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DOE OSTI2021

Parton distributions and lattice-QCD calculations: Toward 3D structure

The strong force which binds hadrons is described by the theory of quantum chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the parton distribution functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by generalized parton distributions (GPDs) and transverse-momentum-dependent parton distribution functions (TMD PDFs). In our previous report Lin et al. (2018), we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice-QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and lattice-QCD communities, and yield improvements for these generalized PDFs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Implications of stop-and-go traffic on training learning-based car-following control

Learning-based car-following control (LCC) of connected and autonomous vehicles (CAVs) is gaining significant attention with the advancement of computing power and data accessibility. While the flexibility and large model capacity of model-free architecture enable LCC to potentially outperform the model-based car-following (CF) model in improving traffic efficiency and mitigating congestion, the generalizability of LCC for traffic conditions different from the training environment/dataset is not well-understood. Herein, this study seeks to explore the impact of stop-and-go traffic in the training dataset on the generalizability of LCC. It uses the characteristics of lead vehicle trajectories to describe stop-and-go traffic, and links the theory of identifiability (i.e., obtaining a unique parameter estimation result using sensor measurements) to the generalizability of behavior cloning (BC) and policy-based deep reinforcement learning (DRL). Correspondingly, the study shows theoretically that: (i) stop-and-go traffic can enable the property of identifiability and enhance the control performance of BC-based LCC in different traffic conditions; (ii) stop-and-go traffic is not necessary for DRL-based LCC to generalize to different traffic conditions; (iii) DRL-based LCC trained with only constant-speed lead vehicle trajectories (not sufficient to ensure identifiability) can be generalized to different traffic conditions; and (iv) stop-and-go traffic increases variance in the training dataset, which improves the convergence of parameter estimation while negatively impacting the convergence of DRL to the optimal control policy. Numerical experiments validate the above findings, illustrating that BC-based LCC entails comprehensive training datasets for generalizing to different traffic conditions, while DRL-based LCC can achieve generalization with simple free-flow traffic training environments. This further suggests DRL as a more promising and cost-effective LCC approach to reduce operational costs, mitigate traffic congestion, and enhance safety and mobility, which can accelerate the deployment and acceptance of CAVs.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Development, Implementation, and Verification of Partially-Ionized Collisional Multifluid Plasma Models in Drekar

We consider the development of multifluid models for partially ionized multispecies plasmas. The models are composed of a standard set of five-moment fluid equations for each species plus a description of electromagnetics. The most general model considered utilizes a full set of fluid equations for each charge state of each atomic species, plus a set of fluid equations for electrons. The fluid equations are coupled through source terms describing electromagnetic coupling, ionization, recombination, charge exchange, and elastic scattering collisions in the low-density coronal limit. The form of each of these source terms is described in detail, and references for required rate coefficients are identified for a diverse range of atomic species. Initial efforts have been made to extend these models to incorporate some higher-density collisional effects, including ionization potential depression and three- body recombination. Some reductions of the general multifluid model are considered. First, a reduced multifluid model is derived which averages over all of the charge states (including neutrals) of each atomic species in the general multifluid model. The resulting model maintains full consistency with the general multifluid model from which it is derived by leveraging a quasi-steady-state collisional ionization equilibrium assumption to recover the ionization fractions required to make use of the general collision models. Further reductions are briefly considered to derive certain components of a single-fluid magnetohydrodynamics (MHD) model. In this case, a generalized Ohm's law is obtained, and the standard MHD resistivity is expressed in terms of the collisional models used in the general multifluid model. A number of numerical considerations required to obtain robust implementations of these multifluid models are discussed. First, an algebraic flux correction (AFC) stabilization approach for a continuous Galerkin finite element discretization of the multifluid system is described in which the characteristic speeds used in the stabilization of the fluid systems are synchronized across all species in the model. It is demonstrated that this synchronization is crucial in order to obtain a robust discretization of the multifluid system. Additionally, several different formulations are considered for describing the electromagnetics portion of the multifluid system using nodal continuous Galerkin finite element discretizations. The formulations considered include a parabolic divergence cleaning method and an implicit projection method for the traditional curl formulation of Maxwell's equations, a purely- hyperbolic potential-based formulation of Maxwell's equations, and a mixed hyperbolic-elliptic potential-based formulation of Maxwell's equations. Some advantages and disadvantages of each formulation are explored to compare solution robustness and the ease of use of each formulation. Numerical results are presented to demonstrate the accuracy and robustness of various components of our implementation. Analytic solutions for a spatially homogeneous damped plasma oscillation are derived in order to verify the implementation of the source terms for electromagnetic coupling and elastic collisions between fluid species. Ionization balance as a function of electron temperature is evaluated for several atomic species of interest by comparing to steady-state calculations using various sets of ionization and recombination rate coefficients. Several test problems in one and two spatial dimensions are used to demonstrate the accuracy and robustness of the discretization and stabilization approach for the fluid components of the multifluid system. This includes standard test problems for electrostatic and electromagnetic shock tubes in the two-fluid and ideal shock-MHD limits, a cylindrical diocotron instability, and the GEM challenge magnetic reconnection problem. A one-dimensional simplified prototype of an argon gas puff configuration as deployed on Sandia's Z-machine is used as a demonstration to exercise the full range of capabilities associated with the general multifluid model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Use of an Alternative Conceptual Model of Vadose Zone Heterogeneity to Evaluate Past Tank Leaks and Other Unplanned Releases within a Tank Farm at the Hanford Site - 20061

Washington State Department of Ecology (Ecology) requested that U.S. Department of Energy (DOE)-Office of River Protection (ORP) consider an evaluation of effects of fine-grained thin sediment layers on transport with a separate alternative conceptual model in its evaluation of the potential impact of tank leaks and other unplanned releases within the tank farm at the Hanford Site. For this alternative model, Ecology recommended that the model be developed based on the general framework of fine-grained units identified by a stakeholder group in their interpretations of variability in moisture content data collected in the vicinity of Waste Management Area (WMA) C. In discussions with DOE-ORP, Ecology acknowledged that the underlying data and interpretations of the occurrence and lateral continuity of the fine-grained thin layers identified by a stakeholder group are uncertain. However, DOE-ORP agreed to Ecology's recommendation and has provided support for the requested evaluation that involved development of an alternative model based on the general framework of the unpublished report by the stakeholder. DOE-ORP considered this evaluation to be a hypothetical evaluation of vadose zone heterogeneities at WMA C. General observations from the range of simulation cases examined in the evaluation of the effects of hypothetical vadose zone heterogeneities at WMA C are as follows. - The movement of the center of mass of the simulated plumes was generally vertically downward below the source for all simulations, including those that incorporated the hypothetical fine-grained units. - All simulations that incorporated hypothetical heterogeneity produced additional plume spreading over what was produced in simulations using Equivalent Homogeneous Media (EHM) model(s)a. The spreading resulted in a broadening of the fringes of the plume, resulting in a wider region of low concentration, but lower peak concentrations associated with the center of mass of the plume. - Simulations that used the silty-sand hydraulic properties, suggested by Ecology for the hypothetical fine-grained units, generally produced similar spreading and slightly lower peak mass flux at the water table when compared to the EHM modeling results. a The EHM-based models used at WMA C do not explicitly include small-scale fine-grained heterogeneities used in the model advocated by Ecology. - Simulations that used the silty-sand hydraulic properties, suggested by Ecology for the hypothetical fine-grained units, generally produced less spreading and an earlier arrival of mass flux at the water table when compared to the use of another set of hydraulic properties from a silty-sand sample collected at a nearby disposal facility. - The EHM representation of the vadose zone generally produced higher peak mass flux and an earlier occurrence of peak fluxes at the water table compared to all analyses incorporating additional hypothetical heterogeneity. Results of this alternative model evaluation of past leaks provided some insight into the transport effects of vadose zone heterogeneities at WMA C that helped resolve Ecology's comments and issues related to the effects of vadose zone heterogeneities on past leaks and losses from the WMA C tank farms area. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Measurement-based quantum simulation of Abelian lattice gauge theories

Numerical simulation of lattice gauge theories is an indispensable tool in high energy physics, and their quantum simulation is expected to become a major application of quantum computers in the future. In this work, for an Abelian lattice gauge theory in d d spacetime dimensions, we define an entangled resource state (generalized cluster state) that reflects the spacetime structure of the gauge theory. We show that sequential single-qubit measurements with the bases adapted according to the former measurement outcomes induce a deterministic Hamiltonian quantum simulation of the gauge theory on the boundary. Our construction includes the (2+1) ( 2 + 1 ) -dimensional Abelian lattice gauge theory simulated on three-dimensional cluster state as an example, and generalizes to the simulation of Wegner’s lattice models M_{(d,n)} M ( d , n ) that involve higher-form Abelian gauge fields. We demonstrate that the generalized cluster state has a symmetry-protected topological order with respect to generalized global symmetries that are related to the symmetries of the simulated gauge theories on the boundary.Our procedure can be generalized to the simulation of Kitaev’s Majorana chain on a fermionic resource state. We also study the imaginary-time quantum simulation with two-qubit measurements and post-selections, and a classical-quantum correspondence, where the statistical partition function of the model M_{(d,n)} M ( d , n ) is written as the overlap between the product of two-qubit measurement bases and the wave function of the generalized cluster state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Effective entropy of quantum fields coupled with gravity

Entanglement entropy, or von Neumann entropy, quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this paper, we propose a generalization of the quantum field theory entanglement entropy by including dynamical gravity. The generalized quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a replica calculation. The replicated theory is defined as a gravitational path integral with multiple copies of the original boundary conditions, with a co-dimension-2 brane at the boundary of region we are studying. We discuss different approaches to define the region in a gauge invariant way, and show that the effective entropy satisfies the quantum extremal surface formula. When the quantum fields carry a significant amount of entanglement, the quantum extremal surface can have a topology transition, after which an entanglement island region appears. Our result generalizes the Hubeny-Rangamani-Takayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime. We apply the formula to two example systems, a closed two-dimensional universe and a four-dimensional maximally extended Schwarzchild black hole. We discuss the analog of the effective entropy in random tensor network models, which provides more concrete understanding of quantum information properties in general dynamical geometries. We show that, in absence of a large boundary like in AdS space case, it is essential to introduce ancilla that couples to the original system, in order for correctly characterizing quantum states and correlation functions in the random tensor network. Using the superdensity operator formalism, we study the system with ancilla and show how quantum information in the entanglement island can be reconstructed in a state-dependent and observer-dependent map. We study the closed universe (without spatial boundary) case and discuss how it is related to open universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Thermal conductivity and theory of inelastic scattering of phonons by collective fluctuations

We study the intrinsic scattering of phonons by a general quantum degree of freedom, i.e., a fluctuating “field” Q, which may have completely general correlations, restricted only by unitarity and translational invariance. From the induced scattering rates, generalizing the model studied in a companion paper [Mangeolle et al., Phys. Rev. X 12, 041031 (2022)], we obtain the consequences on the thermal conductivity tensor of the phonons. We confirm that, even within our generalized model, the off-diagonal scattering rates involve a minimum of three- to four-point correlation functions of the Q fields, and we discuss the “semiclassical” versus “quantum” nature of all contributions. We obtain general and explicit forms for these correlations which isolate the contributions to the Hall conductivity, and we provide a general discussion of the implications of symmetry and equilibrium; this elaborates on, and extends, the results of Mangeolle et al. [Phys. Rev. X 12, 041031 (2022)]. We also extend the discussion and evaluation of these two- (diagonal scattering) and four-point correlation functions, and hence the thermal transport, for the illustrative example of an ordered two-dimensional antiferromagnet, where the Q field is a composite of magnon operators arising from spin-lattice coupling, and confirm numerically that the results, while satisfying all the necessary symmetry restrictions, lead to nonvanishing scattering and Hall effects. In particular, we investigate, both analytically and numerically, the dependence of such intrinsic scattering on a crucial parameter—the magnon to phonon velocity ratio v. We in particular confirm that within some range of v of order 1 the skew-scattering mechanism leads to comparable thermal Hall conductivity for thermal currents within and normal to the plane of the antiferromagnetism, and we discover that the temperature scaling of the longitudinal conductivity displays a threshold effect and a nonuniversal, continuous variation of the scaling exponent with v.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Heat exchanger

A heat exchanger that includes first and second headers, a first flow conduit fluidly connecting the first and second headers to allow for a flow of a first fluid through the heat exchanger, the first flow conduit being bounded by a first generally planar wall section extending between the first and second headers, a second flow conduit to allow for a flow of the second fluid through the heat exchanger, the second flow conduit being bounded by a second generally planar wall section spaced apart from the first generally planar wall section to define a gap therebetween, and a thermally conductive structure arranged within the gap and joined to the first and second generally planar wall sections to transfer heat therebetween. The thermally conductive structure is isolated from the first fluid by the first generally planar wall section and from the second fluid by the second generally planar wall section.

42 ENGINEERING↗
DOE OSTI2021

Algebraic Structures in the Coupling of Gravity to Gauge Theories

Highlights: • Geometric foundation for Quantum General Relativity coupled to Quantum Electrodynamics. • Rigorous introduction to Hopf algebraic renormalization. • Appropriate modifications in case renormalization Hopf algebra is ill-defined. • Generalization of Furry’s Theorem to include gravitons and ghosts. • Discussion of obstructions to multiplicative renormalization. This article is an extension of the author’s second master thesis, Prinz (2017). It aims to introduce to the theory of perturbatively quantized General Relativity coupled to Spinor Electrodynamics, provide the results thereof and set the notation to serve as a starting point for further research in this direction. It includes the differential geometric and Hopf algebraic background, as well as the corresponding Lagrange density and some renormalization theory. Then, a particular problem in the renormalization of Quantum General Relativity coupled to Quantum Electrodynamics is addressed and solved by a generalization of Furry’s Theorem. Next, the restricted combinatorial Green’s functions for all two-loop propagators and all one-loop divergent subgraphs thereof are presented. Finally, relations between these one-loop restricted combinatorial Green’s functions necessary for multiplicative renormalization are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Island for gravitationally prepared state and pseudo entanglement wedge

We consider spacetime initiated by a finite-sized initial boundary as a generalization of the Hartle-Hawking no-boundary state. We study entanglement entropy of matter state prepared by such spacetime. We find that the entanglement entropy for large subregion is given either by the initial state entanglement or the entanglement island, preventing the entropy to grow arbitrarily large. Consequently, the entanglement entropy is always bounded from above by the boundary area of the island, leading to an entropy bound in terms of the island. The island I is located in the analytically continued spacetime, either at the bra or the ket part of the spacetime in Schwinger-Keldysh formalism. The entanglement entropy is given by an average of complex pseudo generalized entropy for each entanglement island. We find a necessary condition of the initial state to be consistent with the strong sub-additivity, which requires that any probe degrees of freedom are thermally entangled with the rest of the system. We then find a large parameter region where the spacetime with finite-sized initial boundary, which does not have the factorization puzzle at leading order, dominates over the Hartle-Hawking no-boundary state or the bra ket wormhole. Due to the absence of a moment of time reflection symmetry, the island in our setup is a generalization of the entanglement wedge, called pseudo entanglement wedge. In pseudo entanglement wedge reconstruction, we consider reconstructing the bulk matter transition matrix on A ∪ I, from a fine-grained state on A. The bulk transition matrix is given by a thermofield double state with a projection by the initial state. We also provide an AdS/BCFT model by considering EOW branes with corners. We also find the exponential hardness of such reconstruction task using a generalization of Python’s lunch conjecture to pseudo generalized entropy.

2D gravity↗
DOE OSTI2022

The False Dilemma: Rethinking AF Science and Technology Officer Talent Management

In 2019, Secretary of the Air Force (SECAF) Heather Wilson launched the 2030 Science and Technology (S&T) Strategy by stating, “The advantage will go to those who create the best technologies and who integrate and field them in creative operational ways that provide military advantages.” In 2021, 15% of Air Force general officers responsible for creating and integrating this technological edge had a science, technology, engineering, and math (STEM) graduate degree, and less than 1% of generals had a STEM doctorate. As one point of comparison, at least 32% and 13% of founding CEOs of Fortune 500 technology companies had a master’s and doctoral STEM degree, respectively. The gulf is larger when you consider that these CEOs used their technical degrees throughout their careers whereas most general officers do not. In large organizations, if the leader does not possess technical knowledge, it is difficult to drive innovation systems and connect ideas to reality. The evidence for this disconnect is abundant in acquisition challenges for high-tech systems, significant pushback to the “revolution in military affairs”, and failure of the “Third Offset” to take hold and deliver capabilities to offset Chinese and Russian capabilities. Indeed, when the former Air Force and Space Force Chief Software Officer, Nicolas M. Chaillan, offered his resignation, one of the main reasons for leaving was “the failure of OSD and the Joint Staff to deliver on their own alleged top ‘priority’, JADC2 – they couldn’t ‘walk the walk.’” Senior leaders have recognized this disconnect, and several inquiries and studies regarding STEM competency have been conducted. Many have posed a false dilemma: a large, STEM-cognizant or small, STEM-expert force. However, current and future STEM human capital needs are managed at the unit and functional area level. This leads to “silos” and the tactical “needs of the present” dominating the strategic “needs of the future”, highlighted by only two functional areas systematically tracking future STEM needs. Therefore, the decision on force structure appears to have been historically made by default through these and other perceived structural realities, and a vast majority of recommendations have focused on the small STEM community – an exercise in diminishing returns. In essence, the solution often boils down to finding unicorns – officers that have chartered the unforgiving pathway through the traditional “gates” to general officer while obtaining sufficient STEM proficiency along the way. Fortunately for the Air Force, these officers exist, albeit at a rate below what the evidence would suggest is necessary. However, this approach fundamentally limits the ability to develop a deep pool of officers with the ability to create and integrate technologies and ensures the Dunning-Kruger effect is prevalent. The Dunning-Kruger effect is a cognitive bias where those with limited knowledge in an area lack the expertise necessary to recognize their lack of expertise and consequently are prone to overestimate their knowledge and performance. In short, we need less leaders overestimating their STEM knowledge and more with hard-earned STEM competency required to “walk the walk” to create and integrate technologies for military advantage. This will not be accomplished by restricting the emphasis to the traditional scientists and engineering (S&E) career fields – the pool, only 10% of line officers, and general officer progression is just too small. Fortunately, the recent SECAF’s Management Initiatives and Chief of Staff’s (CSAF) Action Orders, both containing emphasis on organic expertise to “accrue advantage in military-technological competition,” present an opportunity to truly develop a framework for the force of the future.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2023

The sub-leading scattering waveform from amplitudes

We compute the next-to-leading order term in the scattering waveform of uncharged black holes in classical general relativity and of half-BPS black holes in $\mathcal{N}$ = 8 supergravity. We propose criteria, generalizing explicit calculations at next-to-leading or der, for determining the terms in amplitudes that contribute to local observables. For general relativity, we construct the relevant classical integrand through generalized unitary in two distinct ways, (1) in a heavy-particle effective theory and (2) in general relativity minimally-coupled to scalar fields. With a suitable prescription for the matter propagator in the former, we find agreement between the two methods, thus demonstrating the absence of interference of quantum and classically-singular contributions. The classical $\mathcal{N}$ = 8 integrand for massive scalar fields is constructed through dimensional reduction of the known five-point one-loop integrand. Our calculation exhibits novel features compared to conservative calculations and inclusive observables, such as the appearance of master integrals with intersecting matter lines and the appearance of a classical infrared divergence whose absence from classical observables requires a suitable definition of the retarded time.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Linear and Nonlinear Solvers for Simulating Multiphase Flow within Large-Scale Engineered Subsurface Systems

Simulation of multiphase flow in the subsurface is well-known to be computationally challenging. While there have been many studies that have explored approaches to overcoming these challenges, they often utilize relatively simple case studies. In this paper, we focus on the unique numerical challenges posed by modeling large-scale engineered subsurface systems, characterized by discrete features embedded in a heterogeneous natural subsurface setting. The man-made features such as shafts, tunnels, and barriers often cause multiple challenges in modeling the domain for multiphase porous media flow. This flow scenario can have a wide range of applications such as nuclear waste repositories, enhanced recovery of a petroleum reservoir, geothermal engineering, and carbon sequestration. An example of these severe numerical challenges is the case of performance assessment (PA) for Waste Isolation Pilot Plant (WIPP), the only operating deep geological repository in the US, which simulates extreme material properties of bedded salt rock formation and extreme contrast due to open excavation next to the formation. The models have extremes not only of permeability and porosity but also of the constitutive models needed for multiphase flow; additionally, they have process models like salt creep closure reducing porosity over time, fracturing in clay and anhydrite interbeds of the bedded salt, gas generation from the waste materials, and unintentional human borehole intrusions in some scenarios. Numerical simulations require the solution of coupled systems of nonlinear PDEs; in our work, we use the open-source simulator PFLOTRAN which is based on Finite Volume discretization. The solution of the nonlinear equations requires use of the Newton-Raphson iteration at each time step, which entails the solution of the linearized Jacobian system at each iteration. The effects of all the processes (i.e., large number of unknowns, highly nonlinear constitutive relations, large contrasts in material properties in short distances) lead to an ill-conditioned Jacobian matrix that severely challenges traditional linear solver, i.e., stabilized biconjugate gradient with block Jacobi incomplete LU preconditioner (BCGS-ILU) leading to non-convergence for traditional Newton-Raphson nonlinear solver causing unacceptably long computation time for each model. This paper presents linear solvers such as constrained pressure residual (CPR) two-stage preconditioner with alternate-block-factorization (ABF) and quasi- implicit pressure and explicit saturation (QIMPES) decouplers and flexible generalized residual solver (FGMRES). The new general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC), is also introduced to resolve extreme nonlinearities in the models. We demonstrate the effectiveness of each method relative to the default BCGS-Newton solver. The two best cases had nearly 50 times speed-up and achieved completion of a simulation in 14 hours that never completed due to non-convergence with the default solver. We also investigate the strong scalability of each method and discuss some of the deficiencies found for Block Jacobi preconditioner using parallel domain decomposition, and node packing effects of modern processor architecture.

Preconditioner, Nonlinear, Porous media, Multiphas↗
DOE OSTI2023

On the influence of over-parameterization in manifold based surrogates and deep neural operators

Constructing accurate and generalizable approximators (surrogate models) for complex physico-chemical processes exhibiting highly non-smooth dynamics is challenging. The main question is what type of surrogate models we should construct and should these models be under-parameterized or over-parameterized. In this work, we propose new developments and perform comparisons for two promising approaches: manifold-based polynomial chaos expansion (m-PCE) and the deep neural operator (DeepONet), and we examine the effect of over-parameterization on generalization. While m-PCE enables the construction of a mapping by first identifying low-dimensional embeddings of the input functions, parameters, and quantities of interest (QoIs), a neural operator learns the nonlinear mapping via the use of deep neural networks. Here, we demonstrate the performance of these methods in terms of generalization accuracy by solving the 2D time-dependent Brusselator reaction-diffusion system with uncertainty sources, modeling an autocatalytic chemical reaction between two species. We first propose an extension of the m-PCE by constructing a mapping between latent spaces formed by two separate embeddings of the input functions and the output QoIs. To further enhance the accuracy of the DeepONet, we introduce weight self-adaptivity in the loss function. We demonstrate that the performance of m-PCE and DeepONet is comparable for cases of relatively smooth input-output mappings. However, when highly non-smooth dynamics is considered, DeepONet shows higher approximation accuracy. We also find that for m-PCE, modest over-parameterization leads to better generalization, both within and outside of distribution, whereas aggressive over-parameterization leads to over-fitting. In contrast, an even highly over-parameterized DeepONet leads to better generalization for both smooth and non-smooth dynamics. Furthermore, we compare the performance of the above models with another recently proposed operator learning model, the Fourier Neural Operator, and show that its over-parameterization also leads to better generalization. Taken together, our studies show that m-PCE can provide very good accuracy at very low training cost, whereas a highly over-parameterized DeepONet can provide better accuracy and robustness to noise but at higher training cost. In both methods, the inference cost is negligible.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Encoding integers and rationals on neuromorphic computers using virtual neuron

Abstract Neuromorphic computers emulate the human brain while being extremely power efficient for computing tasks. In fact, they are poised to be critical for energy-efficient computing in the future. Neuromorphic computers are primarily used in spiking neural network–based machine learning applications. However, they are known to be Turing-complete, and in theory can perform all general-purpose computation. One of the biggest bottlenecks in realizing general-purpose computations on neuromorphic computers today is the inability to efficiently encode data on the neuromorphic computers. To fully realize the potential of neuromorphic computers for energy-efficient general-purpose computing, efficient mechanisms must be devised for encoding numbers. Current encoding mechanisms (e.g., binning, rate-based encoding, and time-based encoding) have limited applicability and are not suited for general-purpose computation. In this paper, we present the virtual neuron abstraction as a mechanism for encoding and adding integers and rational numbers by using spiking neural network primitives. We evaluate the performance of the virtual neuron on physical and simulated neuromorphic hardware. We estimate that the virtual neuron could perform an addition operation using just 23 nJ of energy on average with a mixed-signal, memristor-based neuromorphic processor. We also demonstrate the utility of the virtual neuron by using it in some of the μ -recursive functions, which are the building blocks of general-purpose computation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Classification of (2 + 1) D invertible fermionic topological phases with symmetry

Here we provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups G f and general values of the chiral central charge c - . Here G f is a central extension of a bosonic symmetry group G b by fermion parity, (-1) F , specified by a second cohomology class [ω 2 ]∈ $\mathscr{H}^2$(Gb,$\mathbb{Z}_2$). Our approach proceeds by gauging fermion parity and classifying the resulting G b symmetry-enriched topological orders while keeping track of certain additional data and constraints. We perform this analysis through two perspectives, using G-crossed braided tensor categories and Spin(2c - ) 1 Chern-Simons theory coupled to a background G gauge field. These results give a way to characterize and classify invertible fermionic topological phases in terms of a concrete set of data and consistency equations, which is more physically transparent and computationally simpler than the more abstract methods using cobordism theory and spectral sequences. Our results also generalize and provide a different approach to the recent classification of fermionic symmetry-protected topological phases by Wang and Gu, which have chiral central charge c - = 0. We show how the tenfold way classification of topological insulators and superconductors fits into our scheme, along with general nonperturbative constraints due to certain choices of c - and G f . Mathematically, our results also suggest an explicit general parametrization of deformation classes of (2 + 1)D invertible topological quantum field theories with G f symmetry.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Perturbative Stability and Error-Correction Thresholds of Quantum Codes

Topologically ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding general Calderbank-Shor-Steane codes and classical linear codes. Our construction encodes correction success probabilities under uncorrelated bit-flip and phase-flip errors, and simultaneously describes a generalized ℤ 2 lattice-gauge theory with quenched disorder. We observe that the clean limit of the latter is precisely the discretized imaginary-time path integral of the corresponding quantum code Hamiltonian when the errors are turned into a perturbative 𝑋 or 𝑍 magnetic field. Motivated by error-correction considerations, we define general order parameters for all such generalized ℤ 2 lattice-gauge theories, and show that they are generally lower bounded by success probabilities of error correction. For CSS codes satisfying the low-density parity-check condition and with a sufficiently large code distance, we prove the existence of a low-temperature ordered phase of the corresponding lattice-gauge theories, particularly for those lacking Euclidean spatial locality and/or when there is a nonzero code rate. We further argue that these results provide evidence for stable phases in the corresponding perturbed quantum Hamiltonians, obtained in the limit of continuous imaginary time. To do so, we distinguish space- and timelike defects in the lattice-gauge theory. A high free-energy cost of spacelike defects corresponds to a successful “memory experiment” and suppresses the energy splitting among the ground states, while a high free-energy cost of timelike defects corresponds to a successful “stability experiment” and points to a nonzero gap to local excitations.

quantum error correction↗
DOE OSTI2023

Risk Factors and Trends for HPV-Associated Subsequent Malignant Neoplasms among Adolescent and Young Adult Cancer Survivors

Subsequent malignant neoplasms (SMN; new cancers that arise after an original diagnosis) contribute to premature mortality among adolescent and young adult (AYA) cancer survivors. Because of the high population prevalence of human papillomavirus (HPV) infection, we identify demographic and clinical risk factors for HPV-associated SMNs (HPV-SMN) among AYA cancer survivors in the SEER-9 registries diagnosed from 1976 to 2015. Outcomes included any HPV-SMN, oropharyngeal-SMN, and cervical-SMN. Follow-up started 2 months after their original diagnosis. Standardized incidence ratios (SIR) compared risk between AYA survivors and general population. Age-period-cohort (APC) models examined trends over time. Fine and Gray's models identified therapy effects controlling for cancer and demographic confounders. Of 374,408 survivors, 1,369 had an HPV-SMN, occurring on average 5 years after first cancer. Compared with the general population, AYA survivors had 70% increased risk for any HPV-SMN [95% confidence interval (CI), 1.61–1.79] and 117% for oropharyngeal-SMN (95% CI, 2.00–2.35); cervical-SMN risk was generally lower in survivors (SIR, 0.85; 95% CI, 0.76–0.95), but Hispanic AYA survivors had a 8.4 significant increase in cervical-SMN (SIR, 1.46; 95% CI, 1.01–2.06). AYAs first diagnosed with Kaposi sarcoma, leukemia, Hodgkin, and non-Hodgkin lymphoma had increased HPV-SMN risks compared with the general population. Oropharyngeal-SMN incidence declined over time in APC models. Chemotherapy and radiation were associated with any HPV-SMN among survivors with first HPV-related cancers, but not associated among survivors whose first cancers were not HPV-related. HPV-SMN in AYA survivors are driven by oropharyngeal cancers despite temporal declines in oropharyngeal-SMN. Hispanic survivors are at risk for cervical-SMN relative to the general population. Encouraging HPV vaccination and cervical and oral cancer screenings may reduce HPV-SMN burden among AYA survivors.

60 APPLIED LIFE SCIENCES↗