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At least 595 records · Page 33

Reflected entropy in random tensor networks. Part III. Triway cuts

For general random tensor network states at large bond dimension, we prove that the integer Rényi reflected entropies (away from phase transitions) are determined by minimal triway cuts through the network. This generalizes the minimal cut description of bipartite entanglement for these states. A natural extrapolation away from integer Rényi parameters, suggested by the triway cut problem, implies the holographic conjecture S R = 2EW, where S R is the reflected entropy and EW is the entanglement wedge cross-section. Minimal triway cuts can be formulated as integer programs which cannot be relaxed to find a dual maximal flow/bit-thread description. This sheds light on the gap between the existence of tripartite entanglement in holographic states and the bipartite entanglement structure motivated by bit-threads. In particular, we prove that the Markov gap that measures tripartite entanglement is lower bounded by the integrality gap of the integer program that computes the triway cut.

AdS-CFT correspondence↗

Regression models using shapes of functions as predictors

Functional variables are often used as predictors in regression problems. A commonly used parametric approach, called scalar-on-function regression, uses the $\mathbb L^2$ inner product to map functional predictors into scalar responses. This method can perform poorly when predictor functions contain undesired phase variability, causing phases to have disproportionately large influence on the response variable. One past solution has been to perform phase–amplitude separation (as a pre-processing step) and then use only the amplitudes in the regression model. In this paper, we propose a more integrated approach, termed elastic functional regression model (EFRM), where phase-separation is performed inside the regression model, rather than as a pre-processing step. This approach generalizes the notion of phase in functional data, and is based on the norm-preserving time warping of predictors. Due to its invariance properties, this representation provides robustness to predictor phase variability and results in improved predictions of the response variable over traditional models. We demonstrate this framework using a number of datasets involving gait signals, NMR data, and stock market prices.

97 MATHEMATICS AND COMPUTING↗

A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to solutions with voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4,518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.

approximation algorithms↗

Two dimensional topology optimization of heat exchangers with the volume fraction method

We perform a comparison study of two topology optimizations methods applied to the design of a two fluids heat exchanger modeled with a coupled thermal-flow problem. The flow follows an isothermal and incompressible Stokes-Brinkman equation and the heat transfer is governed by a convection-diffusion equation without internal generation and high Peclet number. To keep the two fluid phases separated, we solve two Stokes-Brinkman equations, where the Brinkman term models the other phase as a solid. These two velocity fields are then fed to the heat transfer equation. Our goal is to maximize the enthalpy at the cold outlet while constraining the pressure drop. We first solve the design modeling the solid and fluid phases with a volume fraction variable. A SIMP-like penalization in the Brinkman term drives the optimization to a discrete design. The cost and constraint function derivatives are calculated with the library pyadjoint and the optimization is performed by IPOPT. We present optimized designs in two dimensions and discuss the influence of the parameters.

Beck, VictorA.↗

Beyond Classical Searches: Enabling New Discovery Potential at the LHC (Final Technical Report)

The major goals of this project are: • 1. Employ Machine Learning to solve combinatorial problems in searches for new physics phenomena, with a focus on multijet signatures. • 2. Enable high-precision tracking for CMS at the HL-LHC by carrying out the Outer Tracker project for the Phase-II detector upgrade. Compared to the original proposal, the scope is reduced due to reduced resources in final award. In particular, the program of long-lived particle searches was descoped at that time due to lack of resources.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Seeding picoscale solutions for social macro goals: complex thinking in projects for vulnerable communities

This chapter presents lessons learned from two experiences of implementing sociopoliticalsustainability strategies to achieve environmental and economic sustainability.The projects were carried out in rural communities in Guinea-Bissau andJamaica, which are both vulnerable to climate change. Each experience, developedfrom a systemic perspective and under two frameworks (the water–food–energynexus and ‘Appropriate Technology’), is described in four phases (problemcharacterization, solution design, solution pre-evaluation, and implementation),with the significant findings made by the team in terms of challenges, rewards, andessential conditions for development. Both deal with environment-friendly solutionsthat solve the problems of water and energy provision. Based on complex thinking,the experiences are analyzed from the social inclusion, participation, empowerment,and learning theory viewpoints. Finally, the insights gained by the team arehighlighted: communication requirements, the level of dependency of industrializedsolutions, budget constraints, training, testing, and planning recommendations, thediversity of interaction with the communities, and partners’ skills. As a result, futureactions can exploit these experiences and contribute to the success of subsequentprojects.

Pereira Pinto, Joao↗

Investigation of fracture in porous materials: a phase-field fracture study informed by ReaxFF

Microscopic features (e.g, pore shapes, sizes, and distribution) in porous material substantially affect the overall mechanical properties such as stiffness and strength. In turn, these material properties determine the macroscopic behaviors of fracture in the porous material. In certain cases, macroscopic properties can be derived from the porous skeleton and void ratio (i.e., porosity), but in many other cases, such derivation is a challenging task. This paper presents a numerical investigation of microporosity and micropore shapes effect on the macrofracture behavior in porous amorphous silica. For this study, we extend the recently-proposed combined molecular dynamic (MD) and phase-field (PF) fracture modeling approach by including different pore shapes in the atomistic domain. In the MD simulations, we adopt ReaxFF to evaluate the material properties, where four different micropore cases are considered. Based on the material properties derived from MD simulations, the macrofracture propagation of porous media is studied using hybrid PF simulation. In the characterization of the pore structure, the concept of pore ligament is proposed to relate the pore shape and the critical energy release rate. Two classical fracture problems were used to evaluate the effect of pore shape on the macrofracture behavior. The results of the case study show that although the micropore shapes change the macrofracture behaviors, these effects vary with the geometry and loading conditions of macroscopic boundary value problems. Furthermore, the case study also shows that the influence of micropore structure can be captured at the macroscopic level through the material properties derived from the MD simulations.

42 ENGINEERING↗

Watch and learn—a generalized approach for transferrable learning in deep neural networks via physical principles

Transfer learning refers to the use of knowledge gained while solving a machine learning task and applying it to the solution of a closely related problem. Such an approach has enabled scientific breakthroughs in computer vision and natural language processing where the weights learned in state-of-the-art models can be used to initialize models for other tasks which dramatically improve their performance and save computational time. Here we demonstrate an unsupervised learning approach augmented with basic physical principles that achieves fully transferrable learning for problems in statistical physics across different physical regimes. By coupling a sequence model based on a recurrent neural network to an extensive deep neural network, we are able to learn the equilibrium probability distributions and inter-particle interaction models of classical statistical mechanical systems. Our approach, distribution-consistent learning, DCL, is a general strategy that works for a variety of canonical statistical mechanical models (Ising and Potts) as well as disordered interaction potentials. Using data collected from a single set of observation conditions, DCL successfully extrapolates across all temperatures, thermodynamic phases, and can be applied to different length-scales. This constitutes a fully transferrable physics-based learning in a generalizable approach.

97 MATHEMATICS AND COMPUTING↗

Chaotic LLM billiards

Abstract We study null geodesics of the ten-dimensional LLM geometries. In particular, we show that there are a subset of these null geodesics that are confined to the LLM plane. The effective dynamics of these in-plane geodesics is that of a Hamiltonian system with two degrees of freedom (a phase space of dimension 4). We show that these are chaotic. In the two-coloring of the LLM plane, if they start in the empty region, they cannot penetrate the filled region and viceversa. The dynamical problem is therefore very similar to that of a billiards problem with fixed obstacles. We study to what extent LLM geometries with many droplets may be treated as an incipient black hole and draw analogies with the fuzzball proposal. We argue that for in-plane null geodesics deep in the interior of a region with a lot of droplets, in order to exit towards theAdSboundary they will need to undergo a process that resembles diffusion. This mechanism can account for signals getting lost in the putative black hole for a very long time.

Physics↗

Recalibration of missing low-frequency variability and trends in the North Atlantic Oscillation

Abstract Multi-decadal trends in the wintertime North Atlantic Oscillation (NAO) are under-represented by coupled general circulation models (CGCMs), consistent with a lack of autocorrelation in their NAO index series. This study proposes and tests two simple “reddening” approaches for correcting this problem in simulated indices based on simple one parameter short-term (AR; Auto-Regressive order 1) and long-term (FD; Fractional-Difference) time series filters. Using CGCMs from the Coupled Model Intercomparison Project Phase 6 (CMIP6), the FD filter successfully improves the autocorrelation structure of the NAO, and in turn the simulation of extreme trends, while the AR filter is less successful. The 1963–1993 NAO trend is the maximum 31-year trend in the historical period. Raw CGCMs underestimate the likelihood of this trend by a factor of ten but this discrepancy is corrected after reddening. CMIP6 future projections show that long-term (2024–2094) NAO ensemble mean trends systematically increase with the magnitude of radiative forcing: -2.4 to 3.5 hPa/century for low-to-high forcing after reddening (more than double the range using raw output). The related likelihood of future maximum 31year trends comparable to 1963–1993 ranges from 3 to 7% whereas none of these CMIP6 projections simulate this without reddening. Near-term projections of the next 31 years (2024–2054) are less sensitive than long term trends to the future scenario, showing weak-to-no forced trend. However, reddening increases the ensemble range by 74% (to +/-1 standard deviation/decade), which could increase/decrease regional climate change signals in the Northern Hemisphere by magnitudes that are underestimated when using raw CGCM output.

Meteorology & Atmospheric Sciences↗

Extremized nonlinear and linearized responses in soft metamaterials enabled by gradient-based design and grayscale digital light processing

In this study, we develop a gradient-based design approach that exploits grayscale digital light processing (DLP) 3D printing for extremizing the nonlinear and linearized response of soft metamaterials — materials that harness engineered geometric instabilities to undergo large and programmable changes in configuration. Grayscale DLP approaches modulate local mechanical properties at the pixel scale by tuning the light intensity within a single grayscale image, unlocking an exceptionally large design space. To effectively navigate this space, we develop smooth mappings between local light intensity values and global quantities of interest that characterize the behavior of soft metamaterials. Enabling these smooth mappings are robust and differentiable nonlinear finite element simulations powered by a trust region solver. A PDE-constrained optimization problem is then solved to invert these mappings and produce light intensity distributions that endow the printed part with varying stiffness and flexibility in distinctive regions. It is shown that optimizing the distribution of soft and stiff phases throughout a metamaterial structure results in markedly different buckling and self-contact configurations to drive extremized nonlinear compression and linearized vibration responses. Optimized light intensity distributions are translated to grayscale images and directly used to print soft metamaterial samples, showing remarkable agreement between the buckling and self-contact response in simulated and measured deformed configurations.

Additive manufacturing↗

Strain release by 3D atomic misfit in fivefold twinned icosahedral nanoparticles with amorphization and dislocations

Multiple twinning to form fivefold twinned nanoparticles in crystal growth is common and has attracted broad attention ranging from crystallography research to physical chemistry and materials science. Lattice-misfit strain and defects in multiple twinned nanoparticles (MTP) are key to understand and tailor their electronic properties. However, the structural defects and related strain distributions in MTPs are poorly understood in three dimensions (3D). Here, we show the 3D atomic misfit and strain relief mechanism in fivefold twinned icosahedral nanoparticles with amorphization and dislocations by using atomic resolution electron tomography. We discover a two-sided heterogeneity in variety of structural characteristics. A nearly ideal crystallographic fivefold face is always found opposite to a less ordered face, forming Janus-like icosahedral nanoparticles with two distinct hemispheres. The disordered amorphous domains release a large amount of strain. Molecular dynamics simulations further reveal the Janus-like icosahedral nanoparticles are prevalent in the MTPs formed in liquid-solid phase transition. This work provides insights on the atomistic models for the modelling of formation mechanisms of fivefold twinned structures and computational simulations of lattice distortions and defects. We anticipate it will inspire future studies on fundamental problems such as twin boundary migration and kinetics of structures in 3D at atomic level.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Exploration of lattice Hamiltonians for functional and structural discovery via Gaussian process-based exploration–exploitation

Statistical physics models ranging from simple lattice to complex quantum Hamiltonians are one of the mainstays of modern physics that have allowed both decades of scientific discovery and provided a universal framework to understand a broad range of phenomena from alloying to frustrated and phase separated materials to quantum systems. Traditionally, exploration of the phase diagrams corresponding to multidimensional parameter spaces of Hamiltonians was performed using a combination of basic physical principles, analytical approximations, and extensive numerical modeling. However, exploration of complex multidimensional parameter spaces is subject to the classic dimensionality problem, and the behaviors of interest concentrated on low dimensional manifolds remain undiscovered. Here, we demonstrate that a combination of exploration and exploration–exploitation with Gaussian process modeling and Bayesian optimization allows effective exploration of the parameter space for lattice Hamiltonians and effectively maps the regions at which specific macroscopic functionalities or local structures are maximized. We argue that this approach is general and can be further extended well beyond the lattice Hamiltonians to effectively explore the parameter space of more complex off-lattice and dynamic models.

42 ENGINEERING↗

DSP Implementation of a Novel Recurrent Neural Network Controller into a TI Solar Microinverter

Single-phase grid-tied inverters are widely used to integrate small-scale renewable energy sources and distributed generations to the utility grid. A novel Recurrent Neural Network (RNN) current controller is introduced to solve the resonant problem associated with LCL based inverters. The well-trained RNN controller was validated through a Texas Instruments (TI) LCL filter based solar microinverter kit that contains a C2000 TI microcontroller. The inverter closed current loop test without the grid connection was conducted in a laboratory setup to verify the RNN contoller functionality. The laboratory waveform results verified that the RNN current controller produced the strong tracking of the measured inverter AC current to its reference value even at a low sampling frequency of 5KHz. The proposed RNN current controller also proved to perform better than the built-in three-pole-three-zero (3P3Z) current controller provided by TI and produce lower values of Total Harmonic Distortion (THD).

digital signal processor↗

Stochastic minibatch approach to the ptychographic iterative engine

The ptychographic iterative engine (PIE) is a widely used algorithm that enables phase retrieval at nanometer-scale resolution over a wide range of imaging experiment configurations. By analyzing diffraction intensities from multiple scanning locations where a probing wavefield interacts with a sample, the algorithm solves a difficult optimization problem with constraints derived from the experimental geometry as well as sample properties. The effectiveness at which this optimization problem is solved is highly dependent on the ordering in which we use the measured diffraction intensities in the algorithm, and random ordering is widely used due to the limited ability to escape from stagnation in poor-quality local solutions. In this study, we introduce an extension to the PIE algorithm that uses ideas popularized in recent machine learning training methods, in this case minibatch stochastic gradient descent. Our results demonstrate that these new techniques significantly improve the convergence properties of the PIE numerical optimization problem.

47 OTHER INSTRUMENTATION↗

An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications

In this paper, we explore using the Harrow–Hassidim–Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing on domains such as power-grid management and climate projection, we demonstrate the correlations of the accuracy of quantum phase estimation, along with various properties of coefficient matrices, on the final solution and quantum resource cost in iterative and non-iterative numerical methods such as the Newton–Raphson method and finite difference method, as well as their impacts on quantum error correction costs using the Microsoft Azure Quantum resource estimator. We summarize the exponential resource cost from quantum phase estimation before and after quantum error correction and illustrate a potential way to reduce the demands on physical qubits. This work lays down a preliminary step for future investigations, urging a closer examination of quantum algorithms’ scalability and efficiency in domain applications.

hybrid software for QC-HPC↗

GradientGraph

Under this SBIR Phase II, Reservoir Labs has developed G2 Analytics, a new technology that allows network operators to analyze bottleneck and flow performance with high precision. G2 delivers a new analytical approach and framework to resolve a variety of key problems found in modern communication networks, including: traffic engineering, routing, flow scheduling, network design, capacity planning, resiliency analysis, network slicing, or service level agreement (SLA) management, among others. G2 leverages the bottleneck structure of congestion-controlled communication networks, a recent mathematical discovery by the Reservoir team [RL19b, RL20a, RL20b, RL21a]. Bottleneck structures reveal how perturbations on flows and links propagate through the network, providing an analytical framework to measure (qualitatively and quantitatively) the ripple effects induced as they traverse the network. Leveraging the mathematics of bottleneck structures, Reservoir Labs is developing the G2 technology to provide network operators with a framework to design, optimize and troubleshoot network performance. This delivery includes the G2 software stack.

Yellamraju, Sruthi↗

Learning viscoelasticity models from indirect data using deep neural networks

In this study, we propose a novel approach to model viscoelasticity materials, where rate-dependent and non-linear constitutive relationships are approximated with deep neural networks. We assume that inputs and outputs of the neural networks are not directly observable, and therefore common training techniques with input–output pairs for the neural networks are inapplicable. To that end, we develop a novel computational approach to both calibrate parametric and learn neural-network-based constitutive relations of viscoelasticity materials from indirect displacement data in the context of multiple-physics systems. We show that limited displacement data holds sufficient information to quantify the viscoelasticity behavior. We formulate the inverse computation – modeling viscoelasticity properties from observed displacement data – as a PDE-constrained optimization problem and minimize the error functional using a gradient-based optimization method. The gradients are computed by a combination of automatic differentiation and implicit function differentiation rules. The effectiveness of our method is demonstrated through numerous benchmark problems in geomechanics and porous media transport.

97 MATHEMATICS AND COMPUTING↗