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At least 253 records · Page 14

Porting Classical Approaches for Quantum Simulations to Quantum Computers

Simulating quantum many-body systems is one of the most promising problems in which we might anticipate that quantum computers should show quantum advantage. Unfortunately, there is still a gap between this promise and actual practice. New quantum algorithms need to be developed and the current quantum algorithms have various difficulties - e.g efficient state preparation - which must be overcome and improved upon. In many cases, classical approaches need to be ported over to quantum devices. In this project we have developed a suite of new quantum algorithms which makes progress in this regard. We developed a new optimization scheme for variational quantum eigensolvers, UBOS, which mitigates problems with local minimas and barren plateaus while improving convergence to the ground state by an order of magnitude. We developed a new way to utilize qubitization to find ground states of nearly frustration-free Hamiltonians faster than all previous methods. We developed a series of state preparation techniques which helps initialize parameterized quantum circuits into reasonable starting points on which quantum algorithms are then applied. In addition to the development of novel algorithms, it is critical to have classical simulation techniques for approximately simulating quantum circuits which can be used to benchmark and understand quantum algorithms. Toward that end, we developed a novel POVM formalism to simulate quantum circuits as well as exemplify the massive parallelization of tensor network methodologies. Finally, we developed physical understanding of entanglement phase transitions such as many-body localization and random tensor networks.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Finite-Time Analysis of Whittle Index based Q-Learning for Restless Multi-Armed Bandits with Neural Network Function Approximation

Whittle index policy is a heuristic to the intractable restless multi-armed bandits (RMAB) problem. Although it is provably asymptotically optimal, finding Whittle indices remains difficult. In this paper, we present Neural-Q-Whittle, a Whittle index based Q-learning algorithm for RMAB with neural network function approximation, which is an example of nonlinear two-timescale stochastic approximation with Q-function values updated on a faster timescale and Whittle indices on a slower timescale. Despite the empirical success of deep Q-learning, the non-asymptotic convergence rate of Neural-Q-Whittle, which couples neural networks with two-timescale Q-learning largely remains unclear. This paper provides a finite-time analysis of Neural-Q-Whittle, where data are generated from a Markov chain, and Q-function is approximated by a ReLU neural network. Our analysis leverages a Lyapunov drift approach to capture the evolution of two coupled parameters, and the nonlinearity in value function approximation further requires us to characterize the approximation error. Combing these provide Neural-Q-Whittle with convergence rate, where is the number of iterations.

reinforcement learning, structured learning, conve↗

Electrical Conductivities and Association Constants in Dilute Aqueous NdCl 3 Solutions from 298 to 523 K along an Isobar of 25 MPa

Here, electrical measurements were performed in dilute aqueous NdCl 3 solutions from 298 to 523 K along the 25 MPa isobar to obtain limiting conductivities and association constants. The specific conductivity data were estimated using a continuous flow cell and a Markov Chain Monte Carlo (MCMC) correction algorithm. The limiting conductivities for the salts in water were derived by regressing the mean spherical approximation model and speciation analyses based on the MCMC algorithm and the deep earth water model. The limiting conductivities derived from the experimental data were correlated using the Zimmerman-Arcis-Tremaine correlation and agreed well with a predictive correlation proposed by Smolyakov, Anderko, and Lencka. Only the first association constant between neodymium and chloride could be derived at low temperatures (<373 K) due to the apparent large statistical uncertainty of the second association constant. Above 373 K, both association constants could be derived and show a reasonable agreement with Migdisov and Williams-Jones and Gammons et al.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Spectral density reconstruction with Chebyshev polynomials

Accurate calculations of the spectral density in a strongly correlated quantum many-body system are of fundamental importance to study its dynamics in the linear response regime. Typical examples are the calculation of inclusive and semiexclusive scattering cross sections in atomic nuclei and transport properties of nuclear and neutron star matter. Integral transform techniques play an important role in accessing the spectral density in a variety of nuclear systems. However, their accuracy is in practice limited by the need to perform a numerical inversion which is often ill-conditioned. Here, in the present work we extend a recently proposed quantum algorithm which circumvents this problem. We show how to perform controllable reconstructions of the spectral density over a finite energy resolution with rigorous error estimates. An appropriate expansion in Chebyshev polynomials allows for efficient simulations also on classical computers. We apply our idea to obtain the local density of states for graphene in a magnetic field as a proof of principle. This paves the way for future applications in nuclear and condensed matter physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Estimating Higher-Order Moments Using Symmetric Tensor Decomposition

In this paper, we consider the problem of decomposing higher-order moment tensors, i.e., the sum of symmetric outer products of data vectors. Such a decomposition can be used to estimate the means in a Gaussian mixture model and for other applications in machine learning. The dth-order empirical moment tensor of a set of p observations of n variables is a symmetric d-way tensor. Our goal is to nd a low-rank tensor approximation comprising r $\ll$ p symmetric outer products. The challenge is that forming the empirical moment tensor costs O(pn d ) operations and O(n d ) storage, which may be prohibitively expensive; additionally, the algorithm to compute the low-rank approximation costs O(n d ) per iteration. Our contribution is avoiding formation of the moment tensor, computing the low-rank tensor approximation of the moment tensor implicitly using O(pnr) operations per iteration and no extra memory. This advance opens the door to more applications of higher-order moments since they can now be efficiently computed. We present numerical evidence of the computational savings and show an example of estimating the means for higher-order moments.

97 MATHEMATICS AND COMPUTING↗

Quantum Search Approaches to Sampling-Based Motion Planning

In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse environments, we formulate the Quantum Full Path Search Algorithm (q-FPS), which creates a superposition of full random path solutions, manipulates probability amplitudes with Quantum Amplitude Amplification (QAA), and quantum measures a single obstacle free full path solution. For dense unstructured environments, we formulate the Quantum Rapidly Exploring Random Tree algorithm, q-RRT, that creates quantum superpositions of possible parent-child connections, manipulates probability amplitudes with QAA, and quantum measures a single reachable state, which is added to a tree. As performance depends on the number of oracle calls and the probability of measuring good quantum states, we quantify how these errors factor into the probabilistic completeness properties of the algorithm. We then numerically estimate the expected number of database solutions to provide an approximation of the optimal number of oracle calls in the algorithm. We compare the q-RRT algorithm with a classical implementation and verify quadratic run-time speedup in the largest connected component of a 2D dense random lattice. We conclude by evaluating a proposed approach to limit the expected number of database solutions and thus limit the optimal number of oracle calls to a given number.

97 MATHEMATICS AND COMPUTING↗

Real-time dynamics of the Schwinger model as an open quantum system with Neural Density Operators

Ab-initio simulations of multiple heavy quarks propagating in a Quark-Gluon Plasma are computationally difficult to perform due to the large dimension of the space of density matrices. This work develops machine learning algorithms to overcome this difficulty by approximating exact quantum states with neural network parametrisations, specifically Neural Density Operators. As a proof of principle demonstration in a QCD-like theory, the approach is applied to solve the Lindblad master equation in the 1 + 1d lattice Schwinger Model as an open quantum system. Neural Density Operators enable the study of in-medium dynamics on large lattice volumes, where multiple-string interactions and their effects on string-breaking and recombination phenomena can be studied. Thermal properties of the system at equilibrium can also be probed with these methods by variationally constructing the steady state of the Lindblad master equation. Scaling of this approach with system size is studied, and numerical demonstrations on up to 32 spatial lattice sites and with up to 3 interacting strings are performed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

guppy i : a code for reducing the storage requirements of cosmological simulations

ABSTRACT As cosmological simulations have grown in size, the permanent storage requirements of their particle data have also grown. Even modest simulations present a major logistical challenge for the groups which run these boxes and researchers without access to high performance computing facilities often need to restrict their analysis to lower quality data. In this paper, we present guppy, a compression algorithm and code base tailored to reduce the sizes of dark matter-only cosmological simulations by approximately an order of magnitude. guppy is a ‘lossy’ algorithm, meaning that it injects a small amount of controlled and uncorrelated noise into particle properties. We perform extensive tests on the impact that this noise has on the internal structure of dark matter haloes, and identify conservative accuracy limits which ensure that compression has no practical impact on single-snapshot halo properties, profiles, and abundances. We also release functional prototype libraries in C, Python, and Go for reading and creating guppy data.

79 ASTRONOMY AND ASTROPHYSICS↗

Multilevel Convergence Analysis of Multigrid-Reduction-in-Time

This study presents a multilevel convergence framework for multigrid-reduction-in-time (MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori upper bounds on the convergence of MGRIT V- and F-cycles, with different relaxation schemes, by deriving the respective residual and error propagation operators. The residual and error operators are functions of the time-stepping operator, analyzed directly and bounded in the norm, both numerically and analytically. We present various upper bounds of different computational cost and varying sharpness. These upper bounds are complemented by proposing analytic formulae for the approximate convergence factor of V-cycle algorithms that take the number of fine grid time points, the temporal coarsening factors, and the eigenvalues of the time-stepping operator as parameters. The paper concludes with supporting numerical investigations of parabolic (anisotropic diffusion) and hyperbolic (wave equation) model problems. We assess the sharpness of the bounds and the quality of the approximate convergence factors. Observations from these numerical investigations demonstrate the value of the proposed multilevel convergence framework for estimating MGRIT convergence a priori and for the design of a convergent algorithm. We further highlight that observations in the literature are captured by the theory, including that two-level Parareal and multilevel MGRIT with F-relaxation do not yield scalable algorithms and the benefit of a stronger relaxation scheme. An important observation is that with increasing numbers of levels MGRIT convergence deteriorates for the hyperbolic model problem, while constant convergence factors can be achieved for the diffusion equation. The theory also indicates that L-stable Runge--Kutta schemes are more amendable to multilevel parallel-in-time integration with MGRIT than A-stable Runge--Kutta schemes.

97 MATHEMATICS AND COMPUTING↗

PLANC: Parallel Low-rank Approximation with Nonnegativity Constraints

In this work, we consider the problem of low-rank approximation of massive dense nonnegative tensor data, for example, to discover latent patterns in video and imaging applications. As the size of data sets grows, single workstations are hitting bottlenecks in both computation time and available memory. We propose a distributed-memory parallel computing solution to handle massive data sets, loading the input data across the memories of multiple nodes, and performing efficient and scalable parallel algorithms to compute the low-rank approximation. We present a software package called Parallel Low-rank Approximation with Nonnegativity Constraints, which implements our solution and allows for extension in terms of data (dense or sparse, matrices or tensors of any order), algorithm (e.g., from multiplicative updating techniques to alternating direction method of multipliers), and architecture (we exploit GPUs to accelerate the computation in this work). We describe our parallel distributions and algorithms, which are careful to avoid unnecessary communication and computation, show how to extend the software to include new algorithms and/or constraints, and report efficiency and scalability results for both synthetic and real-world data sets.

97 MATHEMATICS AND COMPUTING↗

Are better combinations of DERs more profitable?: Combinatorial optimization for aggregation of DERs in wholesale electricity markets

Recently, regulatory changes in various countries have enabled the participation of small-scale distributed energy resources (DERs) aggregated in virtual power plants (VPPs) in wholesale electricity markets. The inherent uncertainty and variability of resources comprising VPPs can lead to imbalances between forecasted and metered outputs, potentially resulting in the deficient settlement of generation under imbalance settlement rules. To address this challenge, it is essential to manage variability in the planning phase and uncertainty in the operation phase. Most current research focuses on managing forecasting errors in the operational phase, with insufficient attention given to the planning phase. Here, to bridge this gap, this paper proposes an optimal combination strategy for DERs to maximize the market participation revenue of VPPs by proactively managing variability in the planning phase. To estimate the expected revenue, we conducted analyses for homogeneous and heterogeneous DERs using Monte Carlo simulations and genetic algorithms. Remarkably, the proposed method demonstrated approximately 8 % higher revenue compared to the neighboring group case when considering diversity in DER set configuration with equal proportions of photovoltaics and wind.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Empirical validation and comparison of methodologies to simulate micro and macro-encapsulated PCMs in the building envelope

Thermal Energy Storage (TES) has the potential to shift peak electricity demand. Passive TES is usually implemented in building envelope as micro and macro encapsulated phase change materials (PCM) to shift electric energy demand and therefore requires careful heat transfer analysis. Whole building energy modelling with simplified heat transfer analysis has become extremely important for designers, architects, engineers, and researchers to predict energy performance of buildings. It is important to validate PCM modelling algorithms used in building energy programs to quantify their error and prove their capacity to model different PCM encapsulation types. This study uses data from a microencapsulated PCM and two macroencapsulated PCMs (Bio based PCM and hydrate salts) tested in full-scale using the Advanced Multiscale Building Energy Research (AMBER) Lab located at the Colorado School of Mines and is used to validate a numerical algorithm written in MATLAB language. To approximate the heat transfer through a wall assembly with macroencapsulated PCM pouches, several modelling techniques that can reduce 3D heat transfer characteristics to 1D are explored in this research. A parallel path heat transfer modelling approach is found to give the closest agreement with the experimental data for the pouched PCMs in building envelope applications.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Geostatistical interpolation of streambed hydrologic attributes with addition of left censored data and anisotropy

Spatial geostatistical interpolation of point measurements of streambed attributes in the hyporheic zone may be constrained by the streambed anisotropy, and data density and spatial distribution may significantly impact the results. Spatial clustering and low spatial data density can be caused by bedrock outcropping at the streambed limiting installation of in-stream piezometers. This study examines parameter error variability of the geostatistical interpolation using anisotropic interpolation methods and increasing the data density by adding left censored values (i.e., data below measurement limit) to locations where measurements were limited by exposed bedrock lining the streambed. The reduction in relative standard error of the interpolation was determined for the spatial distributions of streambed attributes including hydraulic conductivity, seepage flux, and mercury solute flux measured in two different years along a study reach in East Fork Poplar Creek, Tennessee, USA. Here, two methods to impute the left censored values were compared including the conventional half the detection limit substitution method, and the Stochastic Approximation of Expectation-Maximization (SAEM) algorithm, which both had comparable results. Imputing left censored data increased the data density to recommended ranges, reduced data clustering, increased the spatial dependence for some attributes, and reduced the standard error for each of the three attributes. For the reach considered herein, addition of the left censored values resulted in a larger error reduction than the consideration of anisotropy within the interpolation, which confirms the benefit of data addition to increase data density within data-limited river corridors.

58 GEOSCIENCES↗

On the resolution of dual readout calorimeters

Dual readout calorimeters allow state-of-the-art resolutions for hadronic energy measurements. Their various incarnations are leading candidates for the calorimeter systems for future colliders. In this paper, we present a simple formula for the resolution of a dual readout calorimeter, which we verify with a toy simulation and with full simulation results. This formula can help those new to dual readout calorimetry understand its strengths and limitations. The paper also highlights that the dual readout correction works not just to compensate for binding energy loss, but also for energies escaping the calorimeter or clustering algorithm. Formulae are also presented for approximate resolutions and energy scales in terms of different sources of response.

Calorimeters↗

Topology optimization of an airfoil fin microchannel heat exchanger using artificial intelligence

High-performance microchannel heat exchangers are needed to supply heat for power conversion for nuclear microreactors. An airfoil fin microchannel design, constructed of Alloy 617 with helium as the working fluid, is analyzed and optimized using a design of experiments with artificial intelligence techniques. The use of airfoil fins offers the potential to reduce pressure drop across the heat exchanger, as compared to other types of channel configurations. A framework for topology optimization of airfoil fin printed circuit heat exchangers (PCHEs) has been developed that can be readily extended to different fin sizes and shapes, as well as different inlet and operating conditions, materials of construction, and working fluids. An optimization procedure is developed that employs computational fluid dynamics for a set of design points identified using Latin hypercube sampling. Computational fluid dynamics is used to analyze a simplified two-channel configuration where five design parameters are varied – inlet angle, fin scale, extent of staggering, transverse and longitudinal pitches. Two methods (a 5D polynomial and a regression neural network) are compared for generating surrogate models and the resulting response surface approximation is input to a genetic algorithm that is used to identify a set of optimal parameters. The optimal geometries are found across six channel Reynolds numbers ranging from 1000 to 5000, since inlet conditions affect flow through the heat exchanger. Additionally, a set of optimal designs that maximizes heat transfer and minimizes pressure drop is identified, and a thermal stress analysis is performed on the optimal design. Correlations for the Nusselt number and Darcy friction factor are developed that can be useful for thermal hydraulic analyses using system codes. Thermal stresses are analyzed and a brief discussion of the status of code cases of PCHEs for nuclear applications is given. Testing and thermomechanical modeling is needed to facilitate future code compliance of PCHEs for high pressure and high temperature applications.

42 ENGINEERING↗

Theory of an Automatic Seepage Meter and Ramifications for Applications

A new approach for measuring fluxes across surface water—groundwater interfaces was recently proposed. The Automatic Seepage Meter (ASM) is equipped with a precise water level sensor and digital memory that analyzes water level time series in a vertical tube inserted into a streambed. The ability to infer flux values with high temporal resolution relies on an accurate interpretation of water level dynamics inside the tube. Here, we reduce the three-dimensional hydrodynamic problem that describes the ASM water level in a variety of field conditions to a single ordinary differential equation. This novel general analytical solution for estimating ASM responses is more comprehensive and flexible than previous approaches and is applicable to the entire range of field conditions, including steady or transient stream stages, evaporation, rainfall, and noise. For example, our analysis determines the timing of the nonmonotonic ASM response to a monotonic linear stream stage variation and explains previously used empirical parabolic approximation for estimating fluxes. We present algorithms for simultaneous inference of vertical interface flux and hydraulic conductivity values together with an example code. We quantify how the accuracy of parameter estimation depends on test duration and noise amplitude and propose how our analysis can be used to optimize field test protocols. On this basis, changing the ASM geometry by increasing the radius and decreasing tube insertion depth may enable ASM field test protocols that estimate interface flux and hydraulic conductivity faster while maintaining desired accuracy. Potential applications of joint parameter estimation are suggested.

47 OTHER INSTRUMENTATION↗

Automated remote sensing tools to counter illicit maritime activity: vessel detection, bathymetry and topography from WorldView imagery

Illicit maritime activity, such as piracy and smuggling, is a global issue that often occurs in areas where interdiction authorities are sparse, ground-based monitoring technologies like radar lack range and coverage, and dark vessels abound. Our objective was to assess vessel congregation patterns, identify likely beaching areas based on terrain maps, and use them to narrow the search for potential smuggling transfer and overland routes in a specific region along the Puntland coast of Somalia. To accomplish this goal, we developed automated protocols applied to WorldView satellite imagery for (1) vessel detection and size classification, (2) shallow-water bathymetric characterization, and (3) coastal topography mapping. Utilizing a single sensor for vessel detection and topographic and bathymetric extraction at high spatial resolution and at a high re-visit rate provides a simplification to near-shore characterization for monitoring purposes. The extracted topography and bathymetry are then presented as a single, comprehensive perspective of a coastal region. The vessel-detection algorithm identified all vessels larger than approximately 15 metres in length (35 of 35), but misidentified six artefacts (i.e. false positives), resulting in an overall accuracy of 85%. The combined vessel and terrain maps facilitated the identification of a potential beaching and overland transportation route location.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

SUHMO: an adaptive mesh refinement SUbglacial Hydrology MOdel v1.0

Abstract. Water flowing under ice sheets and glaciers can have a strong influence on ice dynamics, particularly through pressure changes, suggesting that a comprehensive ice sheet model should include the effect of basal hydrology. Modeling subglacial hydrology remains a challenge, however, mainly due to the range of spatial and temporal scales involved – from subglacial channels to vast subglacial lakes. Additionally, networks of subglacial drainage channels dynamically evolve over time. To address some of these challenges, we have developed an adaptive mesh refinement (AMR) model based on the Chombo software framework. We extend the model proposed by Sommers et al. (2018) with a small but significant change to accommodate the transition from unresolved to resolved flow features. We handle the strong nonlinearities present in the equations by resorting to an efficient nonlinear full approximation scheme multigrid (FAS-MG) algorithm. We outline the details of the algorithm and present convergence analysis results demonstrating its good performance. Additionally, we present results validating our approach, using test cases from the Subglacial Hydrology Model Intercomparison Project (SHMIP) (de Fleurian et al., 2018). We finish by presenting a more complex, 100 km-by-100 km synthetic test case with peaks and valleys that we use to investigate the effective pressure distribution as the number of AMR levels increases. These preliminary results suggest that a minimum spatial resolution is needed to properly capture channel features, but additional work is required to precisely quantify this and its impact on accurately modeling the coupled ice sheet–hydrology system. The efficiency of our approach, relying on localized refinement, is also demonstrated. Future work will include coupling the SUbglacial Hydrology MOdel (SUHMO) with the BISICLES AMR ice sheet model (Cornford et al., 2013), both built on the same numerical framework.

58 GEOSCIENCES↗