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At least 145 records · Page 8

Can protein expression be ‘solved’?

Recombinant protein expression is central to biotechnology’s application in academic exploration as well as human health, climate applications and the bioeconomy in general. However, not all proteins can be expressed in all organisms, and the field lacks a predictive model of soluble protein overexpression that could replace laborious experimental trial-and-error. Here, we discuss the state of the field and identify the lack of large, high-fidelity datasets as the primary bottleneck to progress. We review possible assays that could be used for data collection to identify a path toward an extensible experimental platform for collecting soluble recombinant protein overexpression data across organisms. We suggest that the resulting dataset should be used to train increasingly generalizable predictive models of protein expression to answer the question: “How can predictive protein expression be solved?”.

59 BASIC BIOLOGICAL SCIENCES↗

Generative modeling enables molecular structure retrieval from Coulomb explosion imaging

Capturing the structural changes that molecules undergo during chemical reactions in real space and time is a long-standing dream and an essential prerequisite for understanding and ultimately controlling femtochemistry. A key approach to tackle this challenging task is Coulomb explosion imaging, which benefited decisively from recently emerging high-repetition-rate X-ray free-electron laser sources. With this technique, information on the molecular structure is inferred from the momentum distributions of the ions produced by the rapid Coulomb explosion of molecules. Retrieving molecular structures from these distributions poses a highly non-linear inverse problem that remains unsolved for molecules consisting of more than a few atoms. Here, we address this challenge using a diffusion-based Transformer neural network. We show that the network reconstructs unknown molecular geometries from ion-momentum distributions with a mean absolute error below one Bohr radius, which is half the length of a typical chemical bond.

Artificial Intelligence (cs.AI)↗

Inferring building height from footprint morphology data

As cities continue to grow globally, characterizing the built environment is essential to understanding human populations, projecting energy usage, monitoring urban heat island impacts, preventing environmental degradation, and planning for urban development. Buildings are a key component of the built environment and there is currently a lack of data on building height at the global level. Current methodologies for developing building height models that utilize remote sensing are limited in scale due to the high cost of data acquisition. Other approaches that leverage 2D features are restricted based on the volume of ancillary data necessary to infer height. Here, we find, through a series of experiments covering 74.55 million buildings from the United States, France, and Germany, it is possible, with 95% accuracy, to infer building height within 3 m of the true height using footprint morphology data. Our results show that leveraging individual building footprints can lead to accurate building height predictions while not requiring ancillary data, thus making this method applicable wherever building footprints are available. The finding that it is possible to infer building height from footprint data alone provides researchers a new method to leverage in relation to various applications.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Foreword to special issue: Papers from the 63rd annual meeting of the APS Division of Plasma Physics, November 8–12, 2021

The 63rd annual meeting of the APS Division of Plasma Physics (DPP) was held on November 8–12, 2021 in Pittsburgh at the David Lawrence Convention Center with both a live (in person) component and a virtual component. Following guidance from an APS COVID task force, all in-person attendees were fully vaccinated and masked. More than 800 physicists attended, safely, in-person. With both virtual and on-site participants, discussions were lively, and the research presentations showed unmatched mastery in the modern observation, theory, simulation, and manipulation of plasma. The presentations included four invited review talks, 97 invited talks, four tutorials, and four presentations from this year's prize and award recipients. There were more than 1200 contributed poster presentations and 725 contributed oral presentations. Including both in-person and remote attendees, DPP 2021 had a record of 2232 participants. As a hybrid meeting, in-person presentations of all invited presentations were broadcast live and were accompanied by a Q&A discussion. Contributed oral and poster presentations were prerecorded along with options to schedule in-person discussions on demand. Five mini-conferences were held: “Gatekeeper Workshop: Creating a Diverse, Equitable, and Inclusive Pipeline,” “Collisionless Shocks in Laboratory and Space Plasmas,” “The High Repetition Rate Frontier in High-Energy-Density Physics,” “Measuring and Modeling Plasma Surface Interactions,” and “The Second Mini-Conference on Machine Learning, Data Science and Artificial Intelligence in Plasma Research.” Finally, on the day before the official start of the meeting, an afternoon “for students, by students” included lightning talks, plasma trivia, and an informal occasion to connect with other students, learn how to get the most from the DPP Annual Meeting, and share successful ways to connect with colleagues and advance their professional careers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Computational optimal transport for molecular spectra: The fully continuous case

Computational optimal transport is used to analyze the difference between pairs of continuous molecular spectra. It is demonstrated that transport distances which are derived from this approach may be a more appropriate measure of the difference between two continuous spectra than more familiar measures of distance under many common circumstances. Associated with the transport distances is the transport map which provides a detailed analysis of the difference between two molecular spectra and is a key component of our study of quantitative differences between two continuous spectra. The use of optimal transport for comparing molecular spectra is developed in detail here with a set of model spectra, so that the discussion is self-contained. The difference between the transport distance and more common definitions of distance is elucidated for some well-chosen examples and it is shown where transport distances may be very useful alternatives to standard definitions of distance. The transport distance between a theoretical and experimental electronic absorption spectrum for SO 2 is studied and it is shown how the theoretical spectrum can be modified to fit the experimental spectrum better adjusting the theoretical band origin and the resolution of the theoretical spectrum. In conclusion, this analysis includes the calculation of transport maps between the theoretical and experimental spectra suggesting future applications of the methodology.

74 ATOMIC AND MOLECULAR PHYSICS↗

2025 Peregrine in-situ monitoring and training dataset for laser powder bed fusion and binder jet printers

Peregrine, a software tool developed at Oak Ridge National Laboratory (ORNL), was used to collect and analyze in-situ monitoring (ISM) data from a Concept Laser M2 (Colibrium Additive) laser powder bed fusion (L-PBF) printer and an ExOne Innovent (Desktop Metal) binder jet printer. Data for four builds (print jobs) were saved to HDF5 (high performance data) files for release. Additionally, process anomalies were annotated by the authors across 37 image stacks (i.e., print layers) and are also provided as HDF5 files.

36 MATERIALS SCIENCE↗

On the frontiers of coupled extreme environments

Coupled extreme environments pose among the highest demands on materials, stressing the limits of temperature, pressure, electric and magnetic fields, atomic displacement rates, and chemical potentials that can be simultaneously sustained. Here, this issue highlights exciting new materials science methods that will enable rapid progress in what has traditionally been the most difficult materials arena. New opportunities in artificial intelligence, multi-physics simulations capabilities, the use of extreme conditions to synthesize novel materials, and our ability to interrogate materials under relevant conditions provide new avenues to understand and design new materials.

36 MATERIALS SCIENCE↗

Kimberlina 1.2 CCUS Geophysical Models and Synthetic Data Sets

This synthetic multi-scale and multi-physics data set was produced in collaboration with teams at the Lawrence Berkeley National Laboratory, National Energy Technology Laboratory, Los Alamos National Laboratory, and Colorado School of Mines through the Science-informed Machine Learning for Accelerating Real-Time Decisions in Subsurface Applications (SMART) Initiative. Data are associated with the following publication: Alumbaugh, D., Gasperikova, E., Crandall, D., Commer, M., Feng, S., Harbert, W., Li, Y., Lin, Y., and Samarasinghe, S., “The Kimberlina Synthetic Geophysical Model and Data Set for CO2 Monitoring Investigations”, The Geoscience Data Journal, 2023, DOI: 10.1002/gdj3.191. The dataset uses the Kimberlina 1.2 CO2 reservoir flow model simulations based on a hypothetical CO2 storage site in California (Birkholzer et al., 2011; Wainwright et al., 2013). Geophysical properties models (P- and S-wave seismic velocities, saturated density, and electrical resistivity) were produced with an approach similar to that of Yang et al. (2019) and Gasperikova et al. (2022) for 100 Kimberlina 1.2 reservoir models. Links to individual resources are provided below: [CO2 Saturation Models](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-co2-saturation-models); Resistivity Models – [part 1](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-resistivity-models-part-1), [part 2](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-resistivity-models-part-2), and [part 3](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-resistivity-models-part-3); [Vp Velocity Models](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-vp-velocity-models); [Vs Velocity Models](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-vs-velocity-models); [Density Models](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-density-models). The 3D distributions of geophysical properties for the 33 time stamps of the SIM001 model were used to generate synthetic seismic, gravity, and electromagnetic (EM) responses for 33 times between zero and 200 years. Synthetic surface seismic data were generated using 2D and 3D finite-difference codes that simulate the acoustic wave equation (Moczo et al., 2007). 2D data were simulated for six point-pressure sources along a 2D line with 10 m receiver spacing and a time spacing of 0.0005 s. 3D simulations were completed for 25 surface pressure sources using a source separation of 1 km in both the x and y directions and a time spacing of 0.001 s. Links to individual resources are provided below: [2D velocity models](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-2d-velocity-models) and [2D surface seismic data](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-2d-surface-seismic-data). [3D velocity models](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-velocity-models), and 3D seismic data [year0](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year0), [year1](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year1), [year2](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year2), [year5](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year5), [year10](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year10), [year15](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year15), [year20](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year20), [year25](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year25), [year30](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year30), [year35](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year35), [year40](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year40), [year45](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year45), [year49](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year49), [year50](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year50), [year51](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year51), [year52](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year52), [year55](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year55), [year60](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year60), [year65](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year65), [year70](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year70), [year75](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year75), [year80](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year80), [year85](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year85), [year90](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year90), [year95](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year95), [year100](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year100), [year110](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year110), [year120](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year120), [year130](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year130), [year140](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year140), [year150](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year150), [year175](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year175), [year200](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year200). The Python scripts to read these models and data are provided [here](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-python-scripts). EM simulations used a borehole-to-surface survey configuration, with the source located near the reservoir level and receivers on the surface using the code developed by Commer and Newman (2008). Pseudo-2D data for the source at [2500 m](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-pseudo-2d-csem-data-tz2500m) and [3025 m](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-pseudo-2d-csem-data-tz3025m), used a 2D inline receiver configuration to simulate a response over 3D resistivity models. The [3D data](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-csem-data) contain electric fields generated by borehole sources at monitoring well locations and measured over a surface receiver grid. Vector gravity data, both on the surface and in boreholes, were simulated using a modeling code developed by Rim and Li (2015). The simulation scenarios were parallel to those used for the EM: [pseudo-2D data](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-gravity-data) were calculated along the same lines and within the same boreholes, and [3D data](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-gravity-data) were simulated over 3D models on the surface and in three monitoring wells. A series of [synthetic well logs](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-well-logs) of CO2 saturation, acoustic velocity, density, and induction resistivity in the injection well and three monitoring wells are also provided at 0, 1, 2, 5, 10, 15, and 20 years after the initiation of injection. These were constructed by combining the low-frequency trend of the geophysical models with the high-frequency variations of actual well logs collected in the Kimberlina 1 well that was drilled at the proposed site. Measurements of permeability and pore connectivity were made on cores of Vedder Sandstone, which forms the primary reservoir unit: [CT micro scans](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-ct-micro-scans-of-vedder-formation) and [Industrial CT Images](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-industrial-ct-images-vedder-formation). These measurements provide the range of scales in the otherwise synthetic data set to be as close to a real-world situation as possible. References: Birkholzer, J.T., Zhou, Q., Cortis, A. and Finsterle, S., 2011. A sensitivity study on regional pressure buildup from large-scale CO2 storage projects. Energy Procedia, 4, 4371-4378. Commer, M., and Newman, G.A., 2008. New advances in three-dimensional controlled-source electromagnetic inversion, Geophysical Journal International, 172, 513-535. Gasperikova, E., Appriou, D., Bonneville, A., Feng, Z., Huang, L., Gao, K., Yang, X., Daley, T., 2022, Sensitivity of geophysical techniques for monitoring secondary CO2 storage plumes, Int. J. Greenh. Gas Control, Volume 114, 103585, ISSN 1750-5836, https://doi.org/10.1016/j.ijggc.2022.103585. Moczo, P., J.O. Robertsson and L. Eisner, 2007, The finite-difference time-domain method for modeling of seismic wave propagation: Advances in geophysics, 48, 421-516. Rim, H., and Y. Li, 2015, Advantages of borehole vector gravity in density imaging, Geophysics, 80, G1-G13. Wainwright, H. M.; Finsterle, S.; Zhou, Q.; Birkholzer, J. T., 2013. Modeling the Performance of Large-Scale CO2 Storage Systems: A Comparison of Different Sensitivity Analysis Methods. International Journal of Greenhouse Gas Control, 17, 189205. https://doi.org/10.1016/j.ijggc.2013.05.007, DOI: 10.18141/1603331. Yang, X., Buscheck, T.A., Mansoor, K., Wang, Z., Gao, K., Huang, L., Appriou, D., and Carroll, S.A., 2019. Assessment of geophysical monitoring methods for detection of brine and CO2 leakage in drinking water aquifers, International Journal of Greenhouse Gas Control, 90, 102803, https://doi.org/10.1016/j.ijggc.2019.102803.

CCUS↗

Opportunities and Challenges from Artificial Intelligence and Machine Learning for the Advancement of Science, Technology, and the Office of Science Missions

In February 2019, the President signed Executive Order 13859, Maintaining American Leadership in Artificial Intelligence. This order launched the American Artificial Intelligence Initiative, a concerted effort to promote and protect AI technology and innovation in the United States. The Initiative implements a government-wide strategy in collaboration and engagement with the private sector, academia, the public, and like-minded international partners. Among other actions, key directives in the Initiative called for Federal agencies to: Prioritize AI research and development investments, Enhance access to high-quality cyberinfrastructure and data, Ensure that the US maintains an international leadership role in the development of technical standards for AI, and Provide education and training opportunities to prepare the American workforce for the new era of AI. The mission of the Department of Energy (DOE) is to ensure America’s security and prosperity by addressing its energy, environmental, and nuclear challenges through transformative science and technology solutions. In terms of Science and Innovation, the DOE’s mission is to maintain a vibrant US effort in science and engineering as a cornerstone of our economic prosperity with clear leadership in strategic areas. From July to October in 2019, the Argonne, Oak Ridge, and Berkeley National Laboratories hosted a series of four AI for Science Town Hall meetings in Chicago, Oak Ridge, Berkeley, and Washington DC. The four meetings were attended by over 1300 scientists from the 17 DOE Labs, 39 companies, and over 90 universities. The goal of the Town Hall series was ‘to examine scientific opportunities in the areas of artificial intelligence, Big Data, and high-performance computing (HPC) in the next decade, and to capture the big ideas, grand challenges, and next steps to realizing these.’ The discussions at the meetings were captured in the final report of the AI for Science Town Hall meetings.

42 ENGINEERING↗

HFTS-1 Natural Joint Data and Engineering Summary

This report provides an analysis of engineering and geologic data collected from the Hydraulic Fracturing Test Site #1 (HTSF-1) project in the southern Midland Basin, Reagan County, Texas. The site is being studied as part of the Science-informed Machine Learning for Accelerating Real-Time Decisions in Subsurface Applications (SMART) Initiative at the National Energy Technology Laboratory (NETL). The data collected is intended to provide a basis of understanding of the site and to construct simulation models. This report provides a summary analysis of the engineering and geologic data collected from the project to provide a basis of understanding of the site and to construct simulation models. The report examines various possible correlations in engineering properties based on natural fracture data from the program, which consisted of 11 horizontal wells, one vertical well, and one slant well. The horizontal wells are in two horizons: 1) Upper and 2) Middle Wolfcamp formations. Program data include: fracture frequency and fracture orientation data from four core runs in a slant well; fracture spacing and orientation from a vertical pilot well; laboratory triaxial testing and mineralogical determinations; and porosity results from magnetic resonance analyses from various wells, together with observations based on the data collection. In addition, available references were reviewed on the site for additional insights. As the focus of the report is on the natural system, hydraulic fracture data from the site were not examined in detail in this report. Data variability is the chief observation in examination of the database. Fracture frequency in the slant well can range from sections with values as high as five fractures per ft to sections up to 100+ ft in length with no natural observed fractures. Fracture spacing across is typically less than 10 ft, but can range up to hundreds of feet. Apparent fracturing shows the trends in two predominate orientations, E-SW and WNW-ESE, but minor variations exist. The rock units vary across the site from siliceous mudstones to calcareous mudstones, showing a general layering with depth. The laboratory properties such as strength and modulus show no apparent trend with depth, but appear to correlate with rock mineralogy with high strength and modulus values where calcium content is high. In addition, an attempt to examine variability and mineralogy on a larger scale was made using a color-coded system based on gamma ray measurements. A staged colored approach was adopted, presuming that lower gamma ray values indicate higher value of calcium content (blue scale) and that higher gamma ray values indicate higher clay mineral content (orange scale). As provided in report appendices, the system correlated well with visual examination of the slant core and the petrofabric analyses of the vertical pilot well. The results showed large variability in mineral content along the horizontal plane across the site. The change in mineral content was also rapid, on a scale less than that of the average hydraulic fracture stage length of about 180 ft.

42 ENGINEERING↗

Overview of SMART Initiative

The objective of the SMART Initiative, i.e., Science-informed Machine Learning (ML) for Accelerating Real-Time Decisions in Subsurface Applications, is to show how the utilization of ML can significantly improve efficiency and effectiveness of field-scale commercial carbon storage operations in three main areas: real-time visualization, virtual learning, and real-time forecasting. This presentation reports the status of SMART initiative for demonstrating: (a) virtual learning during the pre-injection permitting phase, and (b) ML-assisted operational decision making and visualization.

Siriwardane, Hema↗

Deep nonparametric estimation of operators between infinite dimensional spaces

Learning operators between infinitely dimensional spaces is an important learning task arising in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class. Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation. Our assumptions cover most scenarios in real applications and our results give rise to fast rates by exploiting low dimensional structures of data in operator estimation. We also investigate the influence of network structures (e.g., network width, depth, and sparsity) on the generalization error of the neural network estimator and propose a general suggestion on the choice of network structures to maximize the learning efficiency quantitatively.

97 MATHEMATICS AND COMPUTING↗

Uncertainty Quantification via Stable Distribution Propagation

We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU non-linearity. This allows propagating Gaussian and Cauchy input uncertainties through neural networks to quantify their output uncertainties. To demonstrate the utility of propagating distributions, we apply the proposed method to predicting calibrated confidence intervals and selective prediction on out-of-distribution data. The results demonstrate a broad applicability of propagating distributions and show the advantages of our method over other approaches such as moment matching.

Artificial Intelligence (cs.AI)↗