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At least 1,117 records · Page 62

Solving high-dimensional partial differential equations using deep learning

Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the “curse of dimensionality.” This paper introduces a deep learning-based approach that can handle general high-dimensional parabolic PDEs. To this end, the PDEs are reformulated using backward stochastic differential equations and the gradient of the unknown solution is approximated by neural networks, very much in the spirit of deep reinforcement learning with the gradient acting as the policy function. Numerical results on examples including the nonlinear Black–Scholes equation, the Hamilton–Jacobi–Bellman equation, and the Allen–Cahn equation suggest that the proposed algorithm is quite effective in high dimensions, in terms of both accuracy and cost. Furthermore, this opens up possibilities in economics, finance, operational research, and physics, by considering all participating agents, assets, resources, or particles together at the same time, instead of making ad hoc assumptions on their interrelationships.

97 MATHEMATICS AND COMPUTING↗

Depth of nutrient uptake by deep-rooted plants is regulated by water availability

The capacity of some plants to access water and nutrients at depths greater than one meter is a critical functional trait that confers resistance to drought and impacts both belowground and shallow soil processes. Here, we report water and strontium isotopic data from an alpine meadow transect showing the correlation between water and nutrient acquisition depths. The isotopic compositions of Sr ( 87 Sr/ 86 Sr ratio) and water in rock and soil, and in plant leaf tissues, reveal that deeper-rooted plants acquire a higher proportion of water, Sr, and cation nutrients that are derived from the saprolite, a zone of silicate weathering, than shallow-rooted grass. A three-decade dendrochemical record reveals that reductions of wet precipitation drive deep-rooted plants to acquire cation nutrients from deeper saprolite or bedrock regions. Thus, the depth of cation nutrient acquisition by deep-rooted plant species at this site is tightly coupled with, and likely determined by, water availability in soil, saprolite, and bedrock. The enhanced uptake of cations as well as water from deeper saprolite zones could impact the rate of bedrock weathering and watershed chemistry during drought.

biogeochemistry↗

Reynolds-Averaged Turbulence Modeling Using Deep Learning with Local Flow Features: An Empirical Approach

Reynolds-Averaged Navier-Stoke (RANS) models offer an alternative avenue in predicting flow characteristics when the corresponding experiments are difficult to achieve due to geometry complexity, limited budget, or knowledge. RANS models require the knowledge of subgrid scale physics to solve conservation equations for mass, energy, and momentum. Mechanistic turbulence models, such as k-epsilon, are generally evaluated and calibrated for specific flow conditions with various degrees of uncertainty. These models have limited capability to assimilate a substantial amount of data due to model form constraints. Meanwhile, deep learning (DL) has been proven to be universal approximators with the potential to assimilate available, relevant, and adequately evaluated data. Moreover, deep neural networks (DNNs) can create surrogate models without knowing function forms. Such a data-driven approach can be used in updating fluid models based on observations as opposed to hard-wiring models with precalibrated correlations. The paper presents progress in applying DNNs to model Reynolds stress using two machine learning (ML) frameworks. A novel flow feature coverage mapping is proposed to quantify the physics coverage of DL-based closures. It can be used to examine the sufficiency of training data and input flow features for data-driven turbulence models. The case of a backward-facing step is formulated to demonstrate that not only can DNNs discover underlying correlation behind fluid data but also they can be implemented in RANS to predict flow characteristics without numerical stability issues. Finally, the presented research is a crucial stepping-stone toward the data-driven turbulence modeling, which potentially benefits the design of data-driven experiments that can be used to validate fluid models with ML-based fluid closures.

42 ENGINEERING↗

Popnet : computer vision based deep learning model for forecasting gridded population

Here, this study introduces Popnet, a deep learning model for forecasting 1 km-gridded populations, integrating U-Net, ConvLSTM, a Spatial Autocorrelation module and deep ensemble methods. Using spatial variables and population data from 2000 to 2020, Popnet predicts South Korea’s population trends by age groups (under 14, 15-64 and over 65) up to 2040. In validation, it outperforms traditional machine learning and state-of-the-art computer vision models. The output of this model discovered significant polarisation: population growth in urban areas, especially the capital region, and severe depopulation in rural areas. Popnet is a robust tool for offering significant insights to policymakers and related stakeholders about the detailed future population, which allows them to establish detailed, localised planning and resource allocations.

computer vision↗

Alpert multi-wavelets for functional inverse problems: direct optimization and deep learning

Computational engineering models often contain unknown entities (e.g. parameters, initial and boundary conditions) that require estimation from other measured observable data. Estimating such unknown entities is challenging when they involve spatio-temporal fields because such functional variables often require an infinite-dimensional representation. Here, we address this problem by transforming an unknown functional field using Alpert wavelet bases and truncating the resulting spectrum. Hence the problem reduces to the estimation of few coefficients that can be performed using common optimization methods. We apply this method on a one-dimensional heat transfer problem where we estimate the heat source field varying in both time and space. The observable data is comprised of temperature measured at several thermocouples in the domain. This latter is composed of either copper or stainless steel. The optimization using our method based on wavelets is able to estimate the heat source with an error between 5% and 7%. We analyze the effect of the domain material and number of thermocouples as well as the sensitivity to the initial guess of the heat source. Finally, we estimate the unknown heat source using a different approach based on deep learning techniques where we consider the input and output of a multi-layer perceptron in wavelet form. We find that this deep learning approach is more accurate than the optimization approach with errors below 4%.

97 MATHEMATICS AND COMPUTING↗

Image-based novel fault detection with deep learning classifiers using hierarchical labels

One important characteristic of modern fault classification systems is the ability to flag the system when faced with previously unseen fault types. This work considers the unknown fault detection capabilities of deep neural network-based fault classifiers. Specifically, we propose a methodology on how, when available, labels regarding the fault taxonomy can be used to increase unknown fault detection performance without sacrificing model performance. To achieve this, we propose to utilize soft label techniques to improve the state-of-the-art deep novel fault detection techniques during the training process and novel hierarchically consistent detection statistics for online novel fault detection. Lastly, we demonstrated increased detection performance on novel fault detection in inspection images from the hot steel rolling process, with results well replicated across multiple scenarios and baseline detection methods.

42 ENGINEERING↗

Tracking atomic structure evolution during directed electron beam induced Si-atom motion in graphene via deep machine learning

Using electron beam manipulation, we enable deterministic motion of individual Si atoms in graphene along predefined trajectories. Structural evolution during the dopant motion was explored, providing information on changes of the Si atom neighborhood during atomic motion and providing statistical information of possible defect configurations. The combination of a Gaussian mixture model and principal component analysis applied to the deep learning-processed experimental data allowed disentangling of the atomic distortions for two different graphene sublattices. This approach demonstrates the potential of e-beam manipulation to create defect libraries of multiple realizations of the same defect and explore the potential of symmetry breaking physics. The rapid image analytics enabled via a deep learning network further empowers instrumentation for e-beam controlled atom-by-atom fabrication. Here, the analysis described in the paper can be reproduced via an interactive Jupyter notebook at https://git.io/JJ3Bx.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optical characterization of deep-level defects in n-type Al x In y Ga 1- x - y P for the development of solid-state photomultiplier analogs

Characterizing intrinsic defects is an essential step in evaluating materials for novel optoelectronic device applications. For photomultipliers, suppressing dark currents is critical, but a tradeoff is present between maximizing the band gap while remaining sensitive to the wavelength of interest and minimizing the incorporation of fresh defects by growing not-yet-optimized alloys. We present a series of capacitance-based measurements, including deep-level optical spectroscopy, steady-state photocapacitance, and illuminated capacitance-voltage, on photodiodes with lightly n-type Al x In y Ga 1−x−y P absorber regions. Several deep levels are identified, including one near the midgap. Although the inclusion of aluminum increases each trap density by approximately 10×, the hole capture cross-section also appears to decrease, suggesting that Shockley–Read–Hall dark currents may be suppressed. These materials may be good candidates for the development into silicon photomultiplier analogs with a wider bandgap for scintillator applications.

III–V↗

Augmented signal processing in Liquid Argon Time Projection Chambers with a deep neural network

The Liquid Argon Time Projection Chamber (LArTPC) is an advanced neutrino detector technology widely used in recent and upcoming accelerator neutrino experiments. It features a low energy threshold and high spatial resolution that allow for comprehensive reconstruction of event topologies. In current-generation LArTPCs, the recorded data consist of digitized waveforms on wires produced by induced signal on wires of drifting ionization electrons, which can also be viewed as two-dimensional (2D) (time versus wire) projection images of charged-particle trajectories. For such an imaging detector, one critical step is the signal processing that reconstructs the original charge projections from the recorded 2D images. For the first time, we introduce a deep neural network in LArTPC signal processing to improve the signal region of interest detection. By combining domain knowledge (e.g., matching information from multiple wire planes) and deep learning, this method shows significant improvements over traditional methods. This work details the method, software tools, and performance evaluated with realistic detector simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

GPU coprocessors as a service for deep learning inference in high energy physics

In the next decade, the demands for computing in large scientific experiments are expected to grow tremendously. During the same time period, CPU performance increases will be limited. At the CERN Large Hadron Collider (LHC), these two issues will confront one another as the collider is upgraded for high luminosity running. Alternative processors such as graphics processing units (GPUs) can resolve this confrontation provided that algorithms can be sufficiently accelerated. In many cases, algorithmic speedups are found to be largest through the adoption of deep learning algorithms. We present a comprehensive exploration of the use of GPU-based hardware acceleration for deep learning inference within the data reconstruction workflow of high energy physics. We present several realistic examples and discuss a strategy for the seamless integration of coprocessors so that the LHC can maintain, if not exceed, its current performance throughout its running.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Statistically-informed deep learning for gravitational wave parameter estimation

We introduce deep learning models to estimate the masses of the binary components of black hole mergers, $(m_1,m_2)$, and three astrophysical properties of the post-merger compact remnant, namely, the final spin, $a_\mathrm f$, and the frequency and damping time of the ringdown oscillations of the fundamental $\ell = m = 2$ bar mode, $(\omega_\mathrm R, \omega_\mathrm I)$. Our neural networks combine a modified WaveNet architecture with contrastive learning and normalizing flow. We validate these models against a Gaussian conjugate prior family whose posterior distribution is described by a closed analytical expression. Upon confirming that our models produce statistically consistent results, we used them to estimate the astrophysical parameters $(m_1,m_2, a_\mathrm f, \omega_\mathrm R, \omega_\mathrm I)$ of five binary black holes: GW150914, GW170104, GW170814, GW190521 and GW190630. We use PyCBC Inference to directly compare traditional Bayesian methodologies for parameter estimation with our deep learning based posterior distributions. Our results show that our neural network models predict posterior distributions that encode physical correlations, and that our data-driven median results and 90% confidence intervals are similar to those produced with gravitational wave Bayesian analyses. This methodology requires a single V100 NVIDIA GPU to produce median values and posterior distributions within two milliseconds for each event. Furthermore, this neural network, and a tutorial for its use, are available at the Data and Learning Hub for Science.

79 ASTRONOMY AND ASTROPHYSICS↗

Deep kernel methods learn better: from cards to process optimization

Abstract The ability of deep learning methods to perform classification and regression tasks relies heavily on their capacity to uncover manifolds in high-dimensional data spaces and project them into low-dimensional representation spaces. In this study, we investigate the structure and character of the manifolds generated by classical variational autoencoder (VAE) approaches and deep kernel learning (DKL). In the former case, the structure of the latent space is determined by the properties of the input data alone, while in the latter, the latent manifold forms as a result of an active learning process that balances the data distribution and target functionalities. We show that DKL with active learning can produce a more compact and smooth latent space which is more conducive to optimization compared to previously reported methods, such as the VAE. We demonstrate this behavior using a simple cards dataset and extend it to the optimization of domain-generated trajectories in physical systems. Our findings suggest that latent manifolds constructed through active learning have a more beneficial structure for optimization problems, especially in feature-rich target-poor scenarios that are common in domain sciences, such as materials synthesis, energy storage, and molecular discovery. The Jupyter Notebooks that encapsulate the complete analysis accompany the article.

97 MATHEMATICS AND COMPUTING↗

Integrating AlphaFold and deep learning for atomistic interpretation of cryo-EM maps

Abstract Interpretation of cryo-electron microscopy (cryo-EM) maps requires building and fitting 3D atomic models of biological molecules. AlphaFold-predicted models generate initial 3D coordinates; however, model inaccuracy and conformational heterogeneity often necessitate labor-intensive manual model building and fitting into cryo-EM maps. In this work, we designed a protein model-building workflow, which combines a deep-learning cryo-EM map feature enhancement tool, CryoFEM (Cryo-EM Feature Enhancement Model) and AlphaFold. A benchmark test using 36 cryo-EM maps shows that CryoFEM achieves state-of-the-art performance in optimizing the Fourier Shell Correlations between the maps and the ground truth models. Furthermore, in a subset of 17 datasets where the initial AlphaFold predictions are less accurate, the workflow significantly improves their model accuracy. Our work demonstrates that the integration of modern deep learning image enhancement and AlphaFold may lead to automated model building and fitting for the atomistic interpretation of cryo-EM maps.

59 BASIC BIOLOGICAL SCIENCES↗

A deep learning approach to identify missing is-a relations in SNOMED CT

Abstract Objective SNOMED CT is the largest clinical terminology worldwide. Quality assurance of SNOMED CT is of utmost importance to ensure that it provides accurate domain knowledge to various SNOMED CT-based applications. In this work, we introduce a deep learning-based approach to uncover missing is-a relations in SNOMED CT. Materials and Methods Our focus is to identify missing is-a relations between concept-pairs exhibiting a containment pattern (ie, the set of words of one concept being a proper subset of that of the other concept). We use hierarchically related containment concept-pairs as positive instances and hierarchically unrelated containment concept-pairs as negative instances to train a model predicting whether an is-a relation exists between 2 concepts with containment pattern. The model is a binary classifier leveraging concept name features, hierarchical features, enriched lexical attribute features, and logical definition features. We introduce a cross-validation inspired approach to identify missing is-a relations among all hierarchically unrelated containment concept-pairs. Results We trained and applied our model on the Clinical finding subhierarchy of SNOMED CT (September 2019 US edition). Our model (based on the validation sets) achieved a precision of 0.8164, recall of 0.8397, and F1 score of 0.8279. Applying the model to predict actual missing is-a relations, we obtained a total of 1661 potential candidates. Domain experts performed evaluation on randomly selected 230 samples and verified that 192 (83.48%) are valid. Conclusions The results showed that our deep learning approach is effective in uncovering missing is-a relations between containment concept-pairs in SNOMED CT.

97 MATHEMATICS AND COMPUTING↗

Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble

In this work we explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the same conditions, yet capturing this solution multiplicity remains a significant challenge. A key difficulty lies in providing appropriate initial conditions or guesses, as widely used time-marching schemes and Newton’s method are highly sensitive to these choices when solving complex computational problems. While machine learning models, particularly PINNs, have shown promise in solving DEs, their ability to capture multiple solutions remains underexplored. In this work, we propose a simple and practical approach using PINNs to learn and discover multiple solutions. We first demonstrate that PINNs, when combined with random initialization and deep ensemble method—originally developed for uncertainty quantification—can effectively uncover multiple solutions to nonlinear ordinary and partial DEs. Although training large ensembles of PINNs may appear computationally demanding, this can be done efficiently using vectorization techniques supported by modern deep learning frameworks, allowing many networks to be trained simultaneously. Our approach highlights the critical role of initialization in shaping solution diversity, addressing an often-overlooked aspect of machine learning for scientific computing. Furthermore, we propose utilizing PINN-generated solutions as initial conditions or initial guesses for conventional numerical solvers to enhance accuracy and efficiency in capturing multiple solutions. Extensive numerical experiments, including the Allen–Cahn equation and cavity flow, where our approach successfully identifies both stable and unstable solutions, validate the effectiveness of our method. These findings establish a general and efficient framework for addressing solution multiplicity in nonlinear DEs.

97 MATHEMATICS AND COMPUTING↗

Deep exclusive meson production as a probe to the puzzle of Λ hyperon polarization

In the 1970s, an unexpected transverse Λ polarization in unpolarized proton-beryllium collisions was discovered, which initiated extensive studies on spin phenomena in high-energy physics. Over the past five decades, similar transverse Λ polarization has been observed across various collision systems, including lepton-hadron deep-inelastic scattering, hadron-hadron collisions, and electron-positron collisions. Despite numerous promising theoretical models, the fundamental mechanism underlying this polarization phenomenon remains inconclusive to this day. However, in both longitudinally and transversely polarized lepton-hadron and hadron-hadron collisions, it is found that the Λ hyperon is polarized with respect to the initial parton spin direction. How the Λ hyperon acquires its spin has become one of the most crucial questions to address in order to resolve this puzzle. In this paper, I propose to use an exclusive process that can be measured at the Electron-Ion Collider, the deep exclusive meson production, to explicitly test the mechanism of Λ polarization. The outcomes of this experimental measurement are anticipated to unveil the dominant mechanism by which Λ obtains its spin, eliminating many of the ambiguities that have been encountered in previous studies. Finally, experimental challenges and requirements are discussed. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Deep learning-based spatio-temporal fusion for high-fidelity ultra-high-speed X-ray radiography

Full-field ultra-high-speed (UHS) X-ray imaging experiments have been well established to characterize various processes and phenomena. However, the potential of UHS experiments through the joint acquisition of X-ray videos with distinct configurations has not been fully exploited. In this paper, we investigate the use of a deep learning-based spatio-temporal fusion (STF) framework to fuse two complementary sequences of X-ray images and reconstruct the target image sequence with high spatial resolution, high frame rate and high fidelity. We applied a transfer learning strategy to train the model and compared the peak signal-to-noise ratio (PSNR), average absolute difference (AAD) and structural similarity (SSIM) of the proposed framework on two independent X-ray data sets with those obtained from a baseline deep learning model, a Bayesian fusion framework and the bicubic interpolation method. The proposed framework outperformed the other methods with various configurations of the input frame separations and image noise levels. With three subsequent images from the low-resolution (LR) sequence of a four times lower spatial resolution and another two images from the high-resolution (HR) sequence of a 20 times lower frame rate, the proposed approach achieved average PSNRs of 37.57 dB and 35.15 dB, respectively. When coupled with the appropriate combination of high-speed cameras, the proposed approach will enhance the performance and therefore the scientific value of UHS X-ray imaging experiments.

deep learning↗

Deep-learning methods for contrast enhancement and artifact reduction in cryo-electron tomography: a systematic analysis of the state of the art and proposed improvements

Cryo-electron tomography (cryo-ET) has emerged as the preferred technique for visualizing the organization of macromolecular complexes in situ and resolving their structures at subnanometre resolution [Tegunov et al. (2021)View full citation, Nat. Methods, 18, 186–193]. Despite improvements in data quality as a result of advances in detector technology, microscope stability and stage precision, the analysis and interpretation of tomograms remains challenging due to a low signal-to-noise ratio and reconstruction artifacts stemming from experimental constraints in specimen tilt during data collection resulting in a missing wedge in the Fourier space. Recently, self-supervised deep-learning methods have been proposed for contrast enhancement and reduction of resolution anisotropy in reconstructed tomograms. Here, we evaluate several state-of-the-art deep-learning methods which aim to improve the interpretability of cryo-ET reconstructions, with a focus on their performance on downstream tasks of template matching, sub­tomogram averaging and segmentation. We propose new training architectures and a loss function based on Fourier shell correlation that show improved performance over the standard U-Net with L1/L2 losses. We demonstrate our analysis on four diverse experimental datasets: purified 80S ribosomes, in situ Chlamydomonas reinhardtii, immature HIV-1 virus-like particles and INS-1E cells.

contrast enhancement↗