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nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius $\delta$ goes to zero, and to the fractional Laplacian as $\delta$ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We also provide theoretical convergence rates with respect to $\delta$ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, $\delta$ and $\alpha$, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order $\alpha(y)$, which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as $\delta$. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

97 MATHEMATICS AND COMPUTING↗

Hydraulic characterization of a fault zone from fracture distribution

A quantitative assessment of how faults control the migration of geofluids is critical in many areas of geosciences. Here we integrated geological fieldwork, quantitative analysis of the fractures distribution and numerical modeling to build a geometrical representation of a fault zone and to characterize its hydraulic properties. Our target is a fault located in the Majella Mountain (Italy). We collected 21 scan lines across the fault profile in order to characterize its architecture. The numerical modeling of the fracture network of the damage zones and their hydraulic parameters was performed using both commercial (Move ® ) and open source software (dfnWorks and PFLOTRAN). Move ® was used to build a representative model of the fault zone using fracture spacing as a proxy, and to model the hydraulic parameters of the different fault domains. dfnWorks and PFLOTRAN were employed to infer the hydraulic parameters of the damage zones of the fault and then upscale these properties to an equivalent continuum domain, suitable for fluid flow simulations through the whole fault zone. Our findings show how even in a relatively small area it is possible to describe changes in terms of hydraulic properties of a fault zone and to build models capable to represent these variations.

58 GEOSCIENCES↗

Physics-Informed Neural Networks for Heat Transfer Problems

Abstract Physics-informed neural networks (PINNs) have gained popularity across different engineering fields due to their effectiveness in solving realistic problems with noisy data and often partially missing physics. In PINNs, automatic differentiation is leveraged to evaluate differential operators without discretization errors, and a multitask learning problem is defined in order to simultaneously fit observed data while respecting the underlying governing laws of physics. Here, we present applications of PINNs to various prototype heat transfer problems, targeting in particular realistic conditions not readily tackled with traditional computational methods. To this end, we first consider forced and mixed convection with unknown thermal boundary conditions on the heated surfaces and aim to obtain the temperature and velocity fields everywhere in the domain, including the boundaries, given some sparse temperature measurements. We also consider the prototype Stefan problem for two-phase flow, aiming to infer the moving interface, the velocity and temperature fields everywhere as well as the different conductivities of a solid and a liquid phase, given a few temperature measurements inside the domain. Finally, we present some realistic industrial applications related to power electronics to highlight the practicality of PINNs as well as the effective use of neural networks in solving general heat transfer problems of industrial complexity. Taken together, the results presented herein demonstrate that PINNs not only can solve ill-posed problems, which are beyond the reach of traditional computational methods, but they can also bridge the gap between computational and experimental heat transfer.

Engineering↗

Inference of response functions with the help of machine-learning algorithms

Response functions are a key quantity to describe the near-equilibrium dynamics of strongly interacting many-body systems. Recent techniques that attempt to overcome the challenges of calculating these ab initio have employed expansions in terms of orthogonal polynomials. We employ a neural network prediction algorithm to reconstruct a response function 𝑆⁡(𝜔) defined over a range in frequencies 𝜔. Here, we represent the calculated response function as a truncated Chebyshev series whose coefficients can be optimized to reduce the representation error. We compare the quality of response functions obtained using coefficients calculated using a neural network (NN) algorithm with those computed using the Gaussian integral transform (GIT) method. In the regime where only a small number of terms in the Chebyshev series are retained, we find that the NN scheme outperforms the GIT method.

Kurkcuoglu, Doga Murat [Fermi National Accelerator↗

Reconstructing the neutron star equation of state from observational data via automatic differentiation

Neutron star observables like masses, radii, and tidal deformability are direct probes to the dense matter equation of state (EoS). Here, a novel deep learning method that optimizes an EoS in the automatic differentiation framework of solving inverse problems is presented. The trained neural network EoS yields narrow bands for the relationship between the pressure and speed of sound as a function of the mass density. The results are consistent with those obtained from conventional approaches and the observational bound on the tidal deformability inferred from the gravitational wave event, GW170817.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A Robust and Efficient Deep Learning Method for Dynamical Mass Measurements of Galaxy Clusters

We demonstrate the ability of convolutional neural networks (CNNs) to mitigate systematics in the virial scaling relation and produce dynamical mass estimates of galaxy clusters with remarkably low bias and scatter. We present two models, CNN 1D and CNN 2D , which leverage this deep learning tool to infer cluster masses from distributions of member galaxy dynamics. Our first model, CNN 1D , infers cluster mass directly from the distribution of member galaxy line-of-sight velocities. Our second model, CNN 2D , extends the input space ofCNN 1D to learn on the joint distribution of galaxy line-of-sight velocities and projected radial distances. We train each model as a regression over cluster mass using a labeled catalog of realistic mock cluster observations generated from the MultiDark simulation and UniverseMachine catalog. We then evaluate the performance of each model on an independent set of mock observations selected from the same simulated catalog. The CNN models produce cluster mass predictions with lognormal residuals of scatter as low as 0.132 dex, greater than a factor of 2 improvement over the classical M–σ power-law estimator. Furthermore, the CNN model reduces prediction scatter relative to similar machinelearning approaches by up to 17% while executing in drastically shorter training and evaluation times (by a factor of 30) and producing considerably more robust mass predictions (improving prediction stability under variations in galaxy sampling rate by 30%).

79 ASTRONOMY AND ASTROPHYSICS↗

Classification of Notices to Airmen using Natural Language Processing

This paper establishes the feasibility of using Natural Language Processing (NLP) to classify NOTAMs or Notices to Airmen – a pilot messaging framework to gather real-time situational awareness. Present day air mobility operations heavily rely on NOTAMs. However, pilots often have difficulty interpreting NOTAMs due to the sheer volume of inapplicable messages and unclear abbreviations. Using NLP, the presented study analyzes the accuracy of classifying NOTAMs and, thereby, the efficiency of generating actionable interpretations in real time. To this effect, efficacies of four NLP neural network architectures were analyzed, including three Recurrent Neural Networks (RNNs) with GloVe, Word2Vec, and FastText word embeddings, and one trained Bi-Directional Encoder Representations from Transformers (BERT) model. The four neural networks were trained and evaluated on three open-source datasets of varying text lengths, vocabularies, and grammars, taken from e-commerce product descriptions, social media tweets, and unstructured descriptions for data and analytics services on open data marketplaces such as NASA’s Data and Reasoning Fabric (DRF) platform. This provided cross-analysis of each neural network architecture’s performance per text type. The best performing architecture, BERT, was then fine-tuned on a collection of open-source NOTAM data. Post-training, a real-time NOTAM classification service was implemented to draw inference on new NOTAMs using the trained model, which demonstrated close to 99% accuracy in classification. This modular classification service is envisioned to be integrated with a data and analytics delivery platform, such as the DRF, thus availing real-time contextualization of NOTAMs to air mobility clients, humans, and machines for enhanced decision making.

Aiden C. Szeto↗

Classification of Notices to Airmen using Natural Language Processing

This paper establishes the feasibility of using Natural Language Processing (NLP) to classify NOTAMs or Notices to Airmen – a pilot messaging framework to gather real-time situational awareness. Present day air mobility operations heavily rely on NOTAMs. However, pilots often have difficulty interpreting NOTAMs due to the sheer volume of inapplicable messages and unclear abbreviations. Using NLP, the presented study analyzes the accuracy of classifying NOTAMs and, thereby, the efficiency of generating actionable interpretations in real time. To this effect, efficacies of four NLP neural network architectures were analyzed, including three Recurrent Neural Networks (RNNs) with GloVe, Word2Vec, and FastText word embeddings, and one trained Bi-Directional Encoder Representations from Transformers (BERT) model. The four neural networks were trained and evaluated on three open-source datasets of varying text lengths, vocabularies, and grammars, taken from e-commerce product descriptions, social media tweets, and unstructured descriptions for data and analytics services on open data marketplaces such as NASA’s Data and Reasoning Fabric (DRF) platform. This provided cross-analysis of each neural network architecture’s performance per text type. The best performing architecture, BERT, was then fine-tuned on a collection of open-source NOTAM data. Post-training, a real-time NOTAM classification service was implemented to draw inference on new NOTAMs using the trained model, which demonstrated close to 99% accuracy in classification. This modular classification service is envisioned to be integrated with a data and analytics delivery platform, such as the DRF, thus availing real-time contextualization of NOTAMs to air mobility clients, humans, and machines for enhanced decision making.

Aiden Szeto↗

Neural network methods for radiation detectors and imaging

Recent advances in image data proccesing through deep learning allow for new optimization and performance-enhancement schemes for radiation detectors and imaging hardware. This enables radiation experiments, which includes photon sciences in synchrotron and X-ray free electron lasers as a subclass, through data-endowed artificial intelligence. We give an overview of data generation at photon sources, deep learning-based methods for image processing tasks, and hardware solutions for deep learning acceleration. Most existing deep learning approaches are trained offline, typically using large amounts of computational resources. However, once trained, DNNs can achieve fast inference speeds and can be deployed to edge devices. A new trend is edge computing with less energy consumption (hundreds of watts or less) and real-time analysis potential. While popularly used for edge computing, electronic-based hardware accelerators ranging from general purpose processors such as central processing units (CPUs) to application-specific integrated circuits (ASICs) are constantly reaching performance limits in latency, energy consumption, and other physical constraints. These limits give rise to next-generation analog neuromorhpic hardware platforms, such as optical neural networks (ONNs), for high parallel, low latency, and low energy computing to boost deep learning acceleration (LA-UR-23-32395).

edge computing↗

How Many Elements Matter?

Some studies of stars' multielement abundance distributions suggest at least 5–7 significant dimensions, but others show that many elemental abundances can be predicted to high accuracy from [Fe/H] and [Mg/Fe] (or [Fe/H] and age) alone. We show that both propositions can be, and are, simultaneously true. We adopt a machine-learning technique known as normalizing flow to reconstruct the probability distribution of Milky Way disk stars in the space of 15 elemental abundances measured by APOGEE. Conditioning on T eff and $\mathrm{log}\,g$ minimizes the differential systematics. After further conditioning on [Fe/H] and [Mg/Fe], the residual scatter for most abundances is σ [X/H] ≲ 0.02 dex, consistent with APOGEE's reported statistical uncertainties of ~0.01–0.015 dex and intrinsic scatter of 0.01–0.02 dex. Despite the small scatter, residual abundances display clear correlations between elements, which we show are too large to be explained by measurement uncertainties or by the finite sampling noise. We must condition on at least seven elements to reduce the correlations to a level consistent with the observational uncertainties. Our results demonstrate that cross-element correlations are a much more sensitive probe of a hidden structure than dispersion, and they can be measured precisely in a large sample even if the star-by-star measurement noise is comparable to the intrinsic scatter. We conclude that many elements have an independent story to tell, even for the mundane disk stars and elements produced by the core-collapse and Type Ia supernovae. The only way to learn these lessons is to measure the abundances directly, and not merely infer them.

79 ASTRONOMY AND ASTROPHYSICS↗

Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods. However, quantifying errors and uncertainties in NN-based inference is more complicated than in traditional methods. This is because in addition to aleatoric uncertainty associated with noisy data, there is also uncertainty due to limited data, but also due to NN hyperparameters, overparametrization, optimization and sampling errors as well as model misspecification. Although there are some recent works on uncertainty quantification (UQ) in NNs, there is no systematic investigation of suitable methods towards quantifying the total uncertainty effectively and efficiently even for function approximation, and there is even less work on solving partial differential equations and learning operator mappings between infinite-dimensional function spaces using NNs. In this work, we present a comprehensive framework that includes uncertainty modeling, new and existing solution methods, as well as evaluation metrics and post-hoc improvement approaches. Further, to demonstrate the applicability and reliability of our framework, we present an extensive comparative study in which various methods are tested on prototype problems, including problems with mixed input-output data, and stochastic problems in high dimensions. In the Appendix, we include a comprehensive description of all the UQ methods employed. Further, to help facilitate the deployment of UQ in Scientific Machine Learning research and practice, we present and develop in [1] an open-source Python library (github.com/Crunch-UQ4MI/neuraluq), termed NeuralUQ, that is accompanied by an educational tutorial and additional computational experiments.

11 physics-informed neural networks↗

Coronal structures deduced from photospheric magnetic field and He I lambda 10830 observations

The National Solar Observatory synoptic program provides an extensive and unique data base of high-resolution full-disk observations of the line-of-sight photospheric magnetic fields and of the He I lambda 10830 equivalent width. These data have been taken nearly daily for more than 21 years since 1974 and provide the opportunity to investigate the behavior of the magnetic fields in the photosphere and those inferred for the corona spanning on the time scales of a day to that of a solar cycle. The intensity of structures observed in He I lambda 10830 are strongly modulated by overlying coronal radiation; areas with low coronal emission are generally brighter in He I lambda 10830, while areas with high coronal emission are darker. For this reason, He I lambda 10830 was selected in the mid-1970's as way to identify and monitor coronal holes, magnetic fields with an open configuration, and the sources of high-speed solar wind streams. The He I lambda 10830 spectroheliograms also show a wide variety of other structures from small-scale, short-lived dark points (less than 30 arc-sec, hours) to the large-scale, long-lived two 'ribbon' flare events that follow the filament eruptions (1000 arc-sec, days). Such structures provide clues about the connections and changes in the large-scale coronal magnetic fields that are rooted in concentrations of magnetic network and active regions in the photosphere. In this paper, what observations of the photospheric magnetic field and He I lambda 10830 can tell us about the short- and long-term evolution of the coronal magnetic fields will be discussed, focussing on the quiet Sun and coronal holes. These data and what we infer from them will be compared with direct observations of the coronal structure from the Yohkoh Soft X-ray Telescope.

Harvey, Karen L.↗

Bayesian calibration of bubble size dynamics applied to CO 2 gas fermenters

To accelerate the scale-up of gaseous CO 2 fermentation reactors, computational models need to predict gas-to-liquid mass transfer which requires capturing the bubble size dynamics, i.e. bubble breakup and coalescence. However, the applicability of existing models beyond air–water mixtures remains to be established. Here, an inverse modeling approach, accelerated with a neural network surrogate, calibrates the breakup and coalescence closure models, that are used in class methods for population balance modeling (PBM). The calibration is performed based on experimental results obtained in a CO 2 -air–water-coflowing bubble column reactor. Bayesian inference is used to account for noise in the experimental dataset and bias in the simulation results. To accurately capture gas holdup and interphase mass transfer, the results show that the breakage rate needs to be increased by one order of magnitude. In conclusion, the inferred model parameters are then used on a separate configuration and shown to also improve bubble size distribution predictions.

09 BIOMASS FUELS↗

Multi-scale VLBI observations of the candidate host galaxy of GRB 200716C

We present the discovery and the subsequent follow up of radio emission from SDSS J130402.36+293840.6 (J1304+2938), the candidate host galaxy of the gamma-ray burst (GRB) GRB 200716C. The galaxy is detected in the RACS (0.89 GHz), the NVSS, the Apertif imaging survey, and the FIRST (1.4 GHz), the VLASS (3 GHz), and in public LOFAR (130–170 MHz), WISE (3.4–22 μm), and SDSS (z, i, r, g, u filters) data. The luminosity inferred at 1.4 GHz is (5.1 ± 0.2) × 10 30 erg s -1 Hz -1 . To characterise the emission and distinguish between different components within the galaxy, we performed dedicated, high-sensitivity and high-resolution observations with the European VLBI Network (EVN) + e-MERLIN at 1.6 and 5 GHz. We did not detect any emission from a compact core, suggesting that the presence of a radio-loud active galactic nucleus (AGN) is unlikely, and therefore we ascribe the emission observed in the public surveys to star-forming regions within the galaxy. We confirm and refine the redshift estimate, z = 0.341 ± 0.004, with a dedicated Telescopio Nazionale Galileo (TNG) spectroscopic observation. Finally, we compiled a list of all the known hosts of GRB afterglows detected in radio and computed the corresponding radio luminosity: if GRB 200716C belongs to J1304+2938, this is the third most radio-luminous host of a GRB, implying one of the highest star-formation rates (SFRs) currently known, namely SFR ~ 324±61 M ⊙ yr -1 . On the other hand, through the analysis of the prompt emission light curve, recent works suggest that GRB 200716C might be a short-duration GRB located beyond J1304+2938 and gravitationally lensed by an intermediate-mass black hole (IMBH) hosted by the galaxy. Neither the public data nor our Very Long Baseline Interferometry (VLBI) observations can confirm or rule out the presence of an IMBH acting as a (milli-)lens hosted by the galaxy, a scenario still compatible with the set of radio observations presented in this work.

79 ASTRONOMY AND ASTROPHYSICS↗

Carrier phase ambiguity resolution for the Global Positioning System applied to geodetic baselines up to 2000 km

A technique for resolving the ambiguities in the GPS carrier phase data (which are biased by an integer number of cycles) is described which can be applied to geodetic baselines up to 2000 km in length and can be used with dual-frequency P code receivers. The results of such application demonstrated that a factor of 3 improvement in baseline accuracy could be obtained, giving centimeter-level agreement with coordinates inferred by very-long-baseline interferometry in the western United States. It was found that a method using pseudorange data is more reliable than one using ionospheric constraints for baselines longer than 200 km. It is recommended that future GPS networks have a wide spectrum of baseline lengths (ranging from baselines shorter than 100 km to those longer than 1000 km) and that GPS receivers be used which can acquire dual-frequency P code data.

Blewitt, Geoffrey↗

Real-Time Detection of Charge Jumps in Superconducting Qubits with a Convolutional Neural Network

Ionizing radiation from cosmic rays and gammas can induce discontinuous jumps in the environmental charge of superconducting qubits (charge jumps), causing correlated errors that challenge fault-tolerant quantum computing while simultaneously providing a detection signature for quantum sensing applications. Current detection methods operate offline, introducing latency incompatible with in-the-loop qubit control. In this paper, an online detector of charge jumps for superconducting qubits, based on a dilated causal convolutional neural network (DCCNN) designed for in-the-loop deployment on the Quantum Instrumentation Control Kit (QICK) platform, is presented. The network is trained on synthetic Ramsey tomography scans generated from qubit templates measured at the Northwestern Experimental Underground Site (NEXUS) at Fermilab, and translated to FPGA firmware via hls4ml with ap_fixed$\langle 16,6 \rangle$ quantization, reaching a per-inference latency of $6.19 μ$s on the Zynq UltraScale+ RFSoC ZCU216. At this operating point the DCCNN matches the detection efficiency of the established offline $χ^2$ algorithm ($0.843 \pm 0.022$ vs. $0.866 \pm 0.020$ on $|Δq| \in [0.1, 0.5] e$ at matched false-positive rate), while requiring no per-qubit hyperparameter tuning. This shifts charge-jump detection from a post-hoc diagnostic to a control-loop primitive, enabling adaptive protocols that respond to radiation-induced events in situ, with applications to quantum-computing error mitigation and to the use of superconducting qubits as particle detectors.

Gaytan-Villarreal, Daniel [Carnegie Mellon U.]↗

Direct Bayesian inference for fault severity assessment in Digital-Twin-Based fault diagnosis

For applications in condition-based maintenance of nuclear systems, the assessment of fault severity is crucial. In this work, we developed a framework that allows for direct inference of the probability distributions of possible faults in a system. Here, we employed a model-based approach with model residuals generated from analytical redundancy relations provided by physics-based models of the system components. From real-time sensor readings, the values of the model residuals can be calculated, and the posterior probability distributions of the faults can be computed directly using the methods of Bayesian networks. From the posterior distribution of each fault, one can estimate the fault probability based on a chosen threshold and assess the severity of the fault. By eliminating the discretization and simplifications in middle steps, this approach allows us to leverage the available computational resources to provide more accurate fault probability estimates and severity assessments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Improving deep learning model performance under parametric constraints for materials informatics applications

Abstract Modern machine learning (ML) and deep learning (DL) techniques using high-dimensional data representations have helped accelerate the materials discovery process by efficiently detecting hidden patterns in existing datasets and linking input representations to output properties for a better understanding of the scientific phenomenon. While a deep neural network comprised of fully connected layers has been widely used for materials property prediction, simply creating a deeper model with a large number of layers often faces with vanishing gradient problem, causing a degradation in the performance, thereby limiting usage. In this paper, we study and propose architectural principles to address the question of improving the performance of model training and inference under fixed parametric constraints. Here, we present a general deep-learning framework based on branched residual learning (BRNet) with fully connected layers that can work with any numerical vector-based representation as input to build accurate models to predict materials properties. We perform model training for materials properties using numerical vectors representing different composition-based attributes of the respective materials and compare the performance of the proposed models against traditional ML and existing DL architectures. We find that the proposed models are significantly more accurate than the ML/DL models for all data sizes by using different composition-based attributes as input. Further, branched learning requires fewer parameters and results in faster model training due to better convergence during the training phase than existing neural networks, thereby efficiently building accurate models for predicting materials properties.

36 MATERIALS SCIENCE↗