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At least 937 records · Page 52

Nucleon Axial Radius and Muonic Hydrogen — A New Analysis and Review

Weak capture in muonic hydrogen (μH) as a probe of the chiral properties and nucleon structure predictions of quantum chromodynamics (QCD) is reviewed. A recent determination of the axial-vector charge radius squared, , from a model independent z expansion analysis of neutrino-nucleon scattering data is employed in conjunction with the MuCap measurement of the singlet muonic hydrogen capture rate, , to update the induced pseudoscalar nucleon coupling derived from experiment, and predicted by chiral perturbation theory. Accounting for correlated errors this implies , confirming theory at the 8% level. If instead, the predicted expression for is employed as input, then the capture rate alone determines , or together with the independent z expansion neutrino scattering result, a weighted average . Sources of theoretical uncertainty are critically examined and potential experimental improvements are described that can reduce the capture rate error by about a factor of 3. Muonic hydrogen can thus provide a precise and independent value which may be compared with other determinations, such as ongoing lattice gauge theory calculations. The importance of an improved determination for phenomenology is illustrated by considering the impact on critical neutrino-nucleus cross sections at neutrino oscillation experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The cosmological analysis of the SDSS/BOSS data from the Effective Field Theory of Large-Scale Structure

The Effective Field Theory of Large-Scale Structure is a formalism that allows us to predict the clustering of Cosmological Large-Scale Structure in the mildly non-linear regime in an accurate and reliable way. In this paper, after validating our technique against several sets of numerical simulations, we perform the analysis for the cosmological parameters of the DR12 BOSS data. We assume Λ CDM, a fixed value of the baryon/dark-matter ratio, Ω b /Ω c , and of the tilt of the primordial power spectrum, n s , and no significant input from numerical simulations. By using the one-loop power spectrum multipoles, we measure the primordial amplitude of the power spectrum, A s , the abundance of matter, Ω m , and the Hubble parameter, H 0 , {to about 13% , 3.2% and 3.2% respectively, obtaining ln (10 10 A s )=2.72± 0.13 , 0Ω m =0.309± 0.01 , H 0 =68.5± 2.2 km/(s Mpc) at 68% confidence level. If we then add a CMB prior on the sound horizon, the error bar on H 0 is reduced to 1.6% .} These results are a substantial qualitative and quantitative improvement with respect to former analyses, and suggest that the EFTofLSS is a powerful instrument to extract cosmological information from Large-Scale Structure.

79 ASTRONOMY AND ASTROPHYSICS↗

Active Compensation of Radiation Effects on Optical Fibers for Sensing Applications

Neutron and gamma irradiation is known to compact silica, resulting in macroscopic changes in refractive index (RI) and geometric structure. The change in RI and linear compaction in a radiation environment is caused by three well-known mechanisms: (i) radiation-induced attenuation (RIA), (ii) radiation-induced compaction (RIC), and (iii) radiation-induced emission (RIE). These macroscopic changes induce errors in monitoring physical parameters such as temperature, pressure, and strain in optical fiber-based sensors, which limit their application in radiation environments. We present a cascaded Fabry–Perot interferometer (FPI) technique to measure macroscopic properties, such as radiation-induced change in RI and length compaction in real time to actively account for sensor drift. The proposed cascaded FPI consists of two cavities: the first cavity is an air cavity, and the second is a silica cavity. The length compaction from the air cavity is used to deduce the RI change within the silica cavity. We utilize fast Fourier transform (FFT) algorithm and two bandpass filters for the signal extraction of each cavity. Inclusion of such a simple cascaded FPI structure will enable accurate determination of physical parameters under the test.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Component-wise reduced order model lattice-type structure design

Lattice-type structures can provide a combination of stiffness with light weight that is desirable in a variety of applications. Design optimization of these structures must rely on approximations of the governing physics to render solution of a mathematical model feasible. In this paper, we propose a topology optimization (TO) formulation that approximates the governing physics using component-wise reduced order modeling as introduced in Huynh et al. (2013); Eftang and Patera (2013), which can reduce solution time by multiple orders of magnitude over a full-order finite element model while providing a relative error in the solution of 1%. In addition, the offline training data set from such component-wise models is reusable, allowing its application to many design problems for only the cost of a single offline training phase, and the component-wise method is nearly embarrassingly parallel. We also show how the parameterization chosen in our optimization allows a simplification of the component-wise reduced order model (CWROM) not noted in previous literature, for further speedup of the optimization process. Furthermore, the sensitivity of the compliance with respect to the particular parameterization is derived solely at the component level. In numerical examples, we demonstrate a 1000x speedup over a full-order FEM model with relative error of 1% and show minimum compliance designs for two different cantilever beam examples, one smaller and one larger. Finally, error bounds for the displacement field, compliance, and compliance sensitivity of the CWROM are derived.

97 MATHEMATICS AND COMPUTING↗

Two-layer transient heat transfer using impulse response methods

Solutions to the inverse heat conduction problem (IHCP) are methods that can be used to quantify surface heat flux in multi-layer materials for components in which there are limited subsurface (internal) temperature measurements, such as coated components. A critical consideration is to capture high frequency fluctuations using a practical heat flux sensor. To that end, this paper highlights key parameters for calculating accurate surface heat transfer. Specifically, this research extends the available solutions to the IHCP for multi-substrate structures through an impulse response methodology. The sensitivity of the impulse method was quantified with respect to practical measurements. Further, when compared to the inverse case, the impulse method resulted in lower errors when calculating surface heat flux over a range of conditions. Overall, this work provides a foundation for deducing heat flux from a subsurface heat flux sensor while maintaining a high-frequency response.

42 ENGINEERING↗

A machine learning approach to quantify degradation of nuclear fuels and the effects of fission products

Nuclear fuel performance is critically dependent on understanding the evolution of fuel properties under operational conditions, a complex challenge driven by chemical changes and substantial radiation damage during fission. Traditionally, property evolution has been determined via empirical data collected following irradiation. However, these empirical correlations are limited in their applicability beyond the specific conditions in which they were obtained. This study explores a novel approach to address this challenge by applying materials informatics to develop a machine learning random forest (ML-RF) model that captures the effects of fission products on fuel compounds. The model predicts formation enthalpy (ΔH f ) by leveraging extensive quantum materials property data and correlating it with material descriptors such as composition, atomic and site features, and crystal lattice properties. This ML-RF model enables rapid interpolation across the compositional and structural spaces covered by the training data, thus supporting high-throughput screening and energetic ranking of candidate phases. The model demonstrates the ability to predict ΔH f with a mean absolute error (MAE) of approximately 0.1 to 0.2 eV/atom across a wide range of compounds, including key nuclear fuel systems (U-O, U-N, U-C, U-Si, and U-Mo). For example, it was used to assess shifts in stoichiometry for UO 2 (O/M) and UN (N/M) fuels, revealing their distinct tendencies in chemical potential variation and enabling preliminary convex hull analyses. Furthermore, the model provides insights into how individual fission products affect fuel properties. Results indicate that larger fission products (e.g., Nd, Pu, Ce) have a more pronounced impact on UO 2 , while lighter ones (e.g., Zr) strongly influence UN. Here, the model developed in this work can be used to support the Accelerated Fuel Qualification approach by facilitating preliminary evaluations prior to extensive materials modeling and experimentation. To this end, the trained model has been made available to the fuel community to support ongoing fuel development efforts.

Accelerated fuel qualification↗

S4: A spatial-spectral model for speckle suppression

High dynamic range imagers aim to block or eliminate light from a very bright primary star in order to make it possible to detect and measure far fainter companions; in real systems, a small fraction of the primary light is scattered, diffracted, and unocculted. We introduce S4, a flexible data-driven model for the unocculted (and highly speckled) light in the P1640 spectroscopic coronagraph. The model uses principal components analysis (PCA) to capture the spatial structure and wavelength dependence of the speckles, but not the signal produced by any companion. Consequently, the residual typically includes the companion signal. The companion can thus be found by filtering this error signal with a fixed companion model. The approach is sensitive to companions that are of the order of a percent of the brightness of the speckles, or up to 10{sup –7} times the brightness of the primary star. This outperforms existing methods by a factor of two to three and is close to the shot-noise physical limit.

79 ASTRONOMY AND ASTROPHYSICS↗

HORIZON RUN 3: TOPOLOGY AS A STANDARD RULER

We study the physically self-bound cold dark matter halo distribution, which we associate with the massive galaxies within Horizon Run 3, to estimate the accuracy of the determination of the cosmological distance scale measured by the topology analysis. We apply the routine '''Contour 3D''' to the 108 Mock Survey of π steradians out to redshift z = 0.6, which effectively corresponds to the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) survey, and compare the topology with that of a Gaussian random phase field. We find that given three separate smoothing lengths λ = 15, 21, and 34 h {sup –1} Mpc, the least χ{sup 2} fit genus per unit volume (g) yields a 1.7% fractional uncertainty in smoothing length and angular diameter distance to z = 0.6. This is an improvement on former calibrations and presents an error estimate competitive with baryon acoustic oscillation scale techniques. We also present three-dimensional graphics of the Horizon Run 3 spherical mock survey to show a wealth of large-scale structures of the universe that are expected for surveys like BOSS.

79 ASTRONOMY AND ASTROPHYSICS↗

Simulated rRNA/DNA Ratios Show Potential To Misclassify Active Populations as Dormant

ABSTRACT The use of rRNA/DNA ratios derived from surveys of rRNA sequences in RNA and DNA extracts is an appealing but poorly validated approach to infer the activity status of environmental microbes. To improve the interpretation of rRNA/DNA ratios, we performed simulations to investigate the effects of community structure, rRNA amplification, and sampling depth on the accuracy of rRNA/DNA ratios in classifying bacterial populations as “active” or “dormant.” Community structure was an insignificant factor. In contrast, the extent of rRNA amplification that occurs as cells transition from dormant to growing had a significant effect ( P < 0.0001) on classification accuracy, with misclassification errors ranging from 16 to 28%, depending on the rRNA amplification model. The error rate increased to 47% when communities included a mixture of rRNA amplification models, but most of the inflated error was false negatives (i.e., active populations misclassified as dormant). Sampling depth also affected error rates ( P < 0.001). Inadequate sampling depth produced various artifacts that are characteristic of rRNA/DNA ratios generated from real communities. These data show important constraints on the use of rRNA/DNA ratios to infer activity status. Whereas classification of populations as active based on rRNA/DNA ratios appears generally valid, classification of populations as dormant is potentially far less accurate. IMPORTANCE The rRNA/DNA ratio approach is appealing because it extracts an extra layer of information from high-throughput DNA sequencing data, offering a means to determine not only the seedbank of taxa present in communities but also the subset of taxa that are metabolically active. This study provides crucial insights into the use of rRNA/DNA ratios to infer the activity status of microbial taxa in complex communities. Our study shows that the approach may not be as robust as previously supposed, particularly in complex communities composed of populations employing different growth strategies, and identifies factors that inflate the erroneous classification of active populations as dormant.

59 BASIC BIOLOGICAL SCIENCES↗

A new approach for measuring the carbon and oxygen content of atmospherically relevant compounds and mixtures

Abstract. Due to its complexity, gas- and particle-phase organic carbon in the atmosphere is often classified by its bulk physicochemical properties. However, there is a dearth of robust, moderate-cost approaches to measure the bulk chemical composition of organic carbon in the atmosphere. This is particularly true for the degree of oxygenation, which critically affects the properties and impacts of organic carbon but for which routine measurement approaches are lacking. This gap has limited the understanding of a wide range of atmospheric components, including particulate matter, the mass of which is monitored worldwide due to its health and environmental effects but the chemical characterization of which requires relatively high capital costs and complex operation by highly trained technical personnel. In this work, we demonstrate a new approach to estimate the mass of carbon and oxygen in analytes and mixtures that relies only on robust, moderate-cost detectors designed for use with gas chromatography. Organic compounds entering a flame ionization detector were found to be converted with approximately complete efficiency to CO2, which was analyzed downstream using an infrared detector to measure the mass of carbon analyzed. The ratio of the flame ionization detector (FID) signal generated to CO2 formed (FID∕CO2) was shown to be strongly correlated (R2=0.89) to the oxygen-to-carbon ratio (O∕C) of the analyte. Furthermore, simple mixtures of analytes behaved as the weighted average of their components, indicating that this correlation extends to mixtures. These properties were also observed to correlate well with the sensitivity of the FID estimated by structure activity relationships (quantified as the relative effective carbon number). The relationships between measured FID∕CO2, analyte O∕C, and FID sensitivity allow the estimation of one property from another with <15 % error for mixtures and <20 % error for most individual analytes. The approach opens the possibility of field-deployable, autonomous measurement of the carbon and oxygen content of particulate matter using time-tested, low-maintenance detectors, though such an application would require some additional testing on complex mixtures. With some instrumental modifications, similar measurements on gas-phase species may be feasible. Moreover, the potential expansion to additional gas chromatography detectors may provide concurrent measurement of other elements (e.g., sulfur, nitrogen).

42 ENGINEERING↗

Data for: Climatic Imprint on Interfacially-Controlled Platinum-Palladium Resources

Data package for manuscript "Climatic Imprint on Interfacially-Controlled Platinum-Palladium Resources" by Emily G. Wright, Ivey Wang, Yihang Fang, Elaine D. Flynn, and Jeffrey G. Catalano. This dataset contains adsorption results from experiments designed to investigate the effect of chloride on Pd(II) adsorption to goethite and Pt(II) adsorption to hematite and goethite, including lab experiments, X-ray absorption fine structure spectroscopy, and models of retention within a laterite. See the associated manuscript for full methods information. The file "Wright2025_PtAds_data.csv" contains the target starting Pt concentration (uM), final aqueous Pt and associated error (in uM), calculated adsorbed Pt and associated error (in umol/m2), target and measured aqueous chloride (mM), target aqueous nitrate (mM), final pH, and mineral concentration/loading (g/L). Associated mineral-free controls (mineral loading = 0 g/L) are included; the aqueous Pd error was not calculated and chloride was not measured in every sample. These data appear in Figures 1, S3, S4, S5, S20, and S22 in the associated manuscript. The file "Wright2025_PdAds_data.csv" contains the target starting Pd concentration (uM), final aqueous Pd and associated error (in uM), calculated adsorbed Pd and associated error (in umol/m2), target and measured aqueous chloride (mM), and mineral concentration/loading (g/L). Associated mineral-free controls (mineral loading = 0 g/L) are included; the aqueous Pd error was not calculated and chloride was not measured in every sample. These data appear in Figures 1, S3, S4, S5, and S20 in the associated manuscript. The file "Wright2025_MineralBatches_data.csv" contains the mineral identity and BET specific surface area (m2/g) for every mineral batch synthesized and used in experiments. The annealing time used is listed for hydrothermally annealed goethite. These data appear in Table S2 in the associated manuscript. The file "Wright2025_XRD_data.csv" contains the XRD patterns for every mineral batch synthesized as the counts as a function of two theta (in degrees). See "Wright2025_MineralBatches_data.csv" for more details on specific mineral batches. These data appear in Figure S2 in the associated manuscript. The file "Wright 2025_ZetaPotential_data.csv" contains the measured zeta potentials for samples of goethite (batch G2) at pH 4 the presence of varying amounts of sodium chloride. These data appear in Table S3 in the associated manuscript. The file "Wright2025_XAFSSamples_data.csv" contains the specific mineral batch, measured final aqueous Pd or Pt (uM), measured final aqueous chloride (mM), and estimated adsorbed Pd or Pt (umol/m2) of all XAFS samples. These data appear in Tables S4, S7, S8, and S10 in the associated manuscript. The files "Wright2025_PdXAFS_data.csv" and "Wright2025_PtXAFS_data.csv" contain the normalized spectra of Pd and Pt, respectively, adsorbed to minerals at varying chloride concentrations. See "Wright2025_XAFSSamples_data.csv" for a guide to sample names. Note that "05" in a sample name is equivalent to "0.5". These data appear in Figures 2, S6, S7, S8, S12, S13, and S14 in the associated manuscript. The file "Wright2025_LateriteProfileProfileModelParameters_data.csv" include the ratio of hematite to hematite and goethite in two synthetic, modeled profiles, as well as the modeled surface areas of goethite and hematite as a function of relative depth within the modeled weathering zone. These data were used, in conjunction with equations presented in the paper, to calculate the theoretical concentrations of Pd and Pt (and the resulting Pt/Pd ratio) within the profiles. These data appear in Figure 3 in the associated manuscript. The file "Wright2025_Imagery_data.zip" is a zipped folder containing the TEM and STEM images appear in Figures S18 and S19. Individual files are labeled as either STEM (Fig. S18) or TEM (Fig. S19) with a letter representing the part of the multipart figure.

58 GEOSCIENCES↗

Bridging the time scale in exascale computing of chemical systems (Final Technical Report)

This report summarizes the work carried out with support of the United States Department of Energy under Award DE-SC0019441. The theme of this project was to develop and apply methods that allowed for the acceleration of atomistic calculations, particularly in challenging areas such as multiphase systems, electrified interfaces, uncertainty estimation, and applications requiring chemical accuracy, which tend to be applications where simulation time is severely bottlenecked by the computational time requirements. Much of the focus was on the application of emerging machine-learning methodologies, although a wide range of methodologies were employed. This report has two major sections. The first focuses on the methodological advances themselves. Within this part, we report a number of major advances, a few examples of which are described here. We report the first machine-learning scheme for the acceleration of electronically grand-canonical calculations (that is, those applicable to electrochemistry). We report new methods of performing transfer learning, in which physics-based priors can be used to provide predictions, often with uncertainty estimates, of images well outside of training sets; we also offer ways to fine-tune these transfer-learning models. We provide a new systematic means to generate and apply minimal training data sets to very large (10,000’s of atoms) systems, with only small training sets appropriate for electronic structure. We developed new methodologies to integrate surface vibrations into surface adsorption calculations. We made advances to the applicability of diffusion Monte Carlo methods to allow (learned) force prediction, finite-size error correction, and force-free means of searching for transition states. We integrated machine-learned atomistic predictions into mechanism generation codes. Additionally, we released new software including AmpTorch, a modernized version of our original atomistic machine-learning code Amp. The second part of this report focuses on the scientific applications that accompanied, and were often enabled by, the methodological advances described earlier. A few examples follow, but full details are in the individual chapters of the report. For example, we developed a general theory of phonon-induced friction on molecular adsorbates. We showed fundamentally how solvent influences the adsorption and desorption process and how it differs from the processes typically involved at the solid–gas interface, making aqueous-phase and electrocatalysis different from traditional thermocatalysis. We examined how metal–insulator and magnetic transitions can be probed, and accelerated exciton dynamics via Frenkel Hamiltonian parameters. We showed that the nearsighted force-training approach, developed within this project, can predict both the stability and reactivity of large nanoparticles, and can also lead to insights on catalyst coverage on binding energies and entropies. These applied studies, which generally integrated with our method development, allowed us to push forward the theoretical understanding of several reaction classes.

08 HYDROGEN↗

Dramatic changes in electronic structure revealed by fractionally charged nuclei

Discontinuous changes in the electronic structure upon infinitesimal changes to the Hamiltonian are demonstrated. These are revealed in one and two electron molecular systems by full configuration interaction (FCI) calculations when the realm of the nuclear charge is extended to be fractional. FCI electron densities in these systems show dramatic changes in real space and illustrate the transfer, hopping, and removal of electrons. This is due to the particle nature of electrons seen in stretched systems and is a manifestation of an energy derivative discontinuity at constant number of electrons. Dramatic errors of density functional theory densities are seen in real space as this physics is missing from currently used approximations. The movements of electrons in these simple systems encapsulate those in real physical processes, from chemical reactions to electron transport and pose a great challenge for the development of new electronic structure methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Flexible and Modular Simultaneous Modeling of Flow and Reactive Transport in Rivers and Hyporheic Zones

Investigations of coupled multiphysics processes in rivers and hyporheic zones have extensively used numerical models. Most existing models use a sequential, one-way coupling between the surface and subsurface domains. Such one-way coupling potentially introduces error. To overcome this, a fully coupled model, hyporheicFoam, was developed using the open-source computational platform OpenFOAM. It captures the coupled flow and multicomponent reactive transport processes within both surface and subsurface domains and across their interface. The coupling between two domains is implemented by mapping conservative flux boundary conditions at the interface through an iterative algorithm. Reactive transport is enabled by specifying a reaction network. To start, we have implemented reaction kinetics following the double Monod-type model with inhibition. The model capability is illustrated through modeling of both conservative and reactive hyporheic flow and transport through dune bedforms. With the novel coupled model, it is now possible to quantify reactions wherein the reactants and products are constantly exchanging between domains and have feedbacks. hyporheicFoam can simulate large, three-dimensional cases owing to the computational flexibility and power offered by the code structure and parallel design of OpenFOAM.

58 GEOSCIENCES↗

Unsupervised acoustic detection of fatigue-induced damage modes from wind turbine blades

This paper proposes a new in-situ damage detection approach for wind turbine blades, which leverages blade-internal non-stationary acoustic pressure fluctuations caused by the mechanical loading as the main source of excitation. This acoustic excitation was leveraged for the detection of fatigue-related damage modes on a full-scale wind turbine blade undergoing edgewise fatigue testing. An unsupervised, data-driven structural health monitoring strategy was developed to learn the normal cavity-internal acoustic sequences generated by the blade’s load cycles and to detect damage-related anomalies in the context of those sequences. A linear cepstral-coefficient based feature set was used to characterize the cavity-internal acoustics and LSTM-autoencoders were trained to accurately reconstruct healthy-case sequences. The reconstruction error was then used to characterize anomalous acoustic patterns within the blade cavity. The technique was able to detect a damage event earlier than a strain-based system by 120,000 load cycles.

17 WIND ENERGY↗

On the elimination of the electronic structure bottleneck in on the fly nonadiabatic dynamics for small to moderate sized (10-15 atom) molecules using fit diabatic representations based solely on ab initio electronic structure data: The photodissociation of phenol

In this work, we demonstrate that for moderate sized systems, here a system with 13 atoms, global coupled potential energy surfaces defined for several electronic states over a wide energy range and for distinct regions of nuclear coordinate space characterized by distinct electron configurations, can be constructed with precise energetics and an excellent description of non-adiabatic interactions in all regions. This is accomplished using a recently reported algorithm for constructing quasi-diabatic representations, H{sup d}, of adiabatic electronic states coupled by conical intersections. In this work, the algorithm is used to construct an H{sup d} to describe the photodissociation of phenol from its first and second excited electronic states. The representation treats all 33 internal degrees of freedom in an even handed manner. The ab initio adiabatic electronic structure data used to construct the fit are obtained exclusively from multireference configuration interaction with single and double excitation wave functions comprised of 88 × 10{sup 6} configuration state functions, at geometries determined by quasi-classical trajectories. Since the algorithm uses energy gradients and derivative couplings in addition to electronic energies to construct H{sup d}, data at only 7379 nuclear configurations are required to construct a representation, which describes all nuclear configurations involved in H atom photodissociation to produce the phenoxyl radical in its ground or first excited electronic state, with a mean unsigned energy error of 202.9 cm{sup −1} for electronic energies <60 000 cm{sup −1}.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Newly Characterized Region of CP190 Associates with Microtubules and Mediates Proper Spindle Morphology in Drosophila Stem Cells

CP190 is a large, multi-domain protein, first identified as a centrosome protein with oscillatory localization over the course of the cell cycle. During interphase it has a well-established role within the nucleus as a chromatin insulator. Upon nuclear envelope breakdown, there is a striking redistribution of CP190 to centrosomes and the mitotic spindle, in addition to the population at chromosomes. Here, we investigate CP190 in detail by performing domain analysis in cultured Drosophila S2 cells combined with protein structure determination by X-ray crystallography, in vitro biochemical characterization, and in vivo fixed and live imaging of cp190 mutant flies. Our analysis of CP190 identifies a novel N-terminal centrosome and microtubule (MT) targeting region, sufficient for spindle localization. This region consists of a highly conserved BTB domain and a linker region that serves as the MT binding domain. We present the 2.5 Å resolution structure of the CP190 N-terminal 126 amino acids, which adopts a canonical BTB domain fold and exists as a stable dimer in solution. The ability of the linker region to robustly localize to MTs requires BTB domain-mediated dimerization. Deletion of the linker region using CRISPR significantly alters spindle morphology and leads to DNA segregation errors in the developing Drosophila brain neuroblasts. Collectively, we highlight a multivalent MT-binding architecture in CP190, which confers distinct subcellular cytoskeletal localization and function during mitosis.

59 BASIC BIOLOGICAL SCIENCES↗

Generalization error guaranteed auto-encoder-based nonlinear model reduction for operator learning

Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this context, seeks to extract these physical processes from empirical data, which is challenging due to the infinite or high dimensionality of data. An integral component in addressing this challenge is model reduction, which reduces both the data dimensionality and problem size. In this paper, we utilize low-dimensional nonlinear structures in model reduction by investigating Auto-Encoder-based Neural Network (AENet). AENet first learns the latent variables of the input data and then learns the transformation from these latent variables to corresponding output data. Our numerical experiments validate the ability of AENet to accurately learn the solution operator of nonlinear partial differential equations. Furthermore, we establish a mathematical and statistical estimation theory that analyzes the generalization error of AENet. Finally, our theoretical framework shows that the sample complexity of training AENet is intricately tied to the intrinsic dimension of the modeled process, while also demonstrating the robustness of AENet to noise.

Auto-encoder↗