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Emergence of local scaling relations in adsorption energies on high-entropy alloys

Alloying has been proposed to circumvent scaling relations between the adsorption energies thus allowing for the complete optimization of multistep reactions. Herein the fidelity of scaling rules on high-entropy alloy (HEA) surfaces is assessed focusing on hydrogen-containing molecules, *AH x for A = C and N (x = 0, 1, 2, 3), A = S (x = 0, 1, 2) and A = O (x = 0, 1). Using an adsorbate- and site-specific deep learning model to rapidly compute the adsorption energies on CoMoFeNiCu HEA surfaces, the energies of *AH x and *A are shown to be linearly correlated if *A and *AH x have identical adsorption site symmetry. However, a local linear dependence emerges between the configuration-averaged adsorption energies irrespective of the site symmetry. Although these correlations represent a weaker form of the scaling relationships, they are sufficient to prohibit the optimization of multistep reactions. The underpinning of this behavior is twofold (1) the nearsightedness principle and (2) the narrow distribution of the adsorption energies around the mean-field value. While the nearsightedness is general for all electronic systems, the second criterion applies in HEAs with relatively strong reactive elements. The present findings strongly suggest that alloys may not generally enable the breaking of scaling relationships.

36 MATERIALS SCIENCE↗

Transforming microseismic clouds into near real-time visualization of the growing hydraulic fracture

SUMMARY Microseismic observations during unconventional reservoir stimulation are typically seen as a proxy for clusters of hydraulic fractures and the extent of the stimulated reservoir. Such straightforward interpretation is often misleading and fails to provide a physically reasonable image of the fracturing process. This paper demonstrates the application of a physics-based machine learning algorithm which enables a rapid and accurate fracture mapping from the microseismic data. Our training and validation data set relies on a history-matched geomechanical modelling workflow implemented in GEOS software for the Hydraulic Fracturing Test Site 1 (HFTS-1) project. For this study we augmented the simulated fracture growth through geostatistical modelling of induced seismicity, so that the synthetic microseismic catalogue matches the main statistical properties of the field observations. We formulated the problem of mapping the actual fracture in the clutter of events to parallel common video segmentation workflows: several past video frames (microseismic density snapshots) are passed through a deep convolutional network to classify whether a given voxel is associated with a fracture or intact rock. We found that for accurate fracture mapping, the network’s input and architecture must be augmented to incorporate the fluid injection parameters (pressure, rate, concentration of proppant, and location of the perforation within the cluster). The error rate for the network reached as little as 10 per cent of the fracture area, while a conventional microseismic interpretation approach yielded ∼300 per cent. Our approach also yields must faster predictions than conventional methods (minutes instead of weeks), and could enable engineers to make rapid decisions regarding engineering parameters (pumping rate, viscosity) in real time during stimulation.

58 GEOSCIENCES↗

Capsule network-based semantic segmentation model for thermal anomaly identification on building envelopes

Thermography technology is widely used to inspect thermal anomalies in building façade systems. Computer vision-based techniques provide opportunities to autonomously detect such heat anomalies to significantly improve the efficiency of decision-making for building envelope retrofitting and maintenance. Here, in this work, we propose a novel Capsule Network-based deep learning model – CapsLab – that detects and identifies thermal anomalies by semantic segmentation. CapsLab is built based on our proposed prediction-tuning capsule (PT-Capsule) layer. Different from a traditional capsule layer, which consists of part-whole transformation and capsule-routing process, the proposed layer is composed of a prediction and tuning process, which helps decreasing the number of model parameters significantly. While the applicability of traditional Capsule Networks (CapsNets) has been limited to simpler tasks and smaller datasets due to their scalability issue, we can leverage the lightweight of the proposed PT-Capsule layer, and apply it to the semantic segmentation task. In this work, we also employ our previously presented performance metric, referred to as the Anomaly Identification Metric (AIM) (Kakillioglua et al. 2021), to evaluate the segmentation outputs. Traditional performance metrics do not accurately reflect the true performance of the segmentation models in thermal anomaly identification due to the high subjectivity in the annotation process and higher overlap ratio sensitivity of the standard metrics. AIM, on the other hand, is robust to these drawbacks. Experimental results show, both qualitatively and quantitatively, that our proposed segmentation method can effectively segment the thermal anomalies. Specifically, our model provides 9.38% and 13.53% improvements over the baseline model – DeepLabV3+ – based on traditional mIoU score and the AIM score, respectively, while requiring less model parameters and less computation at the same time. In addition, the scores that the AIM metric generates better align with the scores provided by building performance experts.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Pulsed Thermal Tomography Nondestructive Examination of Additively Manufactured Reactor Materials and Components. Third Annual Progress Report

Additive manufacturing (AM) of high-strength corrosion resistance alloys for nuclear energy applications, such as stainless steel and Inconel, is currently based on laser powder bed fusion (LPBF) process. Some of the challenges with using LPBF method for nuclear manufacturing include the possibility of introducing pores into metallic structures. Probability of crack initiation at the pore depends on size, shape, and orientation of the defect. Pulsed Infrared Thermography Imaging (PIT) provides a capability for non-destructive evaluation (NDE) of sub-surface defects in arbitrary size structures. The PIT method is based on recording material surface temperature transients with infrared (IR) camera following thermal pulse delivered on material surface with flash light. The PIT method has advantages for NDE of actual AM structures because the method involves one-sided non-contact measurements and fast processing of large sample areas captured in one image. Following initial qualification of an AM component for deployment in a nuclear reactor, a PIT system can also be used for in-service nondestructive evaluation (NDE) applications. In this report, we describe recent progress in enhancing PIT capabilities in detecting microscopic subsurface defects in metals, and classifying shapes and orientation of pores in thermal images. For detection of microscopic defects in PIT imaging data, we have developed Spatial Temporal Denoised Thermal Source Separation (STDTSS) unsupervised machine learning (ML) image processing algorithm. We show that flat bottom hole (FBH) defects as small as 200µm in SS316 and IN718 specimens, can be detected with STDTSS algorithm. To the best of our knowledge, these are the smallest detected defects which are reported in literature. For classification of defects shapes, we have previously developed thermal tomography (TT) algorithm to obtain depth reconstructions of material defects from data cube of sequentially recorded surface temperatures. However, interpretation of TT images is non-trivial because of blurring with increasing depth. To address this challenge, we have developed a deep learning convolutional neural network (CNN) to classify size and orientation subsurface defects in simulated TT images.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Robust In-Situ Strain Measurements to Monitor CO 2 Storage

The goal of this project was to develop and demonstrate robust instrumentation to monitor the in-situ strain tensor in order to improve the reliability and security of CO 2 storage in geologic formations. We met the original goals of the project and the major overarching accomplishment is the advancement of strain tensor monitoring from an intriguing concept to a commercially available technology with a solid foundation of novel instruments supported by theoretical analyses and validation experiments. The main accomplishments of the project are summarized below. We designed, built and evaluated nine new optical fiber strainmeters and tiltmeters using Michelson interferometers to measure deformation with ultra-high resolution at both shallow and deep point locations in the subsurface. These are the robust strainmeters that motivated the title of the project. We designed, built and evaluated a novel method of measuring distributed strain in optical fibers with nanostrain resolution, and cm-scale location, and sampling into the seismic band. The new method is called Coherence-length-gated Microwave Photonics Interfereometry (CMPI). CMPI technology has advantages over existing commercial DAS and DSS methods. We developed and demonstrated capabilities to deploy instruments in the field and used them to measure strain caused by ambient signals like barometric pressure and tides, as well as induced signals like surface loading and pore pressure changes from pumping tests. We deployed a working strainmeter at 1,700 ft depth, slightly above an active reservoir. This is to our knowledge the greatest depth a strainmeter has been deployed and the techniques we used can readily be extended to greater depths. Optical fiber borehole tensor strainmeter techology was advanced from a TRL 4 at the start, to a TRL of 7 at the conclusion of the project. The project included advances in simulations and theoretical analyses. We developed and demonstrated a computational workflow that uses machine learning to reduce the computational requirements and make it practical to use Bayesian inversion to solve large numerical poroelastic analyses needed to interpret strain tensor field data. We evaluated the strain tensor fields and time series that would be caused by leaks of CO 2 or other fluids from reservoirs. These simulations demonstrated that signals from leaks could be measured with instruments developed for the project, opening a potentially new method for ensuring storage security. We showed that strains in caprock can be used to estimate pressure in a reservoir. This avoids the need to drill monitoring wells into the reservoir, and it expands the capabilities of monitoring in the caprock. The project includes a derivation and application of a novel analytical solution to the strains in the vicinity of a pressurized poroelastic inclusion. This solution explains field data measured during injeciton tests at the North Avant Field, and it will simplify future interpretation of strain tensor data. The project included a broad range of experiments, and of the most significant is the characterization of the strain tensor at an array three strainmeters during six injection tests at the North Avant Field, Oklahoma. This demonstrated repeatability of the strain signal measured by the new instruments developed for the project, and it showed similarities between the strain signal at shallow depths and pressure in the underlying reservoir. We also demonstrated that useful strain data can be measured at reservoir depths. This confirms that strain tensor data can be measured throughout the caprock over a reservoir. The project demonstrated the feasibility of using the strain tensor and distributed strain measured in caprock during a variety of different well tests where the pumping rate was constant, sinusoidal and positive, or a periodic square wave with zero net rate. This further strengthens the validity of using strain data to characterize reservoirs and aquifers. We also demonstrated that strain caused be fluctuations of air pressure and water pressure in the vadose zone can be measured and interpreted, suggesting that high resolution distributed strain measurements hold promise for monitoring the vadose zone. The project partially supported nine graduate students in the Environmental Engineering, Hydrogeology, Electrical Engineering programs at Clemson University. The research was described in nine journal papers, 23 talks and conference abstracts. Additional journal papers are in preparation. A new company called Tensora was started to provide strainmeter technology for commercial applications.

01 COAL, LIGNITE, AND PEAT↗

Topological structure of complex predictions

Abstract Current complex prediction models are the result of fitting deep neural networks, graph convolutional networks or transducers to a set of training data. A key challenge with these models is that they are highly parameterized, which makes describing and interpreting the prediction strategies difficult. We use topological data analysis to transform these complex prediction models into a simplified topological view of the prediction landscape. The result is a map of the predictions that enables inspection of the model results with more specificity than dimensionality-reduction methods such as tSNE and UMAP. The methods scale up to large datasets across different domains. We present a case study of a transformer-based model previously designed to predict expression levels of a piece of DNA in thousands of genomic tracks. When the model is used to study mutations in the BRCA1 gene, our topological analysis shows that it is sensitive to the location of a mutation and the exon structure of BRCA1 in ways that cannot be found with tools based on dimensionality reduction. Moreover, the topological framework offers multiple ways to inspect results, including an error estimate that is more accurate than model uncertainty. Further studies show how these ideas produce useful results in graph-based learning and image classification.

Computer Science↗

Efficient Subset Simulation using Hamiltonian Neural Network enhanced Markov Chain Monte Carlo Methods

The Monte Carlo method delivers an unbiased estimate of the probability of failure. However, the variance of the estimate depends on the number of evaluated samples. This number must be very large for estimations of a low probability of failure. If the evaluation of each sample is computationally expensive, the crude Monte Carlo simulation strategy is impracticable. Therefore, subset simulations are used to reduce the required number of evaluations. Subset simulations require a Markov Chain Monte Carlo sampler, such as the random walk Metropolis-Hastings algorithm. The algorithm, however, struggles with sampling in low-probability regions, especially if they are narrow. As a consequence, advanced Markov Chain Monte Carlo simulations have been developed. In particular, the Hamiltonian Monte Carlo method explores the target distribution rapidly. Driven by the idea of Hamiltonian dynamics, this sampler provides a non-random walk through the target distribution. The incorporation of subset simulation and Hamiltonian Monte Carlo methods has shown promising results for reliability analysis. One downside of the Hamiltonian Monte Carlo method is that gradient evaluations are computationally expensive, especially when dealing with high-dimensional problems and evaluating long trajectories. We show that integrating Hamiltonian neural networks in Hamiltonian Monte Carlo simulations significantly speeds up the sampling task. Furthermore, the enhancement of adaptive trajectory length within the Hamiltonian Monte Carlo results in the efficient proposal of the following states. Based on this recent enhancement, we provide a fast sampling strategy for subset simulations using Hamiltonian neural networks to replace the evaluation of the gradient and significantly speed up the Hamiltonian Monte Carlo simulation.

97 MATHEMATICS AND COMPUTING↗

Statistical characterization of experimental magnetized liner inertial fusion stagnation images using deep-learning-based fuel–background segmentation

Significant variety is observed in spherical crystal x-ray imager (SCXI) data for the stagnated fuel–liner system created in Magnetized Liner Inertial Fusion (MagLIF) experiments conducted at the Sandia National Laboratories Z-facility. As a result, image analysis tasks involving, e.g., region-of-interest selection (i.e. segmentation), background subtraction and image registration have generally required tedious manual treatment leading to increased risk of irreproducibility, lack of uncertainty quantification and smaller-scale studies using only a fraction of available data. We present a convolutional neural network (CNN)-based pipeline to automate much of the image processing workflow. This tool enabled batch preprocessing of an ensemble of N scans = 139 SCXI images across N exp = 67 different experiments for subsequent study. The pipeline begins by segmenting images into the stagnated fuel and background using a CNN trained on synthetic images generated from a geometric model of a physical three-dimensional plasma. The resulting segmentation allows for a rules-based registration. Our approach flexibly handles rarely occurring artifacts through minimal user input and avoids the need for extensive hand labelling and augmentation of our experimental dataset that would be needed to train an end-to-end pipeline. Here we also fit background pixels using low-degree polynomials, and perform a statistical assessment of the background and noise properties over the entire image database. Our results provide a guide for choices made in statistical inference models using stagnation image data and can be applied in the generation of synthetic datasets with realistic choices of noise statistics and background models used for machine learning tasks in MagLIF data analysis. We anticipate that the method may be readily extended to automate other MagLIF stagnation imaging applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Constraints on the Physical Properties of GW190814 through Simulations Based on DECam Follow-up Observations by the Dark Energy Survey

On 2019 August 14, the LIGO and Virgo Collaborations detected gravitational waves from a black hole and a 2.6 solar mass compact object, possibly the first neutron star–black hole merger. In search of an optical counterpart, the Dark Energy Survey (DES) obtained deep imaging of the entire 90% confidence level localization area with Blanco/DECam 0, 1, 2, 3, 6, and 16 nights after the merger. Objects with varying brightness were detected by the DES Pipeline, and we systematically reduced the candidate counterparts through catalog matching, light-curve properties, host-galaxy photometric redshifts, Southern Astrophysical Research spectroscopic follow-up observations, and machine-learning-based photometric classification. All candidates were rejected as counterparts to the merger. To quantify the sensitivity of our search, we applied our selection criteria to full light-curve simulations of supernovae and kilonovae as they would appear in the DECam observations. Because the source class of the merger was uncertain, we utilized an agnostic, three-component kilonova model based on tidally disrupted neutron star (NS) ejecta properties to quantify our detection efficiency of a counterpart if the merger included an NS. We find that, if a kilonova occurred during this merger, configurations where the ejected matter is greater than 0.07 solar masses, has lanthanide abundance less than 10 -8.56 , and has a velocity between 0.18c and 0.21c are disfavored at the 2σ level. Furthermore, we estimate that our background reduction methods are capable of associating gravitational wave signals with a detected electromagnetic counterpart at the 4σ level in 95% of future follow-up observations.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Processing Satellite Imagery To Detect Waste Tire Piles

A methodology for processing commercially available satellite spectral imagery has been developed to enable identification and mapping of waste tire piles in California. The California Integrated Waste Management Board initiated the project and provided funding for the method s development. The methodology includes the use of a combination of previously commercially available image-processing and georeferencing software used to develop a model that specifically distinguishes between tire piles and other objects. The methodology reduces the time that must be spent to initially survey a region for tire sites, thereby increasing inspectors and managers time available for remediation of the sites. Remediation is needed because millions of used tires are discarded every year, waste tire piles pose fire hazards, and mosquitoes often breed in water trapped in tires. It should be possible to adapt the methodology to regions outside California by modifying some of the algorithms implemented in the software to account for geographic differences in spectral characteristics associated with terrain and climate. The task of identifying tire piles in satellite imagery is uniquely challenging because of their low reflectance levels: Tires tend to be spectrally confused with shadows and deep water, both of which reflect little light to satellite-borne imaging systems. In this methodology, the challenge is met, in part, by use of software that implements the Tire Identification from Reflectance (TIRe) model. The development of the TIRe model included incorporation of lessons learned in previous research on the detection and mapping of tire piles by use of manual/ visual and/or computational analysis of aerial and satellite imagery. The TIRe model is a computational model for identifying tire piles and discriminating between tire piles and other objects. The input to the TIRe model is the georeferenced but otherwise raw satellite spectral images of a geographic region to be surveyed. The TIRe model identifies the darkest objects in the images and, on the basis of spatial and spectral image characteristics, discriminates against other dark objects, which can include vegetation, some bodies of water, and dark soils. The TIRe model can identify piles of as few as 100 tires. The output of the TIRe model is a binary mask showing areas containing suspected tire piles and spectrally similar features. This mask is overlaid on the original satellite imagery and examined by a trained image analyst, who strives to further discriminate against non-tire objects that the TIRe model tentatively identified as tire piles. After the analyst has made adjustments, the mask is used to create a synoptic, geographically accurate tire-pile survey map, which can be overlaid with a road map and/or any other map or set of georeferenced data, according to a customer s preferences.

Skiles, Joseph↗

Testing and Development of NEA Scout Solar Sail Deployer Mechanism

The Near Earth Asteroid (NEA) [1] Scout is a deep space CubeSat designed to use an 86 m2 solar sail to navigate to a near earth asteroid called VG 1991. The solar sail deployment mechanism aboard NEA Scout has gone through numerous design cycles and ground tests since its conception in 2014. An engineering development unit (EDU) was constructed in the spring of 2016 and since then, the NEA Scout team has completed numerous ground deployments aiming to mature the deployment system and the ground test methods used to validate that system. Testing a large, non-rigid gossamer system in 1G environments has presented its difficulties to numerous solar sailing programs before, but NEA Scout's size, sail configuration, and budget has led the team to develop new deployment techniques and uncover new practices while improving their test methods. The program has planned and completed 5 separate full scale sail deployments to date, with a flight sail deployment test scheduled for FY18. The paper entitled "Design and Development of NEA Scout Solar Sail Deployer Mechanism" [2] was presented at the 43rd Aerospace Mechanisms Symposia. Since then, the system has matured and completed ascent vent, random vibration, boom deployment and sail deployment tests. This paper will discuss the lessons learned and advancements made while working on solar sail deployment testing and mechanical redesign cycles.

Few, Alex↗

Expanding Accurate Person Recognition to New Altitudes and Ranges: The BRIAR Dataset

Face recognition technology has advanced significantly in recent years due largely to the availability of large and increasingly complex training datasets for use in deep learning models. These datasets, however, typically comprise images scraped from news sites or social media plat-forms and, therefore, have limited utility in more advanced security, forensics, and military applications. These applications require lower resolution, longer ranges, and ele-vated viewpoints. To meet these critical needs, we collected and curated the first and second subsets of a large multi-modal biometric dataset designed for use in the research and development (R&D) of biometric recognition technolo-gies under extremely challenging conditions. Thus far, the dataset includes more than 350,000 still images and over 1,300 hours of video footage of approximately 1,000 sub-jects. To collect this data, we used Nikon DSLR cameras, a variety of commercial surveillance cameras, specialized long-rage R&D cameras, and Group 1 and Group 2 UAV platforms. The goal is to support the development of algorithms capable of accurately recognizing people at ranges up to 1,000 m and from high angles of elevation. These ad-vances will include improvements to the state of the art in face recognition and will support new research in the area of whole-body recognition using methods based on gait and anthropometry. This paper describes methods used to col-lect and curate the dataset, and the dataset's characteristics at the current stage.

Brogan, Joel↗

Interface PINNs (I-PINNs): A physics-informed neural networks framework for interface problems

Here, we present a novel physics-informed neural networks (PINNs) framework for modeling interface problems, termed Interface PINNs (I-PINNs). I-PINNs uses different neural networks for any two subdomains separated by a sharp interface such that the neural networks differ only through their activation functions while the other parameters remain identical. The performance of I-PINNs, conventional PINNs, and other existing domain-decomposition PINNs methods such as extended PINNs (XPINNs) and multi-domain PINN (M-PINN) is compared through several one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems. The results demonstrate that I-PINNs provides a root-mean-square-error accuracy, at least two orders of magnitude better than conventional PINNs and XPINNs at approximately one-tenth of the computational cost of conventional PINNs and half the cost of XPINNs. Additionally, while I-PINNs and M-PINN provide comparable accuracies, M-PINN is found to be approximately 50% more expensive.

42 ENGINEERING↗

Understanding the High Energy Higgs Sector with the CMS Experiment and Artificial Intelligence

This dissertation describes efforts towards understanding the Higgs boson at the highest energies humanly accessible, using the CMS experiment at the Large Hadron Collider and advances in artificial intelligence (AI) and machine learning (ML). We present searches for resonant and nonresonant Higgs-boson (H) pair production in the all-hadronic two beauty-quark and two vector boson (V) final state, using a novel strategy to measure the quartic HHVV coupling and search for new Higgs-like bosons. By targeting highly Lorentz-boosted Higgs pairs, we probe effects of potential new physics in the high energy Higgs sector, which could hold answers to fundamental mysteries of nature such as baryon asymmetry. To enable these and future searches, we introduce as well significant developments in AI/ML, including in the identification of boosted H$\rightarrow$VV decays with deep transformer networks and advances in AI-accelerated fast simulations of the CMS detector. The latter notably includes the development of the first, highly performant generative models for point-cloud data in high energy physics, which have the potential to improve CMS' computational efficiency by up to three orders of magnitude. We also highlight novel solutions to the important and challenging problems of calibrating and validating these ML techniques. Finally, we present new approaches to search for new physics in a model-agnostic manner, using physics-informed ML methods equivariant to Lorentz transformations. The quartic HHVV coupling is observed (expected) to be constrained to $[-0.04, 2.05]$ ($[0.05, 1.98]$) at the 95% confidence level relative to the standard model prediction, representing the second-most sensitive measurement of this coupling by CMS to date. Exclusion limits on the production cross section of new heavy resonances decaying to two Higgs-like bosons are expected to be as low as 0.3 fb for high resonance masses.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Unraveling the impact of initial choices and in-loop interventions on learning dynamics in autonomous scanning probe microscopy

The current focus in Autonomous Experimentation (AE) is on developing robust workflows to conduct the AE effectively. This entails the need for well-defined approaches to guide the AE process, including strategies for hyperparameter tuning and high-level human interventions within the workflow loop. This paper presents a comprehensive analysis of the influence of initial experimental conditions and in-loop interventions on the learning dynamics of Deep Kernel Learning (DKL) within the realm of AE in scanning probe microscopy. We explore the concept of the “seed effect,” where the initial experiment setup has a substantial impact on the subsequent learning trajectory. Additionally, we introduce an approach of the seed point interventions in AE allowing the operator to influence the exploration process. Using a dataset from Piezoresponse Force Microscopy on PbTiO 3 thin films, we illustrate the impact of the “seed effect” and in-loop seed interventions on the effectiveness of DKL in predicting material properties. The study highlights the importance of initial choices and adaptive interventions in optimizing learning rates and enhancing the efficiency of automated material characterization. This work offers valuable insights into designing more robust and effective AE workflows in microscopy with potential applications across various characterization techniques.

47 OTHER INSTRUMENTATION↗

Scalable balanced training of conditional generative adversarial neural networks on image data

Here, we propose a distributed approach to train deep convolutional generative adversarial neural network (DC-CGANs) models. Our method reduces the imbalance between generator and discriminator by partitioning the training data according to data labels, and enhances scalability by performing a parallel training where multiple generators are concurrently trained, each one of them focusing on a single data label. Performance is assessed in terms of inception score, Fréchet inception distance, and image quality on MNIST, CIFAR10, CIFAR100, and ImageNet1k datasets, showing a significant improvement in comparison to state-of-the-art techniques to training DC-CGANs. Weak scaling is attained on all the four datasets using up to 1000 processes and 2000 NVIDIA V100 GPUs on the OLCF supercomputer Summit.

97 MATHEMATICS AND COMPUTING↗

Physics-Informed Machine Learning of Dynamical Systems for Efficient Bayesian Inference

Although the no-u-turn sampler (NUTS) is a widely adopted method for performing Bayesian inference, it requires numerous posterior gradients which can be expensive to compute in practice. Recently, there has been a significant interest in physics-based machine learning of dynamical (or Hamiltonian) systems and Hamiltonian neural networks (HNNs) is a noteworthy architecture. But these types of architectures have not been applied to solve Bayesian inference problems efficiently. We propose the use of HNNs for performing Bayesian inference efficiently without requiring numerous posterior gradients. We introduce latent variable outputs to HNNs (L-HNNs) for improved expressivity and reduced integration errors. We integrate L-HNNs in NUTS and further propose an online error monitoring scheme to prevent sampling degeneracy in regions where L-HNNs may have little training data. We demonstrate L-HNNs in NUTS with online error monitoring consider several complex high-dimensional posterior densities and compare its performance to NUTS.

97 MATHEMATICS AND COMPUTING↗

On Transfer Learning Of Neural Networks Using Bi-Fidelity Data For Uncertainty Propagation

Due to their high degree of expressiveness, neural networks have recently been used as surrogate models for mapping inputs of an engineering system to outputs of interest. Once trained, neural networks are computationally inexpensive to evaluate and remove the need for repeated evaluations of computationally expensive models in uncertainty quantification applications. However, given the highly parameterized construction of neural networks, especially deep neural networks, accurate training often requires large amounts of simulation data that may not be available in the case of computationally expensive systems. In this paper, to alleviate this issue for uncertainty propagation, we explore the application of transfer learning techniques using training data generated from both high- and low-fidelity models. We explore two strategies for coupling these two datasets during the training procedure, namely, the standard transfer learning and the bi-fidelity-weighted learning. In the former approach, a neural network model mapping the inputs to the outputs of interest is trained based on the low-fidelity data. The high-fidelity data are then used to adapt the parameters of the upper layer(s) of the low-fidelity network, or train a simpler neural network to map the output of the low-fidelity network to that of the high-fidelity model. In the latter approach, the entire low-fidelity network parameters are updated using data generated via a Gaussian process model trained with a small high-fidelity dataset. The parameter updates are performed via a variant of stochastic gradient descent with learning rates given by the Gaussian process model. Using three numerical examples, we illustrate the utility of these bi-fidelity transfer learning methods where we focus on accuracy improvement achieved by transfer learning over standard training approaches.

97 MATHEMATICS AND COMPUTING↗