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An incremental Principal Component Pursuit (PCP) algorithm for video background modeling that is able to process one frame at a time while adapting to changes in background, with a computational complexity that allows for real-time processing, having a low memory footprint and is robust to translational and rotational jitter.
In this work, we develop a quartic-scaling implementation of coupled-cluster singles and doubles (CCSD) based on low-rank tensor hypercontraction (THC) factorizations of both the electron repulsion integrals (ERIs) and the doubles amplitudes. This extends our rank-reduced (RR) coupled-cluster method to incorporate higher-order tensor factorizations. The THC factorization of the doubles amplitudes accounts for most of the gain in computational efficiency as it is sufficient, in conjunction with a Cholesky decomposition of the ERIs, to reduce the computational complexity of most contributions to the CCSD amplitude equations. Further THC factorization of the ERIs reduces the complexity of certain terms arising from nested commutators between the doubles excitation operator and the two-electron operator. We implement this new algorithm using graphical processing units and demonstrate that it enables CCSD calculations for molecules with 250 atoms and 2500 basis functions using a single computer node. Furthermore, we show that the new method computes correlation energies with comparable accuracy to the underlying RR-CCSD method.
The Hartree–Fock problem provides the conceptual and mathematical underpinning of a large portion of quantum chemistry. As efforts in quantum technology aim to enhance computational chemistry algorithms, the Hartree–Fock method, central to many other numerical approaches, is a natural target for quantum enhanced algorithms. While quantum computers and quantum simulation offer many prospects for the future of modern chemistry, the non-deterministic polynomial-complete Hartree–Fock problem is not a likely candidate. Here, we highlight this fact from a number of perspectives including computational complexity, practical examples, and the full characterization of energy landscapes for simple systems.
Within the EXAALT project, the SNAP [1] approach is being used to develop high accuracy potentials for use in large-scale long-time molecular dynamics simulations of materials behavior. In particular, we have developed a new SNAP potential that is suitable for describing the interplay between helium atoms and vacancies in high-temperature tungsten[2]. This model is now being used to study plasma-surface interactions in nuclear fusion reactors for energy production. The high-accuracy of SNAP potentials comes at the price of increased computational cost per atom and increased computational complexity. The increased cost is mitigated by improvements in strong scaling that can be achieved using advanced algorithms [3].
We report on the computational characteristics of ab initio nuclear structure calculations in a symmetry-adapted no-core shell model (SA-NCSM) framework. We examine the computational complexity of the current implementation of the SA-NCSM approach, dubbed LSU3shell, by analyzing ab initio results for 6 Li and 12 C in large harmonic oscillator model spaces and SU3-selected subspaces. We demonstrate LSU3shell’s strong-scaling properties achieved with highly-parallel methods for computing the many-body matrix elements. Results compare favorably with complete model space calculations and significant memory savings are achieved in physically important applications. In particular, a well-chosen symmetry-adapted basis affords memory savings in calculations of states with a fixed total angular momentum in large model spaces while exactly preserving translational invariance.
We report on the computational characteristics of ab initio nuclear structure calculations in a symmetry-adapted no-core shell model (SA-NCSM) framework. We examine the computational complexity of the current implementation of the SA-NCSM approach, dubbed LSU3shell, by analyzing ab initio results for 6 Li and 12 C in large harmonic oscillator model spaces and SU(3)-selected subspaces. We demonstrate LSU3shell's strong-scaling properties achieved with highly-parallel methods for computing the many-body matrix elements. Results compare favorably with complete model space calculations and signi cant memory savings are achieved in physically important applications. In particular, a well-chosen symmetry-adapted basis a ords memory savings in calculations of states with a fixed total angular momentum in large model spaces while exactly preserving translational invariance.
Quantum computers perform computations exploiting quantum mechanics to a possible advantage, allowing us to prepare and manipulate states that do not have a classical equivalent. In particular, phenomena like superposition and entanglement may enable quantum computers to outperform their classical counterparts in certain applications. Implementing these useful quantum algorithms is contingent upon building accurate quantum hardware that is not affected by noise. Environmental noise decreases coherence time of qubits, meaning that qubits do not stay in a desired state long enough to carry out a complex computation. To that end, harnessing the full power of quantum computers necessitate characterization of noise sources and how they impact a given quantum system. Often times, T1and T2 are used to quantify noise. In this project, we provide an approach as to how T1 and T2 values are calculated and simulated for quantum systems. In addition, we compare simulated values of T1 and T2 with those of real quantum computer’s measurements. IBMQ Experience, an open source software allowing users to simulate and use real quantum hardware, is used. QuTip, a Python-based toolbox offering quantum simulation tools for open quantum systems, is also used.
This review synthesizes methods for measuring, modeling, and managing hydrologic connectivity, offering pathways to improve practices and address environmental challenges (e.g., climate change) and sustainability. As a key driver of water movement and nutrient cycling, hydrologic connectivity influences flood mitigation, water quality regulation, and biodiversity conservation. However, traditional field-based methods (e.g., dye tracing), indirect measurements (e.g., runoff analysis), and remote sensing techniques (e.g., InSAR) often struggle to capture the complexity of catchment-scale interactions. Similarly, modeling approaches—including process-based and percolation theory-based models, graph theory, and entropy-based metrics—face limitations in fully representing these interconnected processes. Both modeling and measurement techniques are constrained by inadequate spatial and temporal coverage, high data demands, computational complexity, and difficulties in representing subsurface connectivity. Subsequently, we critique current management practices that prioritize isolated variables (e.g., streamflow, sediment transport) over system-wide strategies and emphasize the need for adaptive, connectivity-based approaches in water resource planning and restoration. Moving forward, we highlight the importance of interdisciplinary collaboration, technological innovations (e.g., AI-driven modeling, real-time monitoring), and integrated frameworks to improve connectivity measurement, modeling, and adaptive management to restore fragmented hydrologic networks. This integrated approach sets the stage for transformative water resource management, fostering proactive policy development and stakeholder engagement.
The nodal admittance matrix (NAM)-based approach is well-suited for small-signal stability analysis of large-scale power electronics-based power systems (PEPSs), as it preserves the system structure through its admittance matrix. Previous studies have explored partitioning such systems into subareas and interconnections to reduce computational burden; however, they lacked a formal algorithmic procedure for determining feasible partitions. While several grid partitioning methods, such as those based on graph theory or machine learning, exist in the literature, they cannot be directly applied to NAM-based analysis due to differing objectives and constraints. Here, this paper addresses this gap by presenting a systematic, step-by-step procedure for applying a spectral partitioning algorithm that yields a division of the system into subareas suitable for NAM-based analysis. The computational complexity of the proposed method is also derived to demonstrate its efficiency and justify the practicality of the resulting subarea decomposition. The performance of the partitioning method is evaluated by applying the spectral clustering-derived subareas and interconnections to the NAM-based partitioning approach on a 140-bus system. Computational times for the full-system and partitioned NAM analyses are compared using MATLAB. Additionally, PSCAD simulations of the complete system and partitioned subareas are carried out to verify the effectiveness of the proposed method.
This paper describes the application of a large-scale active learning method to characterize the parameter space of a computational agent-based model developed to investigate the impact of CommunityRx, a clinical information-based health intervention that provides patients with personalized information about local community resources to meet basic and self-care needs. Additionally, the diffusion of information about community resources and their use is modeled via networked interactions and their subsequent effect on agents' use of community resources across an urban population. A random forest model is iteratively fitted to model evaluations to characterize the model parameter space with respect to observed empirical data. We demonstrate the feasibility of using high-performance computing and active learning model exploration techniques to characterize large parameter spaces; by partitioning the parameter space into potentially viable and non-viable regions, we rule out regions of space where simulation output is implausible to observed empirical data. We argue that such methods are necessary to enable model exploration in complex computational models that incorporate increasingly available micro-level behavior data. We provide public access to the model and high-performance computing experimentation code.
We report that community efforts in the computational molecular sciences (CMS) are evolving toward modular, open, and interoperable interfaces that work with existing community codes to provide more functionality and composability than could be achieved with a single program. The Quantum Chemistry Common Driver and Databases (QCDB) project provides such capability through an application programming interface (API) that facilitates interoperability across multiple quantum chemistry software packages. In tandem with the Molecular Sciences Software Institute and their Quantum Chemistry Archive ecosystem, the unique functionalities of several CMS programs are integrated, including CFOUR, GAMESS, NWChem, OpenMM, Psi4, Qcore, TeraChem, and Turbomole, to provide common computational functions, i.e., energy, gradient, and Hessian computations as well as molecular properties such as atomic charges and vibrational frequency analysis. Both standard users and power users benefit from adopting these APIs as they lower the language barrier of input styles and enable a standard layout of variables and data. These designs allow end-to-end interoperable programming of complex computations and provide best practices options by default.
GronOR is a program package for nonorthogonal configuration interaction calculations. Electronic wave functions are constructed in terms of antisymmetrized products of multiconfiguration molecular fragment wave functions. The computational complexity of the nonorthogonal methodologies implemented in GronOR applied to large molecular assemblies requires a design that takes full advantage of massively parallel supercomputer architectures and accelerator technologies. This work describes the implementation strategy and resulting performance characteristics. In addition to parallelization and acceleration, the software development strategy includes aspects of fault resiliency and heterogeneous computing. The program was designed for large-scale supercomputers but also runs effectively on small clusters and workstations for small molecular systems. GronOR is available as open source to the scientific community.
In recent years, energy correlators have emerged as a powerful tool for studying jet substructure, with promising applications such as probing the hadronization transition, analyzing the quark-gluon plasma, and improving the precision of top quark mass measurements. The projected N-point correlator measures correlations between N final-state particles by tracking the largest separation between them, showing a scaling behavior related to DGLAP splitting functions. These correlators can be analytically continued in N, commonly referred to as ν-correlators, allowing access to non-integer moments of the splitting functions. Of particular interest is the ν → 0 limit, where the small momentum fraction behavior of the splitting functions requires resummation. Originally, the computational complexity of evaluating ν-correlators for M particles scaled as 2 2M , making it impractical for real-world analyses. However, by using recursion, we reduce this to M 2M , and through the FastEEC method of dynamically resolving subjets, M is replaced by the number of subjets. This breakthrough enables, for the first time, the computation of ν-correlators for LHC data. In practice, limiting the number of subjets to 16 is sufficient to achieve percent-level precision, which we validate using known integer-ν results and convergence tests for non-integer ν. We have implemented this in an update to FastEEC and conducted an initial study of power-law scaling in the perturbative regime as a function of ν, using CMS Open Data on jets. The results agree with DGLAP evolution, except at small ν, where the anomalous dimension saturates to a value that matches the BFKL anomalous dimension.
Abstract Training machine learning models on classical computers is usually a time and compute intensive process. With Moore’s law nearing its inevitable end and an ever-increasing demand for large-scale data analysis using machine learning, we must leverage non-conventional computing paradigms like quantum computing to train machine learning models efficiently. Adiabatic quantum computers can approximately solve NP-hard problems, such as the quadratic unconstrained binary optimization (QUBO), faster than classical computers. Since many machine learning problems are also NP-hard, we believe adiabatic quantum computers might be instrumental in training machine learning models efficiently in the post Moore’s law era. In order to solve problems on adiabatic quantum computers, they must be formulated as QUBO problems, which is very challenging. In this paper, we formulate the training problems of three machine learning models—linear regression, support vector machine (SVM) and balanced k-means clustering—as QUBO problems, making them conducive to be trained on adiabatic quantum computers. We also analyze the computational complexities of our formulations and compare them to corresponding state-of-the-art classical approaches. We show that the time and space complexities of our formulations are better (in case of SVM and balanced k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.
Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring non-linear models through the construction of similarity functions from data. These methods are particularly preferred in cases where the training data sizes are limited and when prior knowledge of the data similarities is available. Despite their usefulness, they are limited by the computational complexity and their inability to support end-to-end learning with a task specific objective. On the other hand, deep neural networks have become the de facto solution for end-to-end inference in several learning paradigms. In this article, we explore the idea of using deep architectures to perform kernel machine optimization, for both computational efficiency and end-to-end inferencing. To this end, we develop the DKMO (Deep Kernel Machine Optimization) framework, that creates an ensemble of dense embeddings using Nystrõm kernel approximations and utilizes deep learning to generate task-specific representations through the fusion of the embeddings. Intuitively, the filters of the network are trained to fuse information from an ensemble of linear subspaces in the RKHS. Furthermore, we introduce the kernel dropout regularization to enable improved training convergence. Finally, we extend this framework to the multiple kernel case, by coupling a global fusion layer with pre-trained deep kernel machines for each of the constituent kernels. Using case studies with limited training data, and lack of explicit feature sources, we demonstrate the effectiveness of our framework over conventional model inferencing techniques.
Many image processing tasks are naturally expressed as a pipeline of small computational kernels known as stencils. Halide is a popular domain-specific language and compiler designed to implement image processing algorithms. Halide uses simple language constructs to express what to compute and a separate scheduling co-language for expressing when and where to perform the computation. This approach has demonstrated performance comparable to or better than hand-optimized code. Until now, however, Halide has been restricted to parallel shared memory execution, limiting its performance for memory-bandwidth-bound pipelines or large-scale image processing tasks. We present an extension to Halide to support distributed-memory parallel execution of complex stencil pipelines. These extensions compose with the existing scheduling constructs in Halide, allowing expression of complex computation and communication strategies. Existing Halide applications can be distributed with minimal changes, allowing programmers to explore the tradeoff between recomputation and communication with little effort. Approximately 10 new of lines code are needed even for a 200 line, 99 stage application. On nine image processing benchmarks, our extensions give up to a 1.4× speedup on a single node over regular multithreaded execution with the same number of cores, by mitigating the effects of non-uniform memory access. The distributed benchmarks achieve up to 18× speedup on a 16 node testing machine and up to 57× speedup on 64 nodes of the NERSC Cori supercomputer.
Physics-based systems-of-systems models are computationally expensive. Reduced graphical models can decrease computational complexity, but may not proffer an end-to-end model from upstream inputs to downstream outputs. We consequently are interested in reducing models on directed graphs to models on a directed acyclic subgraph such that preserves accurate reconstruction of nodes. The consequence is a model with a topological ordering, providing a one-way flow of computation, and a causal interpr
Highlights: • Two numerical methods are presented to accelerate DMD simulations. • The methods greatly reduce the computation time without much loss of accuracy. • The accelerated DMD model is capable of simulating long-term mass transport at atomistic length scales. • Demonstrated for the propagation of an atomically sharp phase boundary over 30 seconds. - Abstract: Diffusive Molecular Dynamics (DMD) is a class of recently developed computational models for the simulation of long-term diffusive mass transport at atomistic length scales. Compared to previous atomistic models, e.g., transition state theory based accelerated molecular dynamics, DMD allows the use of larger time-step sizes, but has a higher computational complexity at each time-step due to the need to solve a nonlinear optimization problem at every time-step. This paper presents two numerical methods to accelerate DMD based simulations. First, we show that when a many-body potential function, e.g., embedded atom method (EAM), is employed, the cost of DMD is dominated by the computation of the mean of the potential function and its derivatives, which are high-dimensional random variables. To reduce the cost, we explore both first- and second-order mean field approximations. Specifically, we show that the first-order approximation, which uses a point estimate to calculate the mean, can reduce the cost by two to three orders of magnitude, but may introduce relatively large error in the solution. We show that adding an approximate second-order correction term can significantly reduce the error without much increase in computational cost. Second, we show that DMD can be significantly accelerated through subcycling time integration, as the cost of integrating the empirical diffusion equation is much lower than that of the optimization solver. To assess the DMD model and the numerical approximation methods, we present two groups of numerical experiments that simulate the diffusion of hydrogen in palladium nanoparticles. In particular, we show that the computational framework is capable of capturing the propagation of an atomically sharp phase boundary over a time window of more than 30 seconds. The effects of the proposed numerical methods on solution accuracy and computation time are also assessed quantitatively.