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DOE OSTI2024

An Empirical Validation of a Constrained Bin Packing Algorithm for a Home Energy Management System

The increasing number of intelligent electrical appliances and home energy management systems provide a big opportunity for demand response services from residential and small commercial buildings to the grid. Simultaneously, direct control of individual devices by utilities can cause communication bottlenecks, as well as coordination and privacy concerns. These challenges can be addressed by combining the constituent devices into a single house battery equivalent for the purposes of demand response, using Minkowski sum and a 2d bin packing problem. However, the well-studied traditional problems have not been tested in a real house, as implementation carries significant challenges of its own. We deploy the packing problem on residential devices in a controllable house. We report the barriers we found, such as charge forecast and scalability of the algorithm, and discuss our solutions. The study serves as an intermediate step between existing theoretical research and possible future steps, such as prototype deployments of systems that provide residential demand response.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Learning Conservation Laws in Unknown Quantum Dynamics

We present a learning algorithm for discovering conservation laws given as sums of geometrically local observables in quantum dynamics. This includes conserved quantities that arise from local and global symmetries in closed and open quantum many-body systems. The algorithm combines the classical shadow formalism for estimating expectation values of observable and data analysis techniques based on singular value decompositions and robust polynomial interpolation to discover all such conservation laws in unknown quantum dynamics with rigorous performance guarantees. Our method can be directly realized in quantum experiments, which we illustrate with numerical simulations, using closed and open quantum system dynamics in a ℤ 2 gauge theory and in many-body localized spin chains.

Machine learning↗

DOE OSTI2021

Generalized Toeplitz–Hankel matrices and their application to a layered electron gas

We extend the standard result for the eigenspectrum of the Toeplitz matrix C ij = e –κ|i–j| with 0 ≤ i,j ≤ N and κ ϵ C to a combination of a Toeplitz matrix and a Hankel matrix. We apply this result to find the plasma modes of a layered assembly of a 2-dimensional electron gas. We find a sum rule relating the geometric mean of the frequencies of the plasma modes to the determinant of this Toeplitz matrix, for which an analytical expression is obtained. Here, we apply the same technique to the generalized case when the layers are not evenly spaced, where the corresponding matrix is not a Toeplitz-Hankel combination. Despite this fact, it is possible to find properties of the eigenspectrum, and the eigenmodes are localized to a few layers instead of extending across the system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Quest for Multifunctionality: Current Progress in the Characterization of Heterometallic Metal–Organic Frameworks

Metal–organic frameworks (MOFs) are a class of porous, crystalline materials that have been systematically developed for a broad range of applications. Incorporation of two or more metals into a single crystalline phase to generate heterometallic MOFs has been shown to lead to synergistic effects, in which the whole is oftentimes greater than the sum of its parts. Because geometric proximity is typically required for metals to function cooperatively, deciphering and controlling metal distributions in heterometallic MOFs is crucial to establish structure–function relationships. However, determination of short- and long-range metal distributions is nontrivial and requires the use of specialized characterization techniques. Advancements in the characterization of metal distributions and interactions at these length scales is key to rapid advancement and rational design of functional heterometallic MOFs. Further, this perspective summarizes the state-of-the-art in the characterization of heterometallic MOFs, with a focus on techniques that allow metal distributions to be better understood. Using complementary analyses, in conjunction with computational methods, is critical as this field moves toward increasingly complex, multifunctional systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Spin structures and baby universes

We extend a 2d topological model of the gravitational path integral to include sums over spin structure, corresponding to Neveu-Schwarz (NS) or Ramond (R) boundary conditions for fermions. This path integral corresponds to a correlator of boundary creation operators on a non-trivial baby universe Hilbert space, and vanishes when the number of R boundaries is odd. This vanishing implies a non-factorization of the correlator, which necessitates a dual interpretation of the bulk path integral in terms of a product of partition functions (associated to NS boundaries) and Witten indices (associated to R boundaries), averaged over an ensemble of theories with varying Hilbert space dimension and different numbers of bosonic and fermionic states. We also consider a model with End-of-the-World (EOW) branes, for which the dual ensemble then includes a sum over randomly chosen fermionic and bosonic states. We propose two modifications of the bulk path integral which restore an interpretation in a single dual theory: (i) a geometric prescription where we add extra boundaries with a sum over their spin structures, and (ii) an algebraic prescription involving “spacetime D-branes”. We extend our ideas to Jackiw-Teitelboim gravity, and propose a dual description of a single unitary theory with spin structure in a system with eigenbranes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Nonperturbative negative geometries: amplitudes at strong coupling and the amplituhedron

The amplituhedron determines scattering amplitudes in planar N = 4 super Yang-Mills by a single “positive geometry” in the space of kinematic and loop variables. We study a closely related definition of the amplituhedron for the simplest case of four-particle scattering, given as a sum over complementary “negative geometries”, which provides a natural geometric understanding of the exponentiation of infrared (IR) divergences, as well as a new geometric definition of an IR finite observable F(g, z) — dually interpreted as the expectation value of the null polygonal Wilson loop with a single Lagrangian insertion — which is directly determined by these negative geometries. This provides a long-sought direct link between canonical forms for positive (negative) geometries, and a completely IR finite post-loop-integration observable depending on a single kinematical variable z, from which the cusp anomalous dimension Γ cusp (g) can also be straightforwardly obtained. We study an especially simple class of negative geometries at all loop orders, associated with a “tree” structure in the negativity conditions, for which the contributions to F(g, z) and Γ cusp can easily be determined by an interesting non-linear differential equation immediately following from the combinatorics of negative geometries. This lets us compute these “tree” contributions to F(g, z) and Γ cusp for all values of the ‘t Hooft coupling. The result for Γ cusp remarkably shares all main qualitative characteristics of the known exact results obtained using integrability.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Differential equations for cosmological correlators

Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations satisfied by cosmological correlation functions. In this work, we provide a broader perspective on the origin and structure of these differential equations. As a concrete example, we study conformally coupled scalar fields in a power-law cosmology. The wavefunction coefficients in this model have integral representations, with the integrands being the product of the corresponding flat-space results and “twist factors” that depend on the cosmological evolution. Similar twisted integrals arise for loop amplitudes in dimensional regularization, and their recent study has led to the discovery of rich mathematical structures and powerful new tools for computing multi-loop Feynman integrals in quantum field theory. The integrals of interest in cosmology are also part of a finite-dimensional basis of master integrals, which satisfy a system of first-order differential equations. We develop a formalism to derive these differential equations for arbitrary tree graphs. The results can be represented in graphical form by associating the singularities of the differential equations with a set of graph tubings. Upon differentiation, these tubings grow in a local and predictive fashion. In fact, a few remarkably simple rules allow us to predict — by hand — the equations for all tree graphs. While the rules of this “kinematic flow” are defined purely in terms of data on the boundary of the spacetime, they reflect the physics of bulk time evolution. We also study the analogous structures in tr ϕ 3 theory, and see some glimpses of hidden structure in the sum over planar graphs. This suggests that there is an autonomous combinatorial or geometric construction from which cosmological correlations, and the associated spacetime, emerge.

Cosmological models↗

DOE OSTI2022

Jet timing

The measurement of the arrival time of a particle, such as a lepton, a photon, or a pion, reaching the detector provides valuable information. A similar measurement for a hadronic final state, however, is much more challenging as one has to extract the relevant information from a collection of particles. In this paper, we explore various possibilities in defining the time of a jet through the measurable arrival times of the jet constituents. We find that a definition of jet time based on a transverse momentum weighted sum of the times of the constituents has the best performance. For prompt jets, the performance depends on the jet trajectory. For delayed jets, the performance depends on the trajectory of the jet, the trajectory of the mother particle, and the location of the displaced vertex. Compared to the next-best-performing jet time definition, the transverse momentum weighted sum has roughly a factor of ten times better jet time resolution. We give a detailed discussion of the relevant effects and characterize the full geometrical dependence of the performance. These results highlight the critical importance of using a proper definition of jet time with its corresponding detector-dependent calibration and the exciting possibility of deepening our understanding of jets in the time domain.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

High-throughput screening tools facilitate calculation of a combined exposure-bioactivity index for chemicals with endocrine activity

High-throughput and computational tools provide a new opportunity to calculate combined bioactivity of exposure to diverse chemicals acting through a common mechanism. We used high throughput in vitro bioactivity data and exposure predictions from the U.S. EPA’s Toxicity and Exposure Forecaster (ToxCast and ExpoCast) to estimate combined estrogen receptor (ER) agonist activity of non-pharmaceutical chemical exposures for the general U.S. population. High-throughput toxicokinetic (HTTK) data provide conversion factors that relate bioactive concentrations measured in vitro (µM), to predicted population geometric mean exposure rates (mg/kg/day). These data were available for 22 chemicals with ER agonist activity and were estimated for other ER bioactive chemicals based on the geometric mean of HTTK values across chemicals. For each chemical, ER bioactivity across ToxCast assays was compared to predicted population geometric mean exposure at different levels of in vitro potency and model certainty. Dose additivity was assumed in calculating a Combined Exposure-Bioactivity Index (CEBI), the sum of exposure/bioactivity ratios. Combined estrogen bioactivity was also calculated in terms of the percent maximum bioactivity of chemical mixtures in human plasma using a concentration-addition model. Estimated CEBIs vary greatly depending on assumptions used for exposure and bioactivity. In general, CEBI values were <1 when using median of the estimated general population chemical intake rates, while CEBI were ≥1 when using the upper 95th confidence bound for those same intake rates for all chemicals. Concentration-addition model predictions of mixture bioactivity yield comparable results. Based on current in vitro bioactivity data, HTTK methods, and exposure models, combined exposure scenarios sufficient to influence estrogen bioactivity in the general population cannot be ruled out. Future improvements in screening methods and computational models could reduce uncertainty and better inform the potential combined effects of estrogenic chemicals.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Positivity and geometric function theory constraints on pion scattering

This paper presents the fascinating correspondence between the geometric function theory and the scattering amplitudes with O(N) global symmetry. A crucial ingredient to show such correspondence is a fully crossing symmetric dispersion relation in the z-variable, rather than the fixed channel dispersion relation. We have written down fully crossing symmetric dispersion relation for O(N) model in z-variable for three independent combinations of isospin amplitudes. We have presented three independent sum rules or locality constraints for the O(N) model arising from the fully crossing symmetric dispersion relations. We have derived three sets of positivity conditions. We have obtained two-sided bounds on Taylor coefficients of physical Pion amplitudes around the crossing symmetric point (for example, π + π – → π 0 π 0 ) applying the positivity conditions and the Bieberbach-Rogosinski inequalities from geometric function theory.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Modular flow in JT gravity and entanglement wedge reconstruction

It has been shown in recent works that JT gravity with matter with two boundaries has a type II ∞ algebra on each side. As the bulk spacetime between the two boundaries fluctuates in quantum nature, we can only define the entanglement wedge for each side in a pure algebraic sense. As we take the semiclassical limit, we will have a fixed long wormhole spacetime for a generic partially entangled thermal state (PETS), which is prepared by inserting heavy operators on the Euclidean path integral. Under this limit, with appropriate assumptions of the matter theory, geometric notions of the causal wedge and entanglement wedge emerge in this background. In particular, the causal wedge is manifestly nested in the entanglement wedge. Different PETS are orthogonal to each other, and thus the Hilbert space has a direct sum structure over sub-Hilbert spaces labeled by different Euclidean geometries. The full algebra for both sides is decomposed accordingly. From the algebra viewpoint, the causal wedge is dual to an emergent type III 1 subalgebra, which is generated by boundary light operators. To reconstruct the entanglement wedge, we consider the modular flow in a generic PETS for each boundary. We show that the modular flow acts locally and is the boost transformation around the global RT surface in the semiclassical limit. It follows that we can extend the causal wedge algebra to a larger type III 1 algebra corresponding to the entanglement wedge. Within each sub-Hilbert space, the original type II ∞ reduces to type III 1 .

2D Gravity↗

DOE OSTI2023

Online transfer learning strategy for enhancing the scalability and deployment of deep reinforcement learning control in smart buildings

In recent years, advanced control strategies based on Deep Reinforcement Learning (DRL) proved to be effective in optimizing the management of integrated energy systems in buildings, reducing energy costs and improving indoor comfort conditions when compared to traditional reactive controllers. However, the scalability and implementation of DRL controllers are still limited since they require a considerable amount of time before converging to a near-optimal solution. This issue is currently addressed in literature through the offline pre-training of the DRL agent. However this solution results in two main critical issues: (1) the need to develop a building surrogate model to perform the training task, and (2) the need to perform a fine-tuning process over several training episodes to obtain a near-optimal control policy. In this context, this paper introduces an Online Transfer Learning (OTL) strategy that exploits two knowledge-sharing techniques, weight-initialization and imitation learning, to transfer a DRL control policy from a source office building to various target buildings in a simulation environment coupling EnergyPlus and Python. A DRL controller based on discrete Soft Actor–Critic (SAC) is trained on the source building to manage the operation of a cooling system consisting of a chiller and a thermal storage. Several target buildings are defined to benchmark the performance of the OTL strategy with that of a Rule-Based Controller (RBC) and two DRL-based control strategies, deployed in offline and online fashion. The strategy adopted for OTL emulates the real world implementation with a simulation process by implementing the transferred DRL agent for a single episode in the target buildings. Target buildings have the same geometrical features and are served by the same energy system as the source building, but differ in terms of weather conditions, electricity price schedules, occupancy patterns, and building envelope efficiency levels. The results show that the OTL strategy can reduce the cumulated sum of temperature violations on average by 50% and 80% respectively when compared to RBC and online DRL while enhancing the energy system operation with electricity cost savings ranging between 20% and 40%. Furthermore, the OTL agent performs slightly worse than the offline DRL controller but it does not require any modeling effort and can be implemented directly on target buildings emulating a real-world implementation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Updated neutrino mass constraints from galaxy clustering and CMB lensing-galaxy cross-correlation measurements

In this work, we revisit cosmological constraints on the sum of the neutrino masses Σm v from a combination of full-shape BOSS galaxy clustering [P(k)] data and measurements of the cross-correlation between Planck Cosmic Microwave Background (CMB) lensing convergence and BOSS galaxy overdensity maps [$C_{l}^{kg}$], using a simple but theoretically motivated model for the scale-dependent galaxy bias in auto- and cross-correlation measurements. We improve upon earlier related work in several respects, particularly through a more accurate treatment of the correlation and covariance between P(k) and $C_{l}^{kg}$ measurements. When combining these measurements with Planck CMB data, we find a 95% confidence level upper limit of Σm v sum of neutrino masses < 0.14 eV, while slightly weaker limits are obtained when including small-scale ACTPol CMB data, in agreement with our expectations. We confirm earlier findings that (once combined with CMB data) the full-shape information content is comparable to the geometrical information content in the reconstructed BAO peaks given the precision of current galaxy clustering data, discuss the physical significance of our inferred bias and shot noise parameters, and perform a number of robustness tests on our underlying model. While the inclusion of $C_{l}^{kg}$ measurements does not currently appear to lead to substantial improvements in the resulting Σm v of neutrino mass constraints, we expect the converse to be true for near-future galaxy clustering measurements, whose shape information content will eventually supersede the geometrical one.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Direct microstability optimization of stellarator devices

Turbulent transport is regarded as one of the key issues in magnetic confinement nuclear fusion, both for tokamaks and stellarators. Here, in this work, we show that a significant decrease in a microstability-based proxy, as opposed to a geometric one, for the turbulent heat flux, namely the quasilinear heat flux, can be obtained in an efficient manner by coupling stellarator optimization with linear gyrokinetic simulations. This is accomplished by computing the quasilinear heat flux at each step of the optimization process, as well as the deviation from quasisymmetry, and minimizing their sum, leading to a balance between neoclassical and the turbulent transport proxy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

The quantum $\mathrm{UV}$-$\mathrm{IR}$ map for line defects in $$ \mathfrak{gl} $$(3)-type class $\mathcal{S}$ theories

We consider the quantum UV-IR map for line defects in class S theories of $\mathfrak{gl}$(3)-type. This map computes the protected spin character which counts framed BPS states with spin for the bulk-defect system. We give a geometric method of computing this map motivated by the physics of five-dimensional $\mathcal{N}$ = 2 supersymmetric Yang-Mills theory, and compute it explicitly in various examples. As a spin-off we propose a new way of computing a certain specialization of the HOMFLY polynomial for links in $\mathbb{R}^3$, as a sum over BPS webs attached to the link.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Linear complexity

We present factorization and solution phases for a new linear complexity direct solver designed for concurrent batch operations on fine-grained parallel architectures, for matrices amenable to hierarchical representation. We focus on the strong-admissibility-based $\mathscr{H}^{2}$ format, where strong recursive skeletonization factorization compresses remote interactions. We build upon previous implementations of $\mathscr{H}^{2}$ matrix construction for efficient factorization and solution algorithm design, which are illustrated graphically in stepwise detail. The algorithms are ‘blackbox’ in the sense that the only inputs are the matrix and right-hand side, without analytical or geometrical information about the origin of the system. We demonstrate linear complexity scaling in both time and memory on four representative families of dense matrices up to one million in size. Parallel scaling up to 16 threads is enabled by a multi-level matrix graph coloring and avoidance of dynamic memory allocations thanks to prefix-sum memory management. An experimental backward error analysis is included. We break down the timings of different phases, identify phases that are memory-bandwidth limited, and discuss alternatives for phases that may be sensitive to the trend to employ lower precisions for performance.

Boukaram, Wajih↗

DOE OSTI2020

Efficient Low-Order Refined Preconditioners for High-Order Matrix-Free Continuous and Discontinuous Galerkin Methods

In this paper, we design preconditioners for the matrix-free solution of high-order continuous and discontinuous Galerkin discretizations of elliptic problems based on finite element method--spectral element method (FEM-SEM) equivalence and additive Schwarz methods. The high-order operators are applied without forming the system matrix, making use of sum factorization for efficient evaluation. The system is preconditioned using a spectrally equivalent low-order (p = 1) finite element operator discretization on a refined mesh. The low-order refined mesh is anisotropic and not shape regular in the polynomial degree of the high-order operator, requiring specialized solvers to treat the anisotropy. We make use of an element-structured, geometric multigrid V-cycle with ordered ILU(0) smoothing. The preconditioner is parallelized through an overlapping additive Schwarz method that is robust in h and p. The method is extended to interior penalty and Bassi and Rebay (BR2) discontinuous Galerkin discretizations, for which it is also robust in the size of the penalty parameter. Finally, numerical results are presented on a variety of examples, verifying the uniformity of the preconditioner.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Theory of Trotter Error with Commutator Scaling

The Lie-Trotter formula, together with its higher-order generalizations, provides a simple approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, nearly matching or even outperforming the best previous results. Our applications include: (i) a simulation of second-quantized plane-wave electronic structure, nearly matching the interaction-picture algorithm of Low and Wiebe; (ii) a simulation of $k$-local Hamiltonians almost with induced one-norm scaling, faster than the qubitization algorithm of Low and Chuang; (iii) a simulation of rapidly decaying power-law interactions, outperforming the Lieb-Robinson-based approach of Tran et al.; (iv) a hybrid simulation of clustered Hamiltonians, dramatically improving the result of Peng, Harrow, Ozols, and Wu; and (v) quantum Monte Carlo simulations of the transverse field Ising model and quantum ferromagnets, tightening previous analyses of Bravyi and Gosset. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound nearly matching a recent result of Tran et al. Our analysis reproduces known tight bounds for first- and second-order formulas. We further investigate the tightness of our bounds for higher-order formulas. For quantum simulation of a one-dimensional Heisenberg model with an even-odd ordering of terms, our result overestimates the complexity by only a factor of $5$. Our bound is also close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both the asymptotic scaling and the constant prefactor.

quantum computing, numerical analysis↗