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At least 1,783 records · Page 99

Real-Time Krylov Theory for Quantum Computing Algorithms

Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in extracting eigenstate information, but the full capabilities of such approaches are still not understood. In recent work, we developed the variational quantum phase estimation (VQPE) method, a compact and efficient real-time algorithm to extract eigenvalues on quantum hardware. Here we build on that work by theoretically and numerically exploring a generalized Krylov scheme where the Krylov subspace is constructed through a parametrized real-time evolution, which applies to the VQPE algorithm as well as others. We establish an error bound that justifies the fast convergence of our spectral approximation. We also derive how the overlap with high energy eigenstates becomes suppressed from real-time subspace diagonalization and we visualize the process that shows the signature phase cancellations at specific eigenenergies. We investigate various algorithm implementations and consider performance when stochasticity is added to the target Hamiltonian in the form of spectral statistics. To demonstrate the practicality of such real-time evolution, we discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems.

97 MATHEMATICS AND COMPUTING↗

Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study

Here, we explore the performance of the exponential time differencing (ETD) method applied to the rotating shallow water equations. Comparing with explicit time stepping of the same order accuracy in time, the ETD algorithms could reduce the computational time in many cases by allowing the use of large time step sizes while still maintaining numerical stability. To accelerate the ETD simulations, we propose a localized approach that synthesizes the ETD method and overlapping domain decomposition. By dividing the original problem into many subdomain problems of smaller sizes and solving them locally, the proposed approach could speed up the calculation of matrix exponential vector products. Several standard test cases for shallow water equations of one or multiple layers are considered. The results show great potential of the localized ETD method for high-performance computing because each subdomain problem can be naturally solved in parallel at every time step.

58 GEOSCIENCES↗

Scaling Wind Power Innovation Assessment for Rapid Energy Transition with Artificial Intelligence

Planning for energy system decarbonization requires new insights into the potential of renewable technologies, deployed at unprecedented scale, to meet urgent sustainability goals. However, limited scalability of current wind energy research tools restricts characterization of innovation impacts to isolated reference sites, challenging investment and decision making under rapid growth. We demonstrate the transformative potential of artificial intelligence (AI) to inform future technology advancement and energy systems design by leveraging a state-of-the-art surrogate model to conduct a series of fleet-wide wind plant layout optimizations for greater than 6,800 projected U.S. onshore buildout locations. We show how innovative wake steering technology can address an array of barriers to large-scale deployment and integration of wind power. Specifically, wake steering reduces required plant area by an average of 18% and could preserve upwards of 13,000 km2 for future greenfield deployment, potentially easing siting challenges associated with wind energy infrastructure. Further, by enabling reduced turbine spacing and increased energy production, flexible operations of wake steering improve levelized cost of energy, particularly for large plants and in land-constrained settings. Finally, optimizations that consider dynamic energy prices can deliver increased power production and revenue capture during high-value (often low-wind) periods, further bolstering plant economics. Our computationally efficient approach offers a pathway to accelerate nationwide geographic evaluation of innovative technologies.

graph neural networks↗

Adaptive Mesh Refinement Simulations for Turbulent Reacting Flow

With the increased availability of exascale computing hardware, detailed simulations of realistic devices can be performed at practically relevant time and length scales. Insights into the multiscale driving mechanisms in compressible reacting flow systems with complex geometry, such as combustors, can be used for design optimization and technology improvements. However, to effectively perform these simulations, advanced numerical algorithms must be used to maintain solution accuracy without incurring undue computational costs. PeleC, part of the Pele suite of codes, leverages block-structured adaptive mesh refinement (AMR) through the AMReX library to capture fine-scale flow features in compressible reacting flows. In this talk, we discuss recent improvements to the numerical algorithms, particularly in regard to describing flows at complex boundary structures, and PeleC's performance on exascale computing hardware. We will demonstrate that PeleC is well-suited for modern, extreme-scale, heterogenous compute platforms.

combustion↗

Dual-unitary shadow tomography

We introduce a classical shadow tomography scheme based on dual-unitary brick-wall circuits termed "dual-unitary shadow tomography" (DUST). For this we study operator spreading and Pauli weight dynamics in one-dimensional qubit systems, evolved by random two-local dual-unitary gates arranged in a brick-wall structure, ending with a final measurement layer. We do this by deriving general constraints on the Pauli weight transfer matrix and specializing to the case of dual-unitarity. We first show that dual-unitaries must have a minimal amount of entropy production. Remarkably, we find that operator spreading in these circuits have a rich structure resembling that of relativistic quantum field theories, with massless chiral excitations that can decay or fuse into each other, which we call left- or right-movers. We develop a mean-field description of the Pauli weight in terms of $\rho(x,t)$, which represents the probability of having nontrivial support at site $x$ and depth $t$ starting from a fixed weight distribution. We develop an equation of state for $\rho(x,t)$, and simulate it numerically using Monte Carlo simulations. Lastly, we demonstrate that the fast-thermalizing properties of dual-unitary circuits make them better at predicting large operators than shallow brick-wall Clifford circuits. Our results are robust to finite-size effects due to the chirality of dual-unitary brick-wall circuits.

97 MATHEMATICS AND COMPUTING↗

Rigorous justification for the space–split sensitivity algorithm to compute linear response in Anosov systems

Ruelle gave a formula for linear response of transitive Anosov diffeomorphisms. Recently, practically computable realizations of Ruelle's formula have emerged that potentially enable sensitivity analysis of certain high-dimensional chaotic numerical simulations encountered in the applied sciences. In this paper, we provide full mathematical justification for the convergence of one such efficient computation, the space–split sensitivity, or S3, algorithm. In S3, Ruelle's formula is computed as a sum of two terms obtained by decomposing the perturbation vector field into a coboundary and a remainder that is parallel to the unstable direction. Such a decomposition results in a splitting of Ruelle's formula that is amenable to efficient computation. Here, we prove the existence of the S3 decomposition and the convergence of the computations of both resulting components of Ruelle's formula.

97 MATHEMATICS AND COMPUTING↗

FPGA-based HPC accelerators: An evaluation on performance and energy efficiency

Hardware specialization is a promising direction for the future of digital computing. Reconfigurable technologies enable hardware specialization with modest non-recurring engineering cost, but their performance and energy efficiency compared to state-of-the-art processor architectures remain an open question. In this article, we use FPGAs to evaluate the benefits of building specialized hardware for numerical kernels found in scientific applications. In order to properly evaluate performance, we not only compare Intel Arria 10 and Xilinx U280 performance against Intel Xeon, Intel Xeon Phi, and NVIDIA V100 GPUs, but we also extend the Empirical Roofline Toolkit (ERT) to FPGAs in order to assess our results in terms of the Roofline model. We show design optimization and tuning techniques for peak FPGA performance at reasonable hardware usage and power consumption. As FPGA peak performance is known to be far less than that of a GPU, we also benchmark the energy efficiency of each platform for the scientific kernels comparing against microbenchmark and technological limits. Results show that while FPGAs struggle to compete in absolute terms with GPUs on memory- and compute-intensive kernels, they require far less power and can deliver nearly the same energy efficiency.

97 MATHEMATICS AND COMPUTING↗

Tighter reformulations using classical Dawson and Sankoff bounds for approximating two-stage chance-constrained programs

We extend and improve recent results given by Singh and Watson on using classical bounds on the union of sets in a chance-constrained optimization problem. Specifically, we revisit the so-called Dawson and Sankoff bound that provided one of the best approximations of a chance constraint in the previous analysis. Next, we show that our work is a generalization of the previous work, and in fact the inequality employed previously is a very relaxed approximation with assumptions that do not generally hold. Computational results demonstrate on average over a 43% improvement in the bounds. As a byproduct, we provide an exact reformulation of the floor function in optimization models.

97 MATHEMATICS AND COMPUTING↗

A novel matching formulation for startup costs in unit commitment

Here we present a novel formulation for startup cost computation in the unit commitment problem (UC). Both our proposed formulation and existing formulations in the literature are placed in a formal, theoretical dominance hierarchy based on their respective linear programming relaxations. Our proposed formulation is tested empirically against existing formulations on large-scale UC instances drawn from real-world data. While requiring more variables than the current state-of-the-art formulation, our proposed formulation requires fewer constraints, and is empirically demonstrated to be as tight as a perfect formulation for startup costs. This tightening can reduce the computational burden in comparison to existing formulations, especially for UC instances with large reserve margins and high penetration levels of renewables.

97 MATHEMATICS AND COMPUTING↗

Full Detector Simulation with Unprecedented Background Occupancy at a Muon Collider

In recent years, a Muon collider has attracted a lot of interest in the high-energy physics community, thanks to its ability of achieving clean interaction signatures at multi-TeV collision energies in the most cost-effective way. Estimation of the physics potential of such an experiment must take into account the impact of beam-induced background on the detector performance, which has to be carefully evaluated using full detector simulation. Tracing of all the background particles entering the detector region in a single bunch crossing is out of reach for any realistic computing facility due to the unprecedented number of such particles. To make it feasible a number of optimisations have been applied to the detector simulation workflow. This contribution presents an overview of the main characteristics of the beam-induced background at a Muon collider, the detector technologies considered for the experiment and how they are taken into account to strongly reduce the number of irrelevant computations performed during the detector simulation. Special attention is dedicated to the optimisation of track reconstruction with the conformal tracking algorithm in this high-occupancy environment, which is the most computationally demanding part of event reconstruction.

97 MATHEMATICS AND COMPUTING↗

Pass-efficient methods for compression of high-dimensional turbulent flow data

The future of high-performance computing, specifically on future Exascale computers, will presumably see memory capacity and bandwidth fail to keep pace with data generated, for instance, from massively parallel partial differential equation (PDE) systems. Current strategies proposed to address this bottleneck entail the omission of large fractions of data, as well as the incorporation of in situ compression algorithms to avoid overuse of memory. To ensure that post-processing operations are successful, this must be done in a way that a sufficiently accurate representation of the solution is stored. Moreover, in situations where the input/output system becomes a bottleneck in analysis, visualization, etc., or the execution of the PDE solver is expensive, the number of passes made over the data must be minimized. In the interest of addressing this problem, this work focuses on the utility of pass-efficient, parallelizable, low-rank, matrix decomposition methods in compressing high-dimensional simulation data from turbulent flows. Additionally, a particular emphasis is placed on using coarse representation of the data – compatible with the PDE discretization grid – to accelerate the construction of the low-rank factorization. This includes the presentation of a novel single-pass matrix decomposition algorithm for computing the so-called interpolative decomposition. The methods are described extensively and numerical experiments on two turbulent channel flow data are performed. In the first (unladen) channel flow case, compression factors exceeding 400 are achieved while maintaining accuracy with respect to first- and second-order flow statistics. In the particle-laden case, compression factors of 100 are achieved and the compressed data is used to recover particle velocities. These results show that these compression methods can enable efficient computation of various quantities of interest in both the carrier and disperse phases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Tusas: A fully implicit parallel approach for coupled phase-field equations

In this study, we develop a fully-coupled, fully-implicit approach for phase-field modeling of solidification in metals and alloys. Predictive simulation of solidification in pure metals and metal alloys remains a significant challenge in the field of materials science, as microstructure formation during the solidification process plays a critical role in the properties and performance of the solid material. Our simulation approach consists of a finite element spatial discretization of the fully-coupled nonlinear system of partial differential equations at the microscale, which is treated implicitly in time with a preconditioned Jacobian-free Newton-Krylov method. The approach is algorithmically scalable as well as efficient due to an effective preconditioning strategy based on algebraic multigrid and block factorization. We implement this approach in the open-source Tusas framework, which is a general, flexible tool developed in C++ for solving coupled systems of nonlinear partial differential equations. The performance of our approach is analyzed in terms of algorithmic scalability and efficiency, while the computational performance of Tusas is presented in terms of parallel scalability and efficiency on emerging heterogeneous architectures. We demonstrate that modern algorithms, discretizations, and computational science, and heterogeneous hardware provide a robust route for predictive phase-field simulation of microstructure evolution during additive manufacturing.

97 MATHEMATICS AND COMPUTING↗

Optimal decision-making in high-throughput virtual screening pipelines

Screening large pools of molecular candidates to identify those with specific design criteria or targeted properties is demanding in various science and engineering domains. While a high-throughput virtual screening (HTVS) pipeline can provide efficient means to achieving this goal, its design and operation often rely on experts' intuition, potentially resulting in suboptimal performance. In this paper, we fill this critical gap by presenting a systematic framework that can maximize the return on computational investment (ROCI) of such HTVS campaigns. Based on various scenarios, we empirically validate the proposed framework and demonstrate its potential to accelerate scientific discoveries through optimal computational campaigns, especially in the context of virtual screening.

97 MATHEMATICS AND COMPUTING↗

Moving closer to experimental level materials property prediction using AI

Abstract While experiments and DFT-computations have been the primary means for understanding the chemical and physical properties of crystalline materials, experiments are expensive and DFT-computations are time-consuming and have significant discrepancies against experiments. Currently, predictive modeling based on DFT-computations have provided a rapid screening method for materials candidates for further DFT-computations and experiments; however, such models inherit the large discrepancies from the DFT-based training data. Here, we demonstrate how AI can be leveraged together with DFT to compute materials properties more accurately than DFT itself by focusing on the critical materials science task of predicting “formation energy of a material given its structure and composition”. On an experimental hold-out test set containing 137 entries, AI can predict formation energy from materials structure and composition with a mean absolute error (MAE) of 0.064 eV/atom; comparing this against DFT-computations, we find that AI can significantly outperform DFT computations for the same task (discrepancies of $$>0.076$$ > 0.076 eV/atom) for the first time.

36 MATERIALS SCIENCE↗

An organic electrochemical transistor for multi-modal sensing, memory and processing

By integrating sensing, memory and processing functionalities, biological nervous systems are energy and area efficient. Emulating such capabilities in artificial systems is, however, challenging and is limited by the device heterogeneity of sensing and processing cores. Here we report an organic electrochemical transistor capable of sensing, memory and processing. The device has a vertical traverse architecture and a crystalline–amorphous channel that can be selectively doped by ions to enable two reconfigurable modes: a volatile receptor and a non-volatile synapse. As a volatile receptor, the device is capable of multi-modal sensing and is responsive to stimuli such as ions and light. As a non-volatile synapse, it is capable of 10-bit analogue states, low switching stochasticity and good state retention. We also show that the homogeneous integration of the devices could provide functions such as conditioned reflexes and could be used for real-time cardiac disease diagnoses via reservoir computing.

97 MATHEMATICS AND COMPUTING↗