Techno-economic comparison of various process configurations for post-combustion carbon capture using a single-component water-lean solvent
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Jiang, Yuan (ORCID:0000000250092121)↗
SEARCH · Engineering Papers
Results for “model order reduction”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Practical Considerations for Understanding Surface Reaction Mechanisms Involved in Heterogeneous Catalysis
Acquiring useful knowledge about the active site(s) of a catalyst, nature of reactant–catalyst interactions, nature of reactive intermediates, rate-determining step, reaction rate orders that affect various process parameters, and reaction mechanism as a whole is exceedingly challenging. This is especially true in the case of heterogeneous catalysts due to the complexity of the nature of surface active sites and their nonstatic behavior. Here, we present our perspective on differentiating between various surface reaction mechanisms in light of pioneering studies by leaders in the field, with the aim of clarifying some of the confusion associated with these complex mechanisms, especially the Eley–Rideal mechanism. Using bibliometric analysis, we identify and discuss the following four reactions that most commonly invoke the Eley– Rideal mechanism: H 2 activation, CO oxidation, esterification of alcohols by acids, and selective catalytic reduction (SCR) of NO x with NH 3 . Our analysis of studies utilizing well-suited experimental and computational methodologies for differentiating surface reaction mechanisms suggests that the above-mentioned four reactions do not occur via the Eley–Rideal mechanism. Instead, each reaction occurs via the Langmuir–Hinshelwood mechanism with nonidealities present. Lastly, we highlight practical considerations regarding select experimental (characterization methods and differential kinetics) and computational modeling that we believe can provide useful insights to accurately discern between the various possible reaction mechanisms in heterogeneous catalysis.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Cost function for low-dimensional manifold topology assessment
Abstract In reduced-order modeling, complex systems that exhibit high state-space dimensionality are described and evolved using a small number of parameters. These parameters can be obtained in a data-driven way, where a high-dimensional dataset is projected onto a lower-dimensional basis. A complex system is then restricted to states on a low-dimensional manifold where it can be efficiently modeled. While this approach brings computational benefits, obtaining a good quality of the manifold topology becomes a crucial aspect when models, such as nonlinear regression, are built on top of the manifold. Here, we present a quantitative metric for characterizing manifold topologies. Our metric pays attention to non-uniqueness and spatial gradients in physical quantities of interest, and can be applied to manifolds of arbitrary dimensionality. Using the metric as a cost function in optimization algorithms, we show that optimized low-dimensional projections can be found. We delineate a few applications of the cost function to datasets representing argon plasma, reacting flows and atmospheric pollutant dispersion. We demonstrate how the cost function can assess various dimensionality reduction and manifold learning techniques as well as data preprocessing strategies in their capacity to yield quality low-dimensional projections. We show that improved manifold topologies can facilitate building nonlinear regression models.
42 ENGINEERING↗
Stable heat and particle flux detachment with efficient particle exhaust in the island divertor of Wendelstein 7-X
The island divertor concept is an innovative and promising idea to handle heat and particle exhaust in stellarators. At the Wendelstein 7-X (W7-X) stellarator, this divertor concept plays a central role in the device mission to demonstrate reactor relevant plasma confinement for steady-state time scales of up to 30 minutes in the high-performance campaign (OP2) starting in 2022. During the recently concluded first campaign with the inertially cooled island divertor, a large step in the experimental qualification of this divertor concept has been made. In discharges heated with electron cylotron resonance heating of 5-6 MW, central densities in the range of 0.7-1.2 × 10 20 m -3 have been reached in combination with full divertor heat flux detachment. Also, significant neutral gas pressures and neutral compression ratios were shown for the first time in combination with reduced divertor particle flux. The divertor heat loads drop by an order of magnitude from >5 MW m -2 to below 0.5 MW m-2 with increasing density, and substantial compression of neutrals reaching neutral pressure in the sub-divertor volume of >6.0 × 10 -4 mbar was seen. These elevated neutral pressure levels can be obtained and maintained with an up to 80% reduction of the particle fluxes onto the divertor target tiles. This discharge scenario was held stably detached for up to 28 seconds, which is equivalent to several hundred energy confinement times τ E and longer than the time scales for current relaxation. No impurity accumulation was seen at constant Z eff ≈ 1.5 and the stored energy stayed constant at levels of W dia >600 kJ. The level of neutral pressure and compression reached in this scenario extrapolates well to the steady-state particle exhaust requirements for high-performance steady-state operation in OP2, in which the fully actively cooled high-heat-flux divertor will be available. Finally, an overview of this recently discovered divertor regime is given and the status of the physics understanding based on modeling of these regimes with the EMC3-EIRENE code is presented.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Characterization and identification of HPC applications at leadership computing facility
High Performance Computing (HPC) is an important method for scientific discovery via large-scale simulation, data analysis, or artificial intelligence. Leadership-class supercomputers are expensive, but essential to run large HPC applications. The Petascale era of supercomputers began in 2008, with the first machines achieving performance in excess of one petaflops, and with the advent of new supercomputers in 2021 (e.g., Aurora, Frontier), the Exascale era will soon begin. However, the high theoretical computing capability (i.e., peak FLOPS) of a machine is not the only meaningful target when designing a supercomputer, as the resources demand of applications varies. A deep understanding of the characterization of applications that run on a leadership supercomputer is one of the most important ways for planning its design, development and operation. In order to improve our understanding of HPC applications, user demands and resource usage characteristics, we perform correlative analysis of various logs for different subsystems of a leadership supercomputer. This analysis reveals surprising, sometimes counter-intuitive patterns, which, in some cases, conflicts with existing assumptions, and have important implications for future system designs as well as supercomputer operations. For example, our analysis shows that while the applications spend significant time on MPI, most applications spend very little time on file I/O. Combined analysis of hardware event logs and task failure logs show that the probability of a hardware FATAL event causing task failure is low. Combined analysis of control system logs and file I/O logs reveals that pure POSIX I/O is used more widely than higher level parallel I/O. Based on holistic insights of the application gained through combined and co-analysis of multiple logs from different perspectives and general intuition, we engineer features to "fingerprint" HPC applications. We use t-SNE (a machine learning technique for dimensionality reduction) to validate the explainability of our features and finally train machine learning models to identify HPC applications or group those with similar characteristic. To the best of our knowledge, this is the first work that combines logs on file I/O, computing, and inter-node communication for insightful analysis of HPC applications in production.
Liu, Zhengchun↗
Path Properties of Atmospheric Transitions: Illustration with a Low-Order Sudden Stratospheric Warming Model
Many rare weather events, including hurricanes, droughts, and floods, dramatically impact human life. To accurately forecast these events and characterize their climatology requires specialized mathematical techniques to fully leverage the limited data that are available. Here we describe transition path theory (TPT), a framework originally developed for molecular simulation, and argue that it is a useful paradigm for developing mechanistic understanding of rare climate events. TPT provides a method to calculate statistical properties of the paths into the event. As an initial demonstration of the utility of TPT, we analyze a low-order model of sudden stratospheric warming (SSW), a dramatic disturbance to the polar vortex that can induce extreme cold spells at the surface in the midlatitudes. SSW events pose a major challenge for seasonal weather prediction because of their rapid, complex onset and development. Climate models struggle to capture the long-term statistics of SSW, owing to their diversity and intermittent nature. We use a stochastically forced Holton–Mass-type model with two stable states, corresponding to radiative equilibrium and a vacillating SSW-like regime. In this stochastic bistable setting, from certain probabilistic forecasts TPT facilitates estimation of dominant transition pathways and return times of transitions. These “dynamical statistics” are obtained by solving partial differential equations in the model’s phase space. With future application to more complex models, TPT and its constituent quantities promise to improve the predictability of extreme weather events through both generation and principled evaluation of forecasts.
54 ENVIRONMENTAL SCIENCES↗
Enhancing high-fidelity nonlinear solver with reduced order model
Abstract We propose the use of reduced order modeling (ROM) to reduce the computational cost and improve the convergence rate of nonlinear solvers of full order models (FOM) for solving partial differential equations. In this study, a novel ROM-assisted approach is developed to improve the computational efficiency of FOM nonlinear solvers by using ROM’s prediction as an initial guess. We hypothesize that the nonlinear solver will take fewer steps to the converged solutions with an initial guess that is closer to the real solutions. To evaluate our approach, four physical problems with varying degrees of nonlinearity in flow and mechanics have been tested: Richards’ equation of water flow in heterogeneous porous media, a contact problem in a hyperelastic material, two-phase flow in layered porous media, and fracture propagation in a homogeneous material. Overall, our approach maintains the FOM’s accuracy while speeding up nonlinear solver by 18–73% (through suitable ROM-assisted FOMs). More importantly, the proximity of ROM’s prediction to the solution space leads to the improved convergence of FOMs that would have otherwise diverged with default initial guesses. We demonstrate that the ROM’s accuracy can impact the computational efficiency with more accurate ROM solutions, resulting in a better cost reduction. We also illustrate that this approach could be used in many FOM discretizations (e.g., finite volume, finite element, or a combination of those). Since our ROMs are data-driven and non-intrusive, the proposed procedure can easily lend itself to any nonlinear physics-based problem.
97 MATHEMATICS AND COMPUTING↗
A Solar Fuels Nexus: Molecules and Materials for Light-Driven Catalysis
The American Chemical Society (ACS) selects two groups of graduate students each year to plan and host a one-day symposium at each national meeting (both fall and spring).This year our Graduate Student Symposium Planning Committee (GSSPC), composed of seven students from four universities, proposal entitled “A Solar Fuels Nexus: Molecules and Materials for Light-Driven Catalysis” was selected for the “Crossroads in Chemistry” ACS Meeting that will take place March 23-26, 2023 in Indianapolis, IN. All members of our GSSPC are affiliated with the DOE Fuels from Sunlight Energy Innovation Hub, with two from the Liquid Sunlight Alliance (LiSA) and five from the Center for Hybrid Approaches in Solar Energy to Liquid Fuels (CHASE). Here we request funds to support this symposium. This symposium will highlight research progress and perspectives in the solar fuels generation field and seeks to advance the four priority research objectives (PROs) established by the Department of Energy’s Office of Basic Energy Sciences (DOE-BES) Roundtable Report that are also central to many research goals within LiSA and CHASE. The symposium will consist of research presentations from 10 invited senior researcher speakers on topics such as molecular catalyst design, computational modeling of electron transfer systems, microenvironmental effects on CO2 reduction and H2O oxidation catalysis, and intelligent design of semiconductor interfaces with ample time for discussions. These research topics fit very well with the Solar Photochemistry supported research areas of “light-driven electron and energy transfer in condensed phase and interfacial molecular systems,” “electrocatalysis and photocatalysis of solar fuels reactions,” and “semiconductor photoelectrochemistry.” More broadly, this symposium seeks to advance the DOE-BES’s mission to: “support fundamental research to understand, predict, and ultimately control matter and energy at the level of electrons, atoms, and molecules” by providing a diverse atmosphere where such research will be disseminated, discussed, and debated. There will be a strong focus on Diversity, Equity, and Inclusivity (DEI) in our symposium. Of our 10 speakers, 7 will be from underrepresented demographics in STEM, including 5 who identify as women. Furthermore, we have representatives from academia accompanied by one national lab scientist and one officer from the Office of Fossil Energy and Carbon Management at the DOE. All speakers will be holding a short DEI moment ahead of their talks. In order to support the career development of attending early career scientists, we will also be hosting a luncheon specifically for graduate students and postdocs to provide them opportunities to network with the distinguished speakers and other attendees. DOE funds for this symposium will be used to support the attendance and participation of 15 graduate students from US institutions by defraying travel and registration costs. These funds will promote engagement and conversation between early career scientists in the solar fuels field, while disseminating solar fuels research funded by and relevant to the DOE.
30 DIRECT ENERGY CONVERSION↗
Retrieving Top-k Hyperedge Triplets: Models and Applications
Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions can- not be faithfully modeled as collections of pairwise interactions using graphs and instead require hypergraphs. However, methods that analyze hypergraphs directly, rather than via lossy graph reductions, remain limited. Hypergraph motifs hold promise in this regard, as motif patterns serve as building blocks for larger group interactions which are inexpressible by graphs. Recent work has focused on categorizing and counting hypergraph motifs based on the existence of nodes in hyperedge intersection regions. Here, we argue that the relative sizes of hyperedge inter- sections within motifs contain varied and valuable information. We propose a suite of efficient algorithms for finding top-k triplets of hyperedges based on optimizing the sizes of these intersection patterns. This formulation uncovers interesting local patterns of interaction, finding hyperedge triplets that either (1) are the least similar with each other, (2) have the highest pairwise but not groupwise correlation, or (3) are the most similar with each other. We formalize this as a combinatorial optimization problem and design efficient algorithms based on filtering hyperedges. Our comprehensive experimental evaluation shows that the resulting hyperedge triplets yield insightful information on real-world hypergraphs. Our approach is also orders of magnitude faster than a naive baseline implementation.
hypergraphs, motifs, Combinatorial Algorithms↗
Cross phases of temperature-gradient-driven turbulence as a model basis for I -mode particle transport
As a model for understanding the type of transport behavior characteristic of the tokamak I mode, cross-phase physics for particle-transport is studied analytically for turbulence dominated by either ion-temperature-gradient (ITG) or electron-temperature-gradient (ETG) instability. I mode is a transport-barrier regime of reduced thermal transport but essentially unaffected particle transport. It is assumed that ITG turbulence applies to the baseline L mode, ETG to I mode, and that E × B flow shear is stronger in I mode, lowering all fluxes. In ITG turbulence, particle transport is governed by trapped electrons. Sensitivity to collisions produces the well-known temperature-gradient-driven pinch that offsets density-gradient-driven outward diffusion, weakening particle transport in L mode. In ETG turbulence, nonadiabatic ions are collisionless. Nonzero transport requires an ion spectrum feature whose magnetic-drift resonance supplies the necessary cross phase. If frequencies of order the ion diamagnetic drift frequency dominate the ion part of the spectrum, as would occur with weakly unstable ITG turbulence, all components of the particle transport are outward and can offset flow-shear-induced flux reductions to produce a flux that is similar to the ITG L-mode particle flux. Nonlinear frequencies are potentially relevant and discussed in relation to I mode.
Physics↗
Electrochemical Oxidation in Garnet-Type Solid Electrolyte by Formation of Point Defects
All-solid-state batteries hold greater promise for improving safety and energy density over conventional battery technology employing organic liquid electrolytes. One of the required features of a Li + conducting solid electrolyte is electrochemical stability, attained thermodynamically or kinetically, within the targeted operating voltage and temperature ranges. Therefore, understanding of the oxidative or reductive degradation mechanism is important to allow the design of stable solid electrolyte materials. This work contributes to building an understanding of the oxidative degradation mechanism in lithium solid electrolytes at cell operating conditions. Here, we have focused on resolving the oxidative decomposition mechanism of Al-doped lithium garnet Li 6.28 Al 0.24 La 3 Zr 2 O 12 (LLZO) as a state-of-the-art inorganic ceramic electrolyte. By combining experimental and computational analyses, we show that oxidation of LLZO occurs by simultaneous loss of oxygen and lithium from the structure, resulting in substoichiometric LLZO, at a moderate temperature (80 °C) and a high electrode potential (4.3 V vs Li/Li + ). Based on X-ray absorption and diffraction analyses, we find that the zirconium coordination shells in LLZO contract while the crystal structure experiences positive chemical strain upon electrochemical oxidation. The results from ex situ structural characterization of both the local structure and crystal symmetry are supported by a substoichiometric LLZO with lithium and oxygen vacancies, modeled by density functional theory (DFT) calculations. These chemical and structural changes in LLZO suppress effective lithium-ion conductivity by an order of magnitude. Formation of lithium and oxygen vacancies in LLZO upon electrochemical oxidation is different from prior thermodynamic predictions of phase decomposition of LLZO. The difference here is that the experiments were conducted at near-room temperature, which can hinder the kinetics of phase separation, and thus, the resultant LLZO solid electrolyte is still single-phase but substoichiometric in Li and O. In conclusion, these findings contribute an important degradation mechanism of the electrolyte, relevant for practical operational conditions of solid-state batteries.
36 MATERIALS SCIENCE↗
Spectroscopy and crystallography define carotenoid oxygenases as a new subclass of mononuclear non-heme Fe II enzymes
Carotenoid cleavage dioxygenases (CCDs) are non-heme Fe II enzymes that catalyze the oxidative cleavage of alkene bonds in carotenoids, stilbenoids, and related compounds. How these enzymes control the reaction of dioxygen (O 2 ) with their alkene substrates is unclear. Here, we apply spectroscopy in conjunction with X-ray crystallography to define the iron coordination geometry of a model CCD, CAO1 (Neurospora crassa carotenoid oxygenase 1), in its resting state and following substrate binding and coordination sphere substitutions. Resting CAO1 exhibits a five-coordinate (5C), square pyramidal Fe II center that undergoes steric distortion toward a trigonal bipyramidal geometry in the presence of piceatannol. Titrations with the O 2 -analog, nitric oxide, show a >100-fold increase in iron–nitric oxide affinity upon substrate binding, defining a crucial role for the substrate in activating the Fe II site for O 2 reactivity. The importance of the 5C Fe II structure for reactivity was probed through mutagenesis of the second-sphere Thr151 residue of CAO1, which occludes ligand binding at the sixth coordination position. A T151G substitution resulted in the conversion of the iron center to a six-coordinate state and a 135-fold reduction in apparent catalytic efficiency toward piceatannol compared with the wildtype enzyme. Substrate complexation resulted in partial six-coordinate to 5C conversion, indicating solvent dissociation from the iron center. Additional substitutions at this site demonstrated a general functional importance of the occluding residue within the CCD superfamily. Taken together, these data suggest an ordered mechanism of CCD catalysis occurring via substrate-promoted solvent replacement by O 2 . CCDs thus represent a new class of mononuclear non-heme Fe II enzymes.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Building Energy Codes and Grid-Interactive Efficient Buildings: How building energy codes can enable a more dynamic and energy-efficient built environment
This report considers the role of national model codes to promote grid-interactive efficient buildings (GEBs) as part of the modernization of the U.S. electricity grid. It introduces GEBs, describes their ability to support a clean, resilient grid, and considers challenges and approaches for incorporating GEB measures into national model energy codes and standards. Desirable traits of GEB include being low energy, low peaking, and responsive to grid needs, and minimizing the curtailment of renewable energy resources. In addition, the future grid incurs a time and locational value on these types of building services. Accounting for these considerations in future code development requires a continuation and expansion of code-minimum energy efficiency requirements and inclusion of demand responsive and load flexibility measures while ensuring annual use and cost reductions. Also, efforts to include GEB measures in codes will be limited until they are fully developed into an American National Standards Institute (ANSI)-approved standard. Then it would be straightforward to address GEB measures through points or packages and/or scoring requirements. Otherwise, the building code would have to describe each specific grid responsive strategy. This document reviews topics pertinent to considering codes in this context. Specifically, the study presents the status and direction of current building energy codes, the future smart grid, low-energy buildings, and grid-integrated buildings. The report concludes with recommendations for future code development activities to support low-energy, grid-interactive buildings in order to provide added value to building owners, the grid, and society.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Magnetic frame-dragging correction to the electromagnetic solution of a compact neutron star
ABSTRACT Neutron stars are usually modelled as spherical, rotating perfect conductors with a predominant intrinsic dipolar magnetic field anchored to their stellar crust. Due to their compactness, General Relativity corrections must be accounted for in Maxwell’s equations, leading to modified interior and exterior electromagnetic solutions. We present analytical solutions for slowly rotating magnetized neutron stars, taking into account the magnetic frame-dragging correction. For typical compactness values, i.e. Rs ∼ 0.5 [R*], we show that the new terms lead to a per cent order correction in the magnetic field orientation and strength compared to the case, with no magnetic frame-dragging correction. Also, we obtain a self-consistent redistribution of the surface azimuthal current. We verify the validity of the derived solution through two-dimensional particle-in-cell simulations of an isolated neutron star. Defining the azimuthal electric and magnetic field amplitudes during the transient phase as observables, we prove that the magnetic frame-dragging correction reduces the transient wave amplitude, as expected from the analytical solution. We show that simulations are more accurate and stable, when we include all first-order terms. The increased accuracy at lower spatiotemporal resolutions translates into a reduction in simulation runtimes.
Torres, R. (ORCID:0000000291820228)↗
Carbon Tetrachloride Degradation Results for 200-ZP-1 Operable Unit
Carbon tetrachloride (CT) contamination in the 200-ZP-1 Operable Unit (OU) at the Hanford Site originated from large-volume discharges to the subsurface during plutonium production operations between 1955 and 1973. Contamination migrated through more than 70 meters of unsaturated sediment to reach the underlying unconfined aquifer, where it persists as a large and complex groundwater plume. The 200-ZP-1 OU Record of Decision (ROD) requires that groundwater CT concentrations be reduced to 3.4 µg/L within 125 years. Current groundwater modeling projections estimate that the existing pump-and-treat, even when combined with monitored natural attenuation (specifically hydrolysis), will not achieve this target within the designated timeframe. A fundamental contributor to this shortfall is the extremely slow rate of CT hydrolysis under Hanford aquifer conditions, which has been estimated to have a half-life of 630 years. If faster-acting biotic and abiotic degradation processes are operating within the aquifer, their contribution to CT mass reduction could have a meaningful impact. However, site-specific measurements of these processes and their rates have not previously been performed. This report documents the results of a two-phase laboratory investigation designed to characterize and quantify the capacity of site-specific 200-ZP-1 OU sediments and groundwater to support natural attenuation of CT through biotic and abiotic pathways. In this context, degradation capacity is defined as the intrinsic potential of the subsurface matrix to transform CT under optimized, controlled conditions. System capacity is evaluated in two ways: (1) as rate-limited capacity, which establishes the maximum kinetic velocity of CT transformation and is measured using half-lives and first order rate constants; and (2) as mass limited capacity, which defines the total contaminant mass the batch experimental system can degrade before reactants are exhausted, representing the maximum amount of contaminant the microbial community and reactive mineral phases can transform under the experimental conditions.
abiotic degradation↗
Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes
Uncertainty propagation in complex engineering systems often poses significant computational challenges related to modeling and quantifying probability distributions of model outputs, as those emerge as the result of various sources of uncertainty that are inherent in the system under investigation. Gaussian Processes regression (GPs) is a robust meta-modeling technique that allows for fast model prediction and exploration of response surfaces. Multi-fidelity variations of GPs further leverage information from cheap and low fidelity model simulations in order to improve their predictive performance on the high fidelity model. In order to cope with the high volume of data required to train GPs in high dimensional design spaces, a common practice is to introduce latent design variables that are typically projections of the original input space to a lower dimensional subspace, and therefore substitute the problem of learning the initial high dimensional mapping, with that of training a GP on a low dimensional space. Here in this paper, we present a Bayesian approach to identify optimal transformations that map the input points to low dimensional latent variables. The \projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to be inferred jointly with the GP parameters, conditioned on the available training data. The proposed Bayesian inference scheme relies on a two-step iterative algorithm that samples from the marginal posteriors of the GP parameters and the projection matrix respectively, both using Markov Chain Monte Carlo (MCMC) sampling. In order to take into account the orthogonality constraints imposed on the orthonormal projection matrix, a Geodesic Monte Carlo sampling algorithm is employed, that is suitable for exploiting probability measures on manifolds. We extend the proposed framework to multi-fidelity models using GPs including the scenarios of training multiple outputs together. We validate our framework on three synthetic problems with a known lower-dimensional subspace. The benefits of our proposed framework, are illustrated on the computationally challenging aerodynamic optimization of a last-stage blade for an industrial gas turbine, where we study the effect of an 85-dimensional shape parameterization of a three-dimensional airfoil on two output quantities of interest, specifically on the aerodynamic efficiency and the degree of reaction
42 ENGINEERING↗
Symmetry instability induced by topological phase transitions
The symmetry-topology interplay dictates how to define order parameters and classify material ordered phases. However, current understanding of this interplay has been predominately approached from a one-sided perspective, with topological states being classified within the constraints imposed by specific fixed symmetries. Here, in this study, we complete this full circle by demonstrating spontaneous symmetry breaking that results from a periodic alteration of topological phases induced by light in a centrosymmetric Dirac material ZrTe 5 . The distinguishing feature is the observation of robust correlation and striking anomalies in the fluence and temperature dependence of key transport parameters. First, both shift current 𝐽 𝑠 and displacement current 𝐽 𝑑 , arising from interband transition and infrared phonon driving, respectively, along with charge carrier pumping, exhibit similar behaviors. Second, they all peak at similar low pump fluence, followed by a subsequent reduction as the fluence further increases. This behavior cannot be explained by conventional energetically allowed, direct excitations. Third, all the three observables exhibit anomalies when they approach the topological phase transition temperature. These results highlight the unique low-energy pumping behaviors in ZrTe 5 , characterized by reversible fluence dependence and a “hinge-like” interaction that connects various electronic and lattice observables, including phonons, charge carriers, and currents. Our findings, supported by model analysis, provide key insights into the fragility of crystalline (inversion) and time-reversal symmetries during the dynamics of topological phase transitions. This fragility drives spontaneous symmetry breaking, evidenced by the synchronized emergence of off-resonant infrared phonons and broken-symmetry photocurrents.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Deep nonparametric estimation of intrinsic data structures by chart autoencoders: Generalization error and robustness
Autoencoders have demonstrated remarkable success in learning low-dimensional latent features of high-dimensional data across various applications. Assuming that data are sampled near a low-dimensional manifold, we employ chart autoencoders, which encode data into low-dimensional latent features on a collection of charts, preserving the topology and geometry of the data manifold. Our paper establishes statistical guarantees on the generalization error of chart autoencoders, and we demonstrate their denoising capabilities by considering n noisy training samples, along with their noise-free counterparts, on a d-dimensional manifold. By training autoencoders, we show that chart autoencoders can effectively denoise the input data with normal noise. We prove that, under proper network architectures, chart autoencoders achieve a squared generalization error in the order of n–$\frac{2}{d+2}$log 4 n, which depends on the intrinsic dimension of the manifold and only weakly depends on the ambient dimension and noise level. We further extend our theory on data with noise containing both normal and tangential components, where chart autoencoders still exhibit a denoising effect for the normal component. As a special case, our theory also applies to classical autoencoders, as long as the data manifold has a global parametrization. Furthermore, our results provide a solid theoretical foundation for the effectiveness of autoencoders, which is further validated through several numerical experiments.
97 MATHEMATICS AND COMPUTING↗