Learning Associations between Features and Clusters: An Interpretable Deep Clustering Method
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97 MATHEMATICS AND COMPUTING↗
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Results for “mathematics computing”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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CO₂ Storage prospeCtive Resource Estimation Excel aNalysis (CO₂-SCREEN) User’s Manual
This user’s manual guides the use of the National Energy Technology Laboratory’s (NETL) CO₂ Storage prospeCtive Resource Estimation Excel aNalysis (CO₂-SCREEN) tool, which was developed to aid users screening geologic formations for prospective CO₂ storage resources. This manual is specific to the CO₂-SCREEN 4.0 version which is based in Python. CO₂-SCREEN applies U.S. Department of Energy (DOE) methods and equations for estimating prospective CO₂ storage resources for saline formations, shale formations, and residual oil zones (ROZ). CO₂-SCREEN was developed to be substantive and user-friendly and provide a consistent method for calculating prospective CO₂ storage resources. CO₂-SCREEN uses a Java based graphical user interface for data inputs and uses Python to calculate prospective CO₂ storage resources.
54 ENVIRONMENTAL SCIENCES↗
Basin-Size Mapping: Prediction of Metastable Polymorph Synthesizability Across TaC–TaN Alloys
The sizes of the basins of attraction on the potential energy surface are helpful indicators in determining the experimental synthesizability of metastable phases. In principle, these basins can be controlled with changes in thermodynamic conditions such as composition, pressure, and surface energy. Herein, we use random structure sampling to computationally study how alloying smoothly perturbs basin of attraction sizes. The TaC 1-x N x pseudobinary is an ideal test system given the structural and polymorphic contrast of its parent compounds and their technological relevance as epitaxial substrates for Al 1-x Ga x N. While we find limited thermodynamic stability across all computationally observed phases, random structure sampling shows a significant composition region where the rocksalt basin dominates. As such, we predict the potential for the nonequilibrium synthesis of metastable rocksalt TaC 1-x N x alloys as substrates for Al 1-x Ga x N. At higher nitrogen concentrations, other low-energy metastable polymorphs emerge that continue to retain the hexagonal close packing suitable for III-N growth. Confidence in these trends was established through uncertainty quantification of the basin sizes and energy distributions; such analysis utilized the Beta and Dirichlet distributions. In conclusion, we also find (a) polymorph basin sizes can be rationalized in terms of energetic preferences for different coordination environments; and (b) basin sizes universally shrink with increasing nitrogen content, making the system more prone to amorphous growth.
36 MATERIALS SCIENCE↗
A localized ensemble of approximate Gaussian processes for fast sequential emulation
More attention has been given to the computational cost associated with the fitting of an emulator. Substantially less attention is given to the computational cost of using that emulator for prediction. This is primarily because the cost of fitting an emulator is usually far greater than that of obtaining a single prediction, and predictions can often be obtained in parallel. In many settings, especially those requiring Markov Chain Monte Carlo, predictions may arrive sequentially and parallelization is not possible. In this case, using an emulator procedure which can produce accurate predictions efficiently can lead to substantial time savings in practice. In this paper, we propose a global model approximate Gaussian process framework via extension of a popular local approximate Gaussian process (laGP) framework. Our proposed emulator can be viewed as a treed Gaussian process where the leaf nodes are laGP models, and the tree structure is learned greedily as a function of the prediction stream. The suggested method (called leapGP) has interpretable tuning parameters which control the time‐memory trade‐off. One reasonable choice of settings leads to an emulator with a training cost and makes predictions rapidly with an asymptotic amortized cost of .
97 MATHEMATICS AND COMPUTING↗
Tailoring Microbial Fitness Through Computational Steering and CRISPRi-Driven Robustness Regulation
The widespread application of genetically modified microorganisms (GMMs) across diverse sectors underscores the pressing need for robust strategies to mitigate the risks associated with their potential uncontrolled escape. This study merges computational modeling with CRISPR interference (CRISPRi) to refine GMM metabolic robustness. Utilizing ensemble modeling, we achieved high-throughput in silico screening for enzymatic targets susceptible to expression alterations. Translating these insights, we developed functional CRISPRi, boosting fitness control via multiplexed gene knockdown. Our method, enhanced by an insulator-improved gRNA structure and an off-switch circuit controlling a compact Cas12m, resulted in rationally engineered strains with escape frequencies below National Institutes of Health standards. The effectiveness of this approach was confirmed under various conditions, showcasing its ability for secure GMM management. This research underscores the resilience of microbial metabolism, strategically modifying key nodes to halt growth without provoking significant resistance, thereby enabling more reliable and precise GMM control. A record of this paper's transparent peer review process is included in the supplemental information.
59 BASIC BIOLOGICAL SCIENCES↗
Simulation Apps Bring Us Closer to Mars
My work with mathematical modeling and computer simulations began in earnest in 1987 when I signed on with the National Aeronautics and Space Administration, better known as NASA. At the time I was developing computer simulations to support the design of carbon dioxide (CO2) removal systems for the International Space Station (ISS) life support system. CO2 is a human metabolic waste, produced at a rate of a kilogram per day per crewmember. CO2 must be removed from the crew cabin, as it will quickly become detrimental to crew health. The systems used to remove CO2 are typically based on sorption processes, which include complex interactions of heat transfer, mass transfer, and gas flow through porous media. At this time, there were no commercial options for solving a set of coupled mathematical models such as partial differential equations (PDEs); you either force-fit the physics into a thermal analysis package or wrote your own code, complete with discretization, meshing, and solution algorithms. Unfortunately, coding CO2 removal processes from scratch did not allow an appropriate focus on the challenging yet crucial task of understanding and capturing the underlying physics via appropriate mathematical models. Configuration control was often simply ignored due to tight schedules, resulting in a code that would be quicker for a second party to rewrite than modify. In the early 2000s, I decided to move CO2 removal simulations to a platform with built-in meshing, solvers, and postprocessing capabilities, and that could solve user-defined multiphysics PDEs. The program chosen to meet these needs was COMSOL Multiphysics®. Along with freeing the engineer to focus on the underlying physics, a degree of configuration control was automatically achieved via a consistent user interface, thus allowing COMSOL users to share computer models. My team has developed simulations that are already providing a valuable debugging capability for the ISS CO2 removal system, and will provide guidance in upgrades to that system.
Knox, Jim↗
Shape Optimization for Control and Isolation of Structural Vibrations in Aerospace and Defense Applications
Among the main challenges in shape optimization is the coupling of Finite Element Method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multi-physics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive. There are two mathematically equivalent approaches to computing the shape derivative: the volume method, and the boundary method. Each has a major drawback: the boundary method is less accurate, while the volume method is more invasive to the FEM code. Prior implementations of shape derivatives at Sandia have been based on the volume method. We introduce the strip method, which computes shape derivatives on a strip adjacent to the boundary. The strip method makes code coupling simple. Like the boundary method, it queries the state and adjoint solutions at quadrature nodes, but requires no knowledge of the FEM code implementations. At the same time, it exhibits the higher accuracy of the volume method. The development of the strip method also offers us the opportunity to share some lessons learned about implementing the volume method and boundary method, to show shape optimization results on problems of interest, and to begin addressing the other main challenges at hand: constraints on optimized shapes, and their interplay with optimization algorithms.
97 MATHEMATICS AND COMPUTING↗
Benchmarking the performance of uncertainty quantification methods for neural network-based interatomic potentials
Machine-learned interatomic potentials (ML-IAPs) continue to gain popularity as accurate, computationally efficient replacements for traditional, physics-based interatomic potentials and expensive ab initio methods. Uncertainty quantification (UQ) of ML-IAPs is a growing area of research as UQ is critical in many applications of IAPs, such as developing curated datasets, active learning-based data augmentation, self-improving models, and estimating the uncertainty of molecular dynamics simulations. In this paper, we construct and benchmark a series of different neural network potentials (NNPs) with varying network architectures to determine the performance of these models with respect to both the mean and uncertainty calibration error. Each NNP method is specifically designed to predict either epistemic or aleatoric uncertainty with particular focus on the differences in behavior between the epistemic and aleatoric uncertainty estimates. We benchmark these methods using multiple datasets common in the ML-IAP literature. The results show that the aleatoric uncertainty from single-shot model architectures is a competitive alternative to ensemble-based epistemic uncertainty predictions in regions of sufficient data-density. However, in regions where the representative data is sparse, aleatoric uncertainty models tend to overpredict and epistemic methods tend to underpredict the actual model error. We conclude that the type of UQ is crucial when discussing performance of probabilistic model results as different methods have different performance characteristics depending on the regime in which they are evaluated. Therefore, the type of UQ method should be carefully evaluated against both the data characteristics and requirements for the intended application.
97 MATHEMATICS AND COMPUTING↗
A robust framework for frictional fault contact in geological formations using a stabilized augmented Lagrangian approach
Numerical simulations are essential to evaluate the performance and safety of engineered subsurface systems such as geological carbon storage sites, enhanced geothermal fields, and oil and gas reservoirs. A key challenge lies in accurately modeling the frictional contact behavior along fault surfaces. This problem involves inequality constraints that arise from the physics of frictional slip, requiring specialized numerical methods to handle the resulting highly nonlinear and path-dependent behavior. Here, in this work, we address this challenge using an Augmented Lagrangian Method (ALM) implemented via the Uzawa algorithm. The formulation employs mixed finite element spaces, combining low-order piecewise linear displacements within the 3D domain cells with piecewise constant tractions defined on the fault surfaces. Furthermore, to ensure stability and satisfy the inf-sup condition, the discrete displacement space is enriched with face bubble functions on both sides of the contact interfaces. This approach offers several advantages over other stabilization techniques that rely on additional terms, and it integrates naturally in the Uzawa framework.
58 GEOSCIENCES↗
Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching
This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the convex quadratic relaxation of the optimal transmission switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. Next, we introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the optimal transmission switching problem in power systems. Using the proposed improvements, along with bound propagation, on 23 medium-sized test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on five instances. The tightened model has promising computational results when compared with state-of-the-art formulations.
97 MATHEMATICS AND COMPUTING↗
Variational Quantum Fidelity Estimation
Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity F ( ρ , σ ) based on the ``truncated fidelity'' F ( ρ m , σ ) , which is evaluated for a state ρ m obtained by projecting ρ onto its m -largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with m . To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize ρ , (2) compute matrix elements of σ in the eigenbasis of ρ , and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where σ is arbitrary and ρ is low rank, which we call low-rank fidelity estimation, and we prove that no classical algorithm can efficiently solve this problem under reasonable assumptions. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.
97 MATHEMATICS AND COMPUTING↗
Applying the FAIR Principles to computational workflows
Recent trends within computational and data sciences show an increasing recognition and adoption of computational workflows as tools for productivity and reproducibility that also democratize access to platforms and processing know-how. As digital objects to be shared, discovered, and reused, computational workflows benefit from the FAIR principles, which stand for Findable, Accessible, Interoperable, and Reusable. The Workflows Community Initiative’s FAIR Workflows Working Group (WCI-FW), a global and open community of researchers and developers working with computational workflows across disciplines and domains, has systematically addressed the application of both FAIR data and software principles to computational workflows. We present recommendations with commentary that reflects our discussions and justifies our choices and adaptations. These are offered to workflow users and authors, workflow management system developers, and providers of workflow services as guidelines for adoption and fodder for discussion. The FAIR recommendations for workflows that we propose in this paper will maximize their value as research assets and facilitate their adoption by the wider community.
97 MATHEMATICS AND COMPUTING↗
A multilayer multi-configurational approach to efficiently simulate large-scale circuit-based quantum computers on classical machines
Here, a multilayer multi-configurational theory framework is adapted to simulate circuit-based quantum computers. Quantum addition of superpositions of an exponential number of summands is performed in polynomial time with high accuracy. We demonstrate numerically accurate calculations including up to one million qubits for entangling benchmarks. Simulation cost can be assessed by entropy-based entanglement measures. For the considered systems, we show that the entanglement only grows weakly with the system size. The present simulations demonstrate how quantum algorithms in low-entropy regimes can be used efficiently on classically simulated quantum computers.
97 MATHEMATICS AND COMPUTING↗
Integrating subsystem embedding subalgebras and coupled cluster Green’s function: a theoretical foundation for quantum embedding in excitation manifold
Here, in this study, we introduce a novel approach to coupled-cluster Green's function (CCGF) embedding by seamlessly integrating conventional CCGF theory with the state-of-the-art sub-system embedding sub-algebras coupled cluster (SES-CC) formalism. This integration focuses primarily on delineating the characteristics of the sub-system and the corresponding segments of the Green's function, defined explicitly by active orbitals. Crucially, our work involves the adaptation of the SES-CC paradigm, addressing the left eigenvalue problem through a distinct form of Hamiltonian similarity transformation. This advancement not only facilitates a comprehensive representation of the interaction between the embedded sub-system and its surrounding environment but also paves the way for the quantum mechanical description of multiple embedded domains, particularly by employing the emergent quantum flow algorithms. Our theoretical underpinnings further set the stage for a generalization to multiple embedded sub-systems. This expansion holds significant promise for the exploration and application of non-equilibrium quantum systems, enhancing the understanding of system–environment interactions. In doing so, the research underscores the potential of SES-CC embedding within the realm of quantum computations and multi-scale simulations, promising a good balance between accuracy and computational efficiency.
97 MATHEMATICS AND COMPUTING↗
Ensemble approximate control variate estimators: Applications to multi-fidelity importance sampling.
The recent growth in multifidelity uncertainty quantification has given rise to a large set of variance reduction techniques that leverage information from model ensembles to provide variance reduction for estimates of the statistics of a high-fidelity model. In this paper we provide two contributions: (1) we utilize an ensemble estimator to account for uncertainties in the optimal weights of approximate control variate (ACV) approaches and derive lower bounds on the number of samples required to guarantee variance reduction; and (2) we extend an existing multifidelity importance sampling (MFIS) scheme to leverage control variates. Our approach directly addresses a limitation of many multifidelity sampling strategies that require the usage of pilot samples to estimate covariances. As such we make significant progress towards both increasing the practicality of approximate control variates—for instance, by accounting for the effect of pilot samples—and using multifidelity approaches more effectively for estimating low-probability events. The numerical results indicate our hybrid MFIS-ACV estimator achieves up to 50% improvement in variance reduction over the existing state-of-the-art MFIS estimator, which had already shown an outstanding convergence rate compared to the Monte Carlo method, on several problems of computational mechanics.
97 MATHEMATICS AND COMPUTING↗
Program Verification for Extreme-Scale Applications (Final Scientific/Technical Report)
The project seeks to develop tools and techniques to help software developers verify the correctness and accuracy of their code. The target domain is scientific software of the kind widely used and developed in the Department of Energy research community, with a particular focus on "extreme scale" programs - those that are expected to involve possibly millions of parallel threads of execution. The report covers the University of Delaware contribution to the collaborative project. The project had a number of successful outcomes, especially regarding the development and extension of the CIVL software verification framework. CIVL is a verification tool for C or Fortran programs that use MPI, OpenMP, CUDA, and/or Pthreads for parallelization. CIVL went through vast improvements and extensions, and was successfully applied to a number of challenging codes. It found a subtle bug in the Devito PDE framework. It was able to verify the functional correctness of a conjugate gradient solver using a novel probabilistic technique with vanishingly small chance of error. CIVL was used very successfully in verification competitions, and the CIVL solutions to the competition challenges were presented and published. CIVL was also used successfully by other researchers on a computational chemistry kernel.
97 MATHEMATICS AND COMPUTING↗
Understanding Interactive and Reproducible Computing With Jupyter Tools at Facilities
Increasingly Jupyter tools are being adopted and incorporated into High Performance Computing (HPC) and scientific user facilities. Adopting Jupyter tools enables more interactive and reproducible computational work at facilities across data life cycles. As the volume, variety, and scope of data grow, scientists need to be able to analyze and share results in user friendly ways. Human-centered research highlights design challenges around computational notebooks, and our qualitative user study shifts focus to better characterize how Jupyter tools are being used in HPC and science user facilities today. We conducted twenty-nine interviews, and obtained 103 survey responses from NERSC Jupyter users, to better understand the increasing role of interactive computing tools in DOE sponsored scientific work. We examine a range of issues that emerge using and supporting Jupyter in HPC ecosystems, including: how Jupyter is being used by scientists in HPC and user facility ecosystems; how facilities are purposefully supporting Jupyter in their ecosystems; feedback NERSC users have about the facility’s deployment, and, discuss features NERSC indicated would be helpful. We offer a variety of takeaways for staff supporting Jupyter at facilities, Project Jupyter and related open source communities, and funding agencies supporting interactive computing work.
97 MATHEMATICS AND COMPUTING↗
Efficient Application of the Factorized form of the Unitary Coupled-Cluster Ansatz for the Variational Quantum Eigensolver Algorithm by Using Linear Combination of Unitaries
The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons with relatively low-depth circuits, which are otherwise difficult to solve on classical computers. The variational eigenstate is constructed from a number of factorized unitary coupled-cluster terms applied onto an initial (single-reference) state. Current algorithms for applying one of these operators to a quantum state require a number of operations that scale exponentially with the rank of the operator. We exploit a hidden SU(2) symmetry to allow us to employ the linear combination of unitaries approach, Our Prepare subroutine uses n+2 ancilla qubits for a rank-n operator. Our Select (U) scheme uses O(n) Cnot gates. This results in a full algorithm that scales like the cube of the rank of the operator n 3 , a significant reduction in complexity for rank five or higher operators. This approach, when combined with other algorithms for lower-rank operators (when compared to the standard implementation), will make the factorized form of the unitary coupled-cluster approach much more efficient to implement on all types of quantum computers.
97 MATHEMATICS AND COMPUTING↗