment and stabilization strategies is demonstrated alongside the preprocessor’s robustness in geometric edge cases. Additionally, the performance and parallel scalability of the implementation are evaluated.

Computer implementation

Fortran mimetic abstraction language (Formal) v0.1.

The Fortran mimetic abstraction language ("Formal") is a domain-specific language (DSL) embedded in Fortran 202Y [1]. Formal provides novel software abstractions for simulating phenomena governed by the partial differential equations (PDEs) of vector and tensor calculus. Such equations model an extremely broad set of physical phenomena, ranging from atmospheric winds to light propagation. Formal's data structures and algorithms mimic in form and behavior continuous functions and operators. Formal supports these mathematical constructs using mimetic discretizations that define a discrete calculus satisfying various tensor calculus theorems, thereby ensuring high-fidelity representations of the physics being modeled. [2] Formal 0.1.0 also lays a foundation for the future use of Fortran 202Y type-safe templates to facilitate the formal verification of tensor contractions in computational physics and artificial intelligence [3]. [1] "Fortran 202Y" is Fortran standard committee's informal designation for the next Fortran revision, which will likely be "Fortran 2028". [2] Corbino, J. and Castillo, J. (2020) Journal of Computational and Applied Mathematics, https://doi.org/10.1016/j.cam.2019.06.042. [3] Haveraaen, M., Järvi, J., & Rouson, D. (2019). Reflecting on Generics for Fortran. https://j3-fortran.org/doc/year/19/19-188.pdf.

Rouson, Damian [Lawrence Berkeley National Laborat

Direct structural retrieval from gas-phase ultrafast diffraction data using a genetic algorithm

Ultrafast scattering techniques such as ultrafast electron diffraction and ultrafast x-ray diffraction have been utilized to elucidate the structural dynamics, reaction intermediates, and final products in molecular reactions following photoexcitation. The time-dependent structures are typically not directly retrieved from the experimental data, but they rely on comparison with calculations. The genetic algorithm (GA), a global optimization strategy, can be used to retrieve the molecular structures directly from diffraction patterns without any theoretical input. However, the robustness of the GA with respect to real experimental conditions such as a limited momentum transfer range, noise, and artifacts has not been studied in detail. In this work, we characterize the performance of the GA with simulated data that mimic realistic experimental conditions. We have developed and implemented a variant of the GA specific to diffraction measurements which performs better in the presence of imperfect data compared to the standard implementation of the GA. We demonstrate this method with both synthetic data and experimental ultrafast electron diffraction data on the UV-induced photodissociation of trifluoroiodomethane (C⁢F 3⁡ I) molecules.

74 ATOMIC AND MOLECULAR PHYSICS

MemFriend: Understanding Memory Performance with Spatial-Temporal Affinity

In HPC applications, memory access behavior is one of the main factors affecting performance. Improving an application’s memory access behavior involves optimizing data layout and/or restructuring code, and requires studying spatial-temporal data locality. Existing data locality analyses focus on single-location metrics and are restricted to evaluating temporal locality. We introduce spatial-temporal affinity metrics that quantify temporal access proximity, forward access correlation, and nearby access correlation between pairs of memory locations. We describe methods for distinguishing between potential vs. realized affinity and for reasoning about affinity at multiple resolutions (3D, 2D, 1D). Finally, we construct spatial-temporal affinity signatures that classify memory behavior and that be used to reason about changes in software (data relayout, code refactoring) or hardware (caching, prefetching). We describe methods for signature visualization, interpretation, and quantitative comparison of signatures. We evaluate our methodology using applications with variants that contrast data structures, data layouts and algorithms. We show that spatial-temporal affinity analysis provides novel insights and enables predictive reasoning about application performance when contrasted with reuse distance analysis.

Suriyakumar, Yasodhadevi

Correlated Anion Disorder in Heteroanionic Cubic TiOF 2

Resolving anion configurations in heteroanionic materials is crucial for understanding and controlling their properties. For anion-disordered oxyfluorides, conventional Bragg diffraction cannot fully resolve the anionic structure, necessitating alternative structure determination methods. We have investigated the anionic structure of anion-disordered cubic (ReO 3 -type) TiOF 2 using X-ray pair distribution function (PDF), 19 F MAS NMR analysis, density functional theory (DFT), cluster expansion modeling, and genetic-algorithm structure prediction. Our computational data predict short-range anion ordering in TiOF 2 , characterized by predominant cis-[O 2 F 4 ] titanium coordination, resulting in correlated anion disorder at longer ranges. To validate our predictions, we generated partially disordered supercells using genetic-algorithm structure prediction and computed simulated X-ray PDF data and 19 F MAS NMR spectra, which we compared directly to experimental data. To construct our simulated 19 F NMR spectra, we derived new transformation functions for mapping calculated magnetic shieldings to predicted magnetic chemical shifts in titanium (oxy)fluorides, obtained by fitting DFT-calculated magnetic shieldings to previously published experimental chemical shift data for TiF 4 . We find good agreement between our simulated and experimental data, which supports our computationally predicted structural model and demonstrates the effectiveness of complementary experimental and computational techniques in resolving anionic structure in anion-disordered oxyfluorides. From additional DFT calculations, we predict that increasing anion disorder makes lithium intercalation more favorable by, on average, up to 2 eV, highlighting the significant effect of variations in short-range order on the intercalation properties of anion-disordered materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Algorithms and file structures to extend and enhance liquid chromatography and ion mobility mass spectrometry workflows (CRADA Final Report)

The purpose of this project was to continue supporting customizations of algorithms and raw data file structures to enhance software workflows for liquid chromatography (LC), mass spectrometry (MS) and ion mobility mass spectrometry (IM-MS)-based protein and metabolite characterization. PNNL worked with Agilent to design, implement, evaluate, and demonstrate new algorithms and integrated them as functionalities into the PNNL-PreProcessor software. The project augmented PNNL’s capabilities to analyze complex proteomics and metabolomics samples. These capabilities are directly beneficial to DOE and PNNL efforts to characterize and analyze these compounds in microbial and plant communities. The project assisted Agilent in further developing improved instrument-software solutions combining liquid chromatography and ion mobility with mass spectrometry for widespread applications in life sciences and other fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

RANGE: A robust adaptive nature-inspired global explorer of potential energy surfaces

With the growing demand for realistic representations of chemical structures and the advent of exascale computing, the intelligent sampling of potential energy surfaces and efficient identification of global minima have become more essential but also more feasible. Building on prior studies demonstrating the efficiency of the Artificial Bee Colony (ABC) swarm intelligence algorithm, we report a hybrid metaheuristic framework that integrates the adaptive exploration capabilities of ABC coupled with the exploitation strengths of genetic algorithms (GA) in a scalable, Python-based implementation. The resulting tool, RANGE (Robust Adaptive Nature-inspired Global Explorer), provides seamless interfaces to multiple potential energy evaluators, either directly or via widely used Python libraries, and is designed for high-performance computing environments. We describe the implementation details of RANGE and evaluate its performance, relative to ABC- or GA-alone based algorithms, on a variety of chemical systems, including molecular clusters and heterogeneous surfaces. In conclusion, our results demonstrate RANGE’s efficiency, robustness, and broad applicability in addressing challenging global optimization problems in computational chemistry and materials science.

Algorithms and data structure

EFIT-Prime: Probabilistic and physics-constrained reduced-order neural network model for equilibrium reconstruction in DIII-D

We introduce EFIT-Prime, a novel machine learning surrogate model for EFIT (Equilibrium FIT) that integrates probabilistic and physics-informed methodologies to overcome typical limitations associated with deterministic and ad hoc neural network architectures. EFIT-Prime utilizes a neural architecture search-based deep ensemble for robust uncertainty quantification, providing scalable and efficient neural architectures that comprehensively quantify both data and model uncertainties. Physically informed by the Grad–Shafranov equation, EFIT-Prime applies a constraint on the current density J tor and a smoothness constraint on the first derivative of the poloidal flux, ensuring physically plausible solutions. Furthermore, the spatial location of the diagnostics is explicitly incorporated in the inputs to account for their spatial correlation. Extensive evaluations demonstrate EFIT-Prime's accuracy and robustness across diverse scenarios, most notably showing good generalization on negative-triangularity discharges that were excluded from training. Timing studies indicate an ensemble inference time of 15 ms for predicting a new equilibrium, offering the possibility of plasma control in real-time, if the model is optimized for speed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Shape effects on the local dynamics of suspensions of spheroidal particles

The effect of shape on the dynamics of suspensions of non-spherical heavy particles is examined by fully resolved numerical simulations of oblate and prolate spheroids, as well as spheres, for a density ratio of ten, volume fractions ranging from 0.5% to 5%, and Reynolds numbers between 20 and 30. The dynamics is determined both by the interactions of the particles with the fluid as well as by collisions, with the number and importance of collisions increasing with volume fractions. A single isolated oblate or prolate spheroid falling under gravity generally falls broadside on, for the governing parameters examined here, and at low-volume fractions, the majority of particles in a suspension fall that way. At higher-volume fractions, the orientation is more random. The slip velocity decreases as the volume fraction increases for all shapes, as expected, but the effect of the shape is much less than seen for a single particle. Furthermore, this seems to be due to two effects. For all volume fractions, the most deformed particles cluster more than spheres and less deformed particles, which increases their slip velocity. As the concentration increases, the increased particle interactions also causes more particles to fall short side-on, which reduces the frontal area and the resulting drag, increasing the slip velocity. This second effect is, of course, absent for spherical particles.

42 ENGINEERING

Quantum many-body linear algebra, Hamiltonian moments, and a coupled-cluster inspired framework

Here, we propose a general strategy to develop quantum many-body approximations of primitives in linear algebra algorithms. As a practical example, we introduce a coupled-cluster inspired framework to produce approximate Hamiltonian moments and demonstrate its application in various linear algebra algorithms for ground state estimation. Through numerical examples, we illustrate the difference between the ground-state energies arising from quantum many-body linear algebra and those from the analogous many-body perturbation theory. Our results support the general idea of designing quantum many-body approximations outside of perturbation theory, providing a route to new algorithms and approximations.

Algorithms and data structure

Orbit-averaging and deposition accuracy for runaway electron beams in hybrid kinetic-MHD simulations of the runaway plateau

We develop a new procedure that combines the kinetic orbit runaway electron code (KORC) and the NIMROD extended-magnetohydrodynamic code to simulate runaway electrons (REs) in the post-disruption plateau. KORC integrates guiding-center orbits, with a barycentric-based binary search strategy providing initial guesses for the Newton–Raphson logical-to-physical coordinate inversion, ensuring reliable particle-to-mesh mapping in NIMROD, whose fields remain static for the present study. Samples are drawn in accord with experimental parallel current profiles of RE beams during the plateau phase. Deposition in NIMROD is verified through comparison with a Python-based finite-element code that ensures periodicity in the poloidal direction and continuity at the magnetic axis. Accurate representation of near-axis fields requires finer mesh resolution to prevent under- and overshoots in current density from orbit inaccuracies. Yet, at a fixed particle count, increasing mesh resolution amplifies statistical noise in the deposited fields. An orbit-averaging method accumulates partial current deposits over multiple kinetic steps and reduces the statistical noise with little added computational cost. By coupling kinetic routines from KORC directly into the NIMROD codebase, these developments lay essential groundwork for future self-consistent KORC–NIMROD coupling.

Algorithms and data structure

Shadow molecular dynamics for flexible multipole models

Shadow molecular dynamics provide an efficient and stable atomistic simulation framework for flexible charge models with long-range electrostatic interactions. Shadow molecular dynamics simulations are driven by approximate “shadow” Born–Oppenheimer potentials for which the exact charges and forces are directly accessible without relying on costly (and approximate) iterative solvers. While previous implementations have been limited to atomic monopole charge distributions, we extend this approach to flexible multipole models. We derive detailed expressions for the shadow energy functions, potentials, and force terms, explicitly incorporating monopole–monopole, dipole–monopole, and dipole–dipole interactions. In our formulation, both atomic monopoles and atomic dipoles are treated as extended dynamical variables alongside the propagation of the nuclear degrees of freedom. We demonstrate that introducing the additional dipole degrees of freedom preserves the stability and accuracy previously seen in monopole-only shadow molecular dynamics simulations. In addition, we present a shadow molecular dynamics scheme where the monopole charges are held fixed while the dipoles remain flexible. Our extended shadow dynamics provide a framework for stable, computationally efficient, and versatile molecular dynamics simulations involving long-range interactions between flexible multipoles. This is of particular current interest in combination with machine-learned interatomic potentials, including long-range electrostatic interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Simultaneous prediction of structural properties in epitaxially–grown GaN with quantum and conventional multi–output learning algorithms

Hundreds of GaN thin film crystal plasma–assisted molecular beam epitaxy synthesis experiment records spanning two decades were organized into a dataset correlating the growth experiment design parameters with discrete, binary determinations of crystallinity and surface morphology. Conventional data science techniques as well as both quantum and classical multi–output supervised machine learning algorithms were implemented to investigate the relationships between the operating parameter data and the structural figures of merit. Correlation coefficients, decision tree nodes, p–values, and SHAP values all support substrate temperature and gallium effusion cell conditions as being statistically significant for simultaneously influencing GaN crystallinity and surface morphology. Here, a conventional deep neural network learned best from the data, followed by a quantum–classical hybrid gradient boosting algorithm. When combined with calculations of uncertainty intervals based on VennAbers predictors, machine learning predictions of both structural properties show good agreement with results reported in published experimental literature.

36 MATERIALS SCIENCE

Development of a TSR-based method for understanding structural relationships of cofactors and local environments in photosystem I

All chemical forms of energy and oxygen on Earth are generated via photosynthesis where light energy is converted into redox energy by two photosystems (PS I and PS II). There is an increasing number of PS I 3D structures deposited in the Protein Data Bank (PDB). The Triangular Spatial Relationship (TSR)-based algorithm converts 3D structures into integers (TSR keys). A comprehensive study was conducted, by taking advantage of the PS I 3D structures and the TSR-based algorithm, to answer three questions: (i) Are electron cofactors including P700, A -1 and A 0 , which are chemically identical chlorophylls, structurally different? (ii) There are two electron transfer chains (A and B branches) in PS I. Are the cofactors on both branches structurally different? (iii) Are the amino acids in cofactor binding sites structurally different from those not in cofactor binding sites? The key contributions and important findings include: (i) a novel TSR-based method for representing 3D structures of pigments as well as for quantifying pigment structures was developed; (ii) the results revealed that the redox cofactor, P700, are structurally conserved and different from other redox factors. Similar situations were also observed for both A -1 and A 0 ; (iii) the results demonstrated structural differences between A and B branches for the redox cofactors P700, A -1 , A 0 and A 1 as well as their cofactor binding sites; (iv) the tryptophan residues close to A 0 and A 1 are structurally conserved; (v) The TSR-based method outperforms the Root Mean Square Deviation (RMSD) and the Ultrafast Shape Recognition (USR) methods. The structural analyses of redox cofactors and their binding sites provide a foundation for understanding the unique chemical and physical properties of each redox cofactor in PS I, which are essential for modulating the rate and direction of energy and electron transfers.

59 BASIC BIOLOGICAL SCIENCES

Refining HPCToolkit for application performance analysis at exascale

As part of the US Department of Energy’s Exascale Computing Project (ECP), Rice University has been refining its HPCToolkit performance tools to better support measurement and analysis of applications executing on exascale supercomputers. To efficiently collect performance measurements of GPU-accelerated applications, HPCToolkit employs novel non-blocking data structures to communicate performance measurements between tool threads and application threads. To attribute performance information in detail to source lines, loop nests, and inlined call chains, HPCToolkit performs parallel analysis of large CPU and GPU binaries involved in the execution of an exascale application to rapidly recover mappings between machine instructions and source code. To analyze terabytes of performance measurements gathered during executions at exascale, HPCToolkit employs distributed-memory parallelism, multithreading, sparse data structures, and out-of-core streaming analysis algorithms. To support interactive exploration of profiles up to terabytes in size, HPCToolkit’s hpcviewer graphical user interface uses out-of-core methods to visualize performance data. The result of these efforts is that HPCToolkit now supports collection, analysis, and presentation of profiles and traces of GPU-accelerated applications at exascale. These improvements have enabled HPCToolkit to efficiently measure, analyze and explore terabytes of performance data for executions using as many as 64K MPI ranks and 64K GPU tiles on ORNL’s Frontier supercomputer. HPCToolkit’s support for measurement and analysis of GPU-accelerated applications has been employed to study a collection of open-science applications developed as part of ECP. This paper reports on these experiences, which provided insight into opportunities for tuning applications, strengths and weaknesses of HPCToolkit itself, as well as unexpected behaviors in executions at exascale.

Adhianto, Laksono

Development of Steady-State and Dynamic Mass and Energy Constrained Neural Networks for Distributed Chemical Systems Using Noisy Transient Data

The paper presents the development of algorithms for mass and energy constrained neural network models that can exactly conserve the overall mass and energy of distributed chemical process systems, even though the noisy transient data used for optimal model training violate the same. In contrast to approximately satisfying mass and energy balance constraints of a system by soft penalization of objective function, algorithms have been developed for solving equality-constrained nonlinear optimization problems, thus providing the guarantee of exactly satisfying the system mass and energy conservation laws. For developing dynamic mass-energy constrained network models for distributed systems, hybrid series and parallel dynamic-static neural networks have been leveraged. The developed algorithms for solving both the training and forward problems are validated using both steady-state and dynamic data in the presence of various noise characteristics. The developed data-driven algorithms are flexible to exactly satisfy mass and energy balance constraints for dynamic chemical processes if the system holdup information is available. The proposed network structures and algorithms are applied to the development of data-driven lumped and distributed models of an adiabatic superheater/reheater system, a nonisothermal continuous stirred tank reactor, as well as an electrically heated plug-flow reactor system where one form of energy gets transformed to another. It has been observed that the mass-energy constrained neural networks yield a root mean squared error of <1% with respect to the system truth for the case studies evaluated in this work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Get Non-Real: Randomized Sketching for High-Dimensional Non-Real Valued Data (Final Report)

In our final report for DE-C0022186, we describe the work we did on this grant towards the goals we proposed. Our first goal was characterizing fundamental limits for sketching of discrete high-dimensional matrices with low-dimensional structures. Our second main goal was designing algorithms for data reconstruction from sketches. We focus on approaches that are either specifically designed for non-real-valued data (binary, finite field) or that will translate more readily to that setting.

97 MATHEMATICS AND COMPUTING

Data Summarization and Inference at Scale

This is the final report for the DOE ASCR grant SC-0022260, Data Summarization and Inference at Scale, PI: Alex Pothen, Purdue University. The goal of the project was to solve data-intensive and compute-intensive problems in the physical sciences, engineering, information science, data science, etc. by designing and implementing new algorithms that could work with a subset of the data. The four subgoals were: (a) The solution of problems where the data is too large to be stored in the memory of a computer. In this streaming model of computation, the data arrives as a stream of elements to the computer, each element is processed as it arrives, and a decision is made to discard the data or to store it; only a small subset of the data proportional to the size of the output solution is stored, and when all the data has been streamed, a solution to the problem is computed from the stored subset. (b) The use of machine learning methods to compute solutions to data-intensive problems. The use of GPUs is critical to obtain high performance on machine learning tasks, but their memory sizes are smaller relative to that of CPUs. For large-scale problems, the data is sampled many times, and small samples are used with repetition, for robustness, to compute solutions to inference tasks. This sampling reduces the memory required to solve the problem, but attention is needed to avoid slow convergence to the solutions, and reduced accuracy of inference. We propose submodular optimization, Large Language Models, and physics-informed neural networks to enable GPU computations here. (c) Modeling and visualization of high-dimensional data using interpretable features. Clinical proteomic data sets from immunology for the detection of cancer and other diseases are temporal and high-dimensional, and algorithms for visualizing these data sets using clinically interpretable features are lacking. We propose methods that compute distances based on the optimal transportation problem and graph edit distances to address this problem. We also propose the use of optimal transport-based distances, spatial statistics, and network structure to classify image data sets, We apply these algorithms to electron micrographs of the peripheral nervous system in the digestive tract. (d) The design of data-intensive algorithms on emerging architectures, specifically, noisy, intermediate-scale quantum (NISQ) devices. Quantum computers offer the possibility of exploring large solution spaces due to the principle of superposition, but current quantum computers are limited by few qubits, short coherence times due to noise, poor interconections among the qubits, etc. We propose the use of the divide and conquer paradigm to solve large-scale problems, wherein collections of small subproblems are solved on the quantum devices, and the solutions to the subproblems are integrated into a solution for the original problem on a classical computer.

97 MATHEMATICS AND COMPUTING