Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Deep”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,261 records · Page 70

MABAL: a Novel Deep-Learning Architecture for Machine-Assisted Bone Age Labeling

Bone age assessment (BAA) is a commonly performed diagnostic study in pediatric radiology to assess skeletal maturity. The most commonly utilized method for assessment of BAA is the Greulich and Pyle method (Pediatr Radiol 46.9:1269–1274, 2016; Arch Dis Child 81.2:172–173, 1999) atlas. The evaluation of BAA can be a tedious and time-consuming process for the radiologist. As such, several computer-assisted detection/diagnosis (CAD) methods have been proposed for automation of BAA. Classical CAD tools have traditionally relied on hard-coded algorithmic features for BAA which suffer from a variety of drawbacks. Recently, the advent and proliferation of convolutional neural networks (CNNs) has shown promise in a variety of medical imaging applications. There have been at least two published applications of using deep learning for evaluation of bone age (Med Image Anal 36:41–51, 2017; JDI 1–5, 2017). However, current implementations are limited by a combination of both architecture design and relatively small datasets. The purpose of this study is to demonstrate the benefits of a customized neural network algorithm carefully calibrated to the evaluation of bone age utilizing a relatively large institutional dataset. In doing so, this study will aim to show that advanced architectures can be successfully trained from scratch in the medical imaging domain and can generate results that outperform any existing proposed algorithm. The training data consisted of 10,289 images of different skeletal age examinations, 8909 from the hospital Picture Archiving and Communication System at our institution and 1383 from the public Digital Hand Atlas Database. The data was separated into four cohorts, one each for male and female children above the age of 8, and one each for male and female children below the age of 10. The testing set consisted of 20 radiographs of each 1-year-age cohort from 0 to 1 years to 14–15+ years, half male and half female. The testing set included left-hand radiographs done for bone age assessment, trauma evaluation without significant findings, and skeletal surveys. A 14 hidden layer-customized neural network was designed for this study. The network included several state of the art techniques including residual-style connections, inception layers, and spatial transformer layers. Data augmentation was applied to the network inputs to prevent overfitting. A linear regression output was utilized. Mean square error was used as the network loss function and mean absolute error (MAE) was utilized as the primary performance metric. MAE accuracies on the validation and test sets for young females were 0.654 and 0.561 respectively. For older females, validation and test accuracies were 0.662 and 0.497 respectively. For young males, validation and test accuracies were 0.649 and 0.585 respectively. Finally, for older males, validation and test set accuracies were 0.581 and 0.501 respectively. The female cohorts were trained for 900 epochs each and the male cohorts were trained for 600 epochs. An eightfold cross-validation set was employed for hyperparameter tuning. Test error was obtained after training on a full data set with the selected hyperparameters. Using our proposed customized neural network architecture on our large available data, we achieved an aggregate validation and test set mean absolute errors of 0.637 and 0.536 respectively. To date, this is the best published performance on utilizing deep learning for bone age assessment. Our results support our initial hypothesis that customized, purpose-built neural networks provide improved performance over networks derived from pre-trained imaging data sets. We build on that initial work by showing that the addition of state-of-the-art techniques such as residual connections and inception architecture further improves prediction accuracy. This is important because the current assumption for use of residual and/or inception architectures is that a large pre-trained network is required for successful implementation given the relatively small datasets in medical imaging. Instead we show that a small, customized architecture incorporating advanced CNN strategies can indeed be trained from scratch, yielding significant improvements in algorithm accuracy. It should be noted that for all four cohorts, testing error outperformed validation error. One reason for this is that our ground truth for our test set was obtained by averaging two pediatric radiologist reads compared to our training data for which only a single read was used. This suggests that despite relatively noisy training data, the algorithm could successfully model the variation between observers and generate estimates that are close to the expected ground truth.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

ESM data downscaling: a comparison of super-resolution deep learning models

Abstract Climate projections at fine spatial resolutions are required to conduct accurate risk assessment for critical infrastructure and design adaptation planning. Generating these projections using advanced Earth system models (ESM) requires significant computational resources. To address this issue, various statistical downscaling techniques have been introduced to generate fine-resolution data from coarse-resolution simulations. In this study, we evaluate and compare five deep learning-based downscaling techniques, namely, super-resolution convolutional neural networks, fast super-resolution convolutional neural network ESM, efficient sub-pixel convolutional neural network, enhanced deep residual network (EDRN), and super-resolution generative adversarial network (SRGAN). These techniques are applied to a dataset generated by the Energy Exascale Earth System Model (E3SM), focusing on key surface variables such as surface temperature, shortwave heat flux, and longwave heat flux. Models are trained and validated using paired fine-resolution (0.25 $$^{\circ }$$ ∘ ) and coarse-resolution (1 $$^{\circ }$$ ∘ ) monthly data obtained from a 9-year simulation. Next, blind testing is performed using monthly data obtained from two different years outside of the training and validation set. To evaluate the efficiency of each technique, different statistical metrics are used, including mean squared error (MSE), peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and learned perceptual image patch similarity (LPIPS). The results show that EDRN outperforms other algorithms in terms of PSNR, SSIM, and MSE, but struggles to capture fine-scale features in the data. In contrast, SRGAN, a generative model that uses perceptual loss, excels in capturing fine details at boundaries and internal structures, resulting in lower LPIPS than other methods.

Pawar, Nikhil M. (ORCID:0000000211613289)↗

An innovative heterogeneous transfer learning framework to enhance the scalability of deep reinforcement learning controllers in buildings with integrated energy systems

Deep Reinforcement Learning (DRL)-based control shows enhanced performance in the management of integrated energy systems when compared with Rule-Based Controllers (RBCs), but it still lacks scalability and generalisation due to the necessity of using tailored models for the training process. Transfer Learning (TL) is a potential solution to address this limitation. However, existing TL applications in building control have been mostly tested among buildings with similar features, not addressing the need to scale up advanced control in real-world scenarios with diverse energy systems. This paper assesses the performance of an online heterogeneous TL strategy, comparing it with RBC and offline and online DRL controllers in a simulation setup using EnergyPlus and Python. The study tests the transfer in both transductive and inductive settings of a DRL policy designed to manage a chiller coupled with a Thermal Energy Storage (TES). The control policy is pre-trained on a source building and transferred to various target buildings characterised by an integrated energy system including photovoltaic and battery energy storage systems, different building envelope features, occupancy schedule and boundary conditions (e.g., weather and price signal). The TL approach incorporates model slicing, imitation learning and fine-tuning to handle diverse state spaces and reward functions between source and target buildings. Results show that the proposed methodology leads to a reduction of 10% in electricity cost and between 10% and 40% in the mean value of the daily average temperature violation rate compared to RBC and online DRL controllers. Moreover, online TL maximises self-sufficiency and self-consumption by 9% and 11% with respect to RBC. Conversely, online TL achieves worse performance compared to offline DRL in either transductive or inductive settings. However, offline Deep Reinforcement Learning (DRL) agents should be trained at least for 15 episodes to reach the same level of performance as the online TL. Therefore, the proposed online TL methodology is effective, completely model-free and it can be directly implemented in real buildings with satisfying performance.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Robust deep learning framework for constitutive relations modeling

Modeling the full-range deformation behaviors of materials under complex loading and materials conditions is a significant challenge for constitutive relations (CRs) modeling. Here, we propose a general encoder-decoder deep learning framework that can model high-dimensional stress-strain data and complex loading histories with robustness and universal capability. The framework employs an encoder to project high-dimensional input information (e.g., loading history, loading conditions, and materials information) to a lower-dimensional hidden space and a decoder to map the hidden representation to the stress of interest. We evaluated various encoder architectures, including gated recurrent unit (GRU), GRU with attention, temporal convolutional network (TCN), and the Transformer encoder, on two complex stress-strain datasets that were designed to include a wide range of complex loading histories and loading conditions. All architectures achieved excellent test results with an root-mean-square error (RMSE) below 1 MPa. Additionally, we analyzed the capability of the different architectures to make predictions on out-of-domain applications, with an uncertainty estimation based on deep ensembles. The proposed approach provides a robust alternative to empirical/semi-empirical models for CRs modeling, offering the potential for more accurate and efficient materials design and optimization.

36 MATERIALS SCIENCE↗

Potential of deep learning methods to enhance satellite-based monitoring of nuclear power plants focusing on remote operation evaluations

The anticipated expansion of the nuclear industry and the deployment of new nuclear reactors (200 + GW of new nuclear capacity by 2050) require the development of monitoring systems that align with safety and security concerns, providing enhanced evaluation capabilities. A remote monitoring system using satellites and deep learning techniques was evaluated for its ability to detect anomalies and capture various features of nuclear reactors independently of the conditions on the ground. Satellite images of current operational and under-construction nuclear power plants were collected from Google Earth Pro as a surrogate database. Subsequently, five datasets were created from the collected images. Transfer learning technique was used for several classification tasks utilizing VGG16, ResNet50V2, Xception, DenseNet121, and MobileNetV2 pre-trained models. In the first task, the capability of the monitoring system to detect abnormal conditions or processes in a nuclear power plant was investigated. In the second task, the ability to capture operational features remotely was examined. As an example, for the purposes of this study, these features included classifying reactors based on type, power range, or onsite condition. Several evaluation metrics were used to compare the performance of the pre-trained models and the overall monitoring system. Here, the evaluation results demonstrated that deep learning techniques and pre-trained models applied to satellite images have the potential to facilitate further and expand capabilities in monitoring systems to assess plant operation details.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Predicting RNA structure and dynamics with deep learning and solution scattering

Advanced deep learning and statistical methods can predict structural models for RNA molecules. However, RNAs are flexible, and it remains difficult to describe their macromolecular conformations in solutions where varying conditions can induce conformational changes. Small-angle x-ray scattering (SAXS) in solution is an efficient technique to validate structural predictions by comparing the experimental SAXS profile with those calculated from predicted structures. There are two main challenges in comparing SAXS profiles to RNA structures: the absence of cations essential for stability and charge neutralization in predicted structures and the inadequacy of a single structure to represent RNA’s conformational plasticity. We introduce a solution conformation predictor for RNA (SCOPER) to address these challenges. This pipeline integrates kinematics-based conformational sampling with the innovative deep learning model, IonNet, designed for predicting Mg 2+ ion binding sites. Validated through benchmarking against 14 experimental data sets, SCOPER significantly improved the quality of SAXS profile fits by including Mg 2+ ions and sampling of conformational plasticity. We observe that an increased content of monovalent and bivalent ions leads to decreased RNA plasticity. Therefore, carefully adjusting the plasticity and ion density is crucial to avoid overfitting experimental SAXS data. SCOPER is an efficient tool for accurately validating the solution state of RNAs given an initial, sufficiently accurate structure and provides the corrected atomistic model, including ions.

59 BASIC BIOLOGICAL SCIENCES↗

A network model for natural ventilation simulation in deep buried underground structures

The study of underground natural ventilation opportunities has become increasingly significant in recent years with its promise of wide application in underground structures such as underground hydro power stations, metro stations, underground parking and laboratories. It is recognized that deployment of natural ventilation constitutes a passive technology that can lead to significant energy conservation if applied judiciously. This paper focuses on underground buildings that are buried deeply and typically consist of an underground complex network of connected structures. The other characteristic is that these structures house machinery and devices that generate heat, leading to elevated internal air temperatures. Combined with the deep location, it implies that buoyancy forces are significant which make natural ventilation through vertical shaft openings a viable option. These characteristics demand a study of the heat transfer processes between ambient conditions, soil and underground buildings. In this paper, we present a dynamic flow network model with loops for multizone airflow and apply it to deep buried underground structures considering the dominant heat transfer characteristics, not only through the elements of the network but also the heat exchange with the envelope and adjacent soil mass. Finally, a small-scale experiment of occurring airflow is conducted and compared with the outcomes of the dynamic simulation of the proposed model. The comparison serves as validation and illustration of the application potential of the network model for natural ventilation investigation and consecutive optimization of its use in underground buildings.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Comprehensive parametric study of CO 2 sequestration in deep saline aquifers

Carbon dioxide injection in deep saline aquifers is a key method for permanently sequestering anthropogenic CO 2 . Here this study employs a reactive transport model to explore mineral precipitation/dissolution and its impact on reservoir properties in deep saline aquifers. We also assess capillary pressure and relative permeability hysteresis on various CO 2 trapping mechanisms. Results from this study reveal the significant influence of initial brine composition on mineral precipitation/dissolution. The dissolution and precipitation of minerals have different effects around the wellbores compared to the overall reservoir. Additionally, salt concentration (Ca ++ and Mg ++ ) and quartz surface area affect CO 2 mineralization, while Na + impacts halite precipitation, altering flow properties. The effect of capillary pressure is significant, as including the capillary pressure in the simulation case resulted in significantly improved CO 2 trapping, achieving almost total dissolution of the injected CO 2 in around 300 years. This study offers novel insights into the interactions of reservoir minerals, brine properties, and the injected CO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

COVID-19 dynamics across the US: A deep learning study of human mobility and social behavior

This paper presents a deep learning framework for epidemiology system identification from noisy and sparse observations with quantified uncertainty. The proposed approach employs an ensemble of deep neural networks to infer the time-dependent reproduction number of an infectious disease by formulating a tensor-based multi-step loss function that allows us to efficiently calibrate the model on multiple observed trajectories. The method is applied to a mobility and social behavior-based SEIR model of COVID-19 spread. The model is trained on Google and Unacast mobility data spanning a period of 66 days, and is able to yield accurate future forecasts of COVID-19 spread in 203 US counties within a time-window of 15 days. Interestingly, a sensitivity analysis that assesses the importance of different mobility and social behavior parameters reveals that attendance of close places, including workplaces, residential, and retail and recreational locations, has the largest impact on the effective reproduction number. Furthermore, the model enables us to rapidly probe and quantify the effects of government interventions, such as lock-down and re-opening strategies. Taken together, the proposed framework provides a robust workflow for data-driven epidemiology model discovery under uncertainty and produces probabilistic forecasts for the evolution of a pandemic that can judiciously provide information for policy and decision making. All codes and data accompanying this manuscript are available at https://github.com/PredictiveIntelligenceLab/DeepCOVID19.

60 APPLIED LIFE SCIENCES↗

Evaluation of low-exergy heating and cooling systems and topology optimization for deep energy savings at the urban district level

District energy systems have the potential to achieve deep energy savings by leveraging the density and diversity of loads in urban districts. However, planning and adoption of district thermal energy systems is hindered by the analytical burden and high infrastructure costs. It is hypothesized that network topology optimization would enable wider adoption of advanced (ambient temperature) district thermal energy systems, resulting in energy savings. In this study, energy modeling is used to compare the energy performance of “conventional” and “advanced” district thermal energy systems at the urban district level, and a partial exhaustive search is used to evaluate a heuristic for the topology optimization problem. For the prototypical district considered, advanced district thermal energy systems mated with low-exergy building heating and cooling systems achieved a source energy use intensity that was 49% lower than that of conventional systems. The minimal spanning tree heuristic was demonstrated to be effective for the network topology optimization problem in the context of a prototypical district, and contributes to mitigating the problem’s computational complexity. The work presented in this paper demonstrates the potential of advanced district thermal energy systems to achieve deep energy savings, and advances to addressing barriers to their adoption through topology optimization.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Building thermal dynamics modeling with deep transfer learning using a large residential smart thermostat dataset

Understanding thermal dynamics and obtaining the computational model of residential buildings enable its scaled application in energy retrofits, control optimization and decarbonization. In this paper, we present a deep learning approach to model building thermal dynamics with smart thermostat data collected from residential buildings, with the goal to investigate model generalizability. In the first stage, we developed and compared different Deep Learning architectures including Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM) models and CNN-LSTM to predict indoor air temperature in a multi-step time horizon. In the second stage, we implemented a Transfer Learning (TL) process, which aims to improve the prediction performance on a new set of buildings (targets), exploiting the knowledge of related or similar buildings (sources). Different TL strategies and source model identification methods were investigated. The study showed that the CNN-LSTM performed the best among the architectures compared, with an average Mean Absolute Error (MAE) of 0.26 °C for one-hour-ahead (twelve 5-min future steps) predictions. Furthermore, the results showed that freezing the LSTM layer and fine-tuning the other layers of the CNN-LSTM achieved the best performance among four TL strategies, which further improved the performance with respect to a machine learning approach by 10%, and proving the effectiveness and generalizability of the proposed approach. A comparison of three different source model identification methods showed that randomly selecting source models constrained by similar building characteristics can provide good TL performance while retaining simplicity comparing with other quantitative source identification methods.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Recent seawater intrusion into deep aquifer determined by the radioactive noble-gas isotopes 81 Kr and 39 Ar

Radioactive noble-gas isotopes tracers 81 Kr and 39 Ar are used for the first time to measure the residence times of deep (~1000 m) saline coastal groundwater, and to determine its connection mode with the sea. The average rate of seawater intrusion into the deep aquifer in Israel, located near the Mediterranean Sea, is estimated. 81 Kr-ages of the saline water samples, found to be younger than 40 ka, contradict previously estimated ages of up to several million years based on hydrogeological considerations. The new results imply a stronger and more recent connection between the aquifer and the sea, and indicate that the intrusion occurred during the sea-level rise that began about 20 ka ago. These coastal aquifers need to be managed with caution because lowering of the adjacent fresh water level due to over pumping could accelerate seawater intrusion in a relatively short time. As a result, this study demonstrates the suitability of these two noble-gas tracers for the examination of hydrogeological systems in general and for the study of seawater intrusion in particular.

39Ar↗

A deep redox proteome profiling workflow and its application to skeletal muscle of a Duchenne Muscular Dystrophy model

Perturbation to the redox state accompanies many diseases and its effects are viewed through oxidation of biomolecules, including proteins, lipids, and nucleic acids. The thiol groups of protein cysteine residues undergo an array of redox post-translational modifications (PTMs) that are important for regulation of protein and pathway function. To better understand what proteins are redox regulated following a perturbation, it is important to be able to comprehensively profile protein thiol oxidation at the proteome level. Herein, we report a deep redox proteome profiling workflow and demonstrate its application in measuring the changes in thiol oxidation along with global protein expression in skeletal muscle from mdx mice, a model of Duchenne Muscular Dystrophy (DMD). In depth coverage of the thiol proteome was achieved with >18,000 Cys sites from 5608 proteins in muscle being quantified. Compared to the control group, mdx mice exhibit markedly increased thiol oxidation, where ~2% shift in the median oxidation occupancy was observed. Further, pathway analysis for the redox data revealed that coagulation system and immune-related pathways were among the most susceptible to increased thiol oxidation in mdx mice, whereas protein abundance changes were more enriched in pathways associated with bioenergetics. This study illustrates the importance of deep redox profiling in gaining greater insight into oxidative stress regulation and pathways/processes that are perturbed in an oxidizing environment.

60 APPLIED LIFE SCIENCES↗

A dual-site Langmuir equation for accurate estimation of high pressure deep shale gas resources

Adsorbed methane makes up a large portion of the total shale gas-in-place (GIP) resource in deep shale formations. In order to accurately estimate the shale GIP resource, it is crucial to understand the relationship between the adsorbed methane quantity and the free methane quantity of shale gas in shale formations (under high pressure conditions). Here this work describes and accurately predicts high pressure methane adsorption behavior in Longmaxi shale (China) using a dual-site Langmuir model. Laboratory measurements of high pressure methane adsorption (303–355 K and up to 27 MPa) are presented. Our findings show that for depths greater than 1000 m (>15 MPa) in the subsurface, the shale gas resources have historically been significantly overestimated. For Longmaxi shale (2500–3000 m in depth), classical approaches overestimate the GIP by up to 35%. The ratio of the adsorbed phase compared to the free gas has been significantly underestimated. The methods used herein allow accurate estimations of the true shale GIP resource and the relative quantity of adsorbed methane at in situ temperatures and pressures representative of deep shale formations.

04 OIL SHALES AND TAR SANDS↗

CO 2 storage site characterization using ensemble-based approaches with deep generative models

Estimating spatially distributed properties such as permeability from available sparse measurements is a great challenge in efficient subsurface CO 2 storage operations. In this paper, a deep generative model that can accurately capture complex subsurface structure is tested with an ensemble-based inversion method for accurate and accelerated characterization of CO 2 storage sites. We chose Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) for its realistic reservoir property representation and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) for its robust data fitting and uncertainty quantification capability. WGAN-GP are trained to generate high-dimensional permeability fields from a low-dimensional latent space and ES-MDA then updates the latent variables by assimilating available measurements. Several subsurface site characterization examples including Gaussian, channelized, and fractured reservoirs are used to evaluate the accuracy and computational efficiency of the proposed method and the main features of the unknown permeability fields are characterized accurately with reliable uncertainty quantification. Furthermore, the estimation performance is compared with a widely-used variational, i.e., optimization-based, inversion approach, and the proposed approach outperforms the variational inversion method in several benchmark cases. We explain such superior performance by visualizing the objective function in the latent space: because of nonlinear and aggressive dimension reduction via generative modeling, the objective function surface becomes extremely complex while the ensemble approximation can smooth out the multi-modal surface during the minimization. This suggests that the ensemble-based approach works well over the variational approach when combined with deep generative models at the cost of forward model runs unless convergence-ensuring modifications are implemented in the variational inversion.

42 ENGINEERING↗

Understanding the contribution of non-carbon dioxide gases in deep mitigation scenarios

The combined 2010 emissions of methane (CH4), nitrous oxide (N2O) and the fluorinated gasses (F-gas) account for about 20-30% of total emissions and about 30% of radiative forcing. At the moment, most studies looking at reaching ambitious climate targets project the emission of carbon dioxide (CO2) to be reduced to zero (or less) by the end of the century. As for non-CO2 gases, the mitigation potential seem to be more constrained, we find that by the end of the century in the current deep mitigation scenarios non-CO2 emissions could form the lion’s share of remaining greenhouse gas emissions. In order to support effective climate policy strategies, in this paper we provide a more in-depth look at the role of non-CO2¬ emission sources (CH4, N2O and F-gases) in achieving deep mitigation targets (radiative forcing target of 2.8 W/m2 in 2100). Specifically, we look at the sectorial mitigation potential and the remaining non-CO2 emissions. By including a set of different models, we provide some insights into the associated uncertainty. Most of the remaining methane emissions in 2100 in the climate mitigation scenario come from the livestock sector. Strong reductions are seen in the energy supply sector across all models. For N2O, less reduction potential is seen compared to methane and the sectoral differences are larger between the models. The paper shows that the assumptions on remaining non-CO2 emissions are critical for the feasibility of reaching ambitious climate targets and the associated costs.

Gernaat, David↗

On the influence of over-parameterization in manifold based surrogates and deep neural operators

Constructing accurate and generalizable approximators (surrogate models) for complex physico-chemical processes exhibiting highly non-smooth dynamics is challenging. The main question is what type of surrogate models we should construct and should these models be under-parameterized or over-parameterized. In this work, we propose new developments and perform comparisons for two promising approaches: manifold-based polynomial chaos expansion (m-PCE) and the deep neural operator (DeepONet), and we examine the effect of over-parameterization on generalization. While m-PCE enables the construction of a mapping by first identifying low-dimensional embeddings of the input functions, parameters, and quantities of interest (QoIs), a neural operator learns the nonlinear mapping via the use of deep neural networks. Here, we demonstrate the performance of these methods in terms of generalization accuracy by solving the 2D time-dependent Brusselator reaction-diffusion system with uncertainty sources, modeling an autocatalytic chemical reaction between two species. We first propose an extension of the m-PCE by constructing a mapping between latent spaces formed by two separate embeddings of the input functions and the output QoIs. To further enhance the accuracy of the DeepONet, we introduce weight self-adaptivity in the loss function. We demonstrate that the performance of m-PCE and DeepONet is comparable for cases of relatively smooth input-output mappings. However, when highly non-smooth dynamics is considered, DeepONet shows higher approximation accuracy. We also find that for m-PCE, modest over-parameterization leads to better generalization, both within and outside of distribution, whereas aggressive over-parameterization leads to over-fitting. In contrast, an even highly over-parameterized DeepONet leads to better generalization for both smooth and non-smooth dynamics. Furthermore, we compare the performance of the above models with another recently proposed operator learning model, the Fourier Neural Operator, and show that its over-parameterization also leads to better generalization. Taken together, our studies show that m-PCE can provide very good accuracy at very low training cost, whereas a highly over-parameterized DeepONet can provide better accuracy and robustness to noise but at higher training cost. In both methods, the inference cost is negligible.

97 MATHEMATICS AND COMPUTING↗

A hybrid deep neural operator/finite element method for ice-sheet modeling

One of the most challenging and consequential problems in climate modeling is to provide probabilistic projections of sea level rise. A large part of the uncertainty of sea level projections is due to uncertainty in ice sheet dynamics. At the moment, accurate quantification of the uncertainty is hindered by the cost of ice sheet computational models. In this work we develop a hybrid approach to approximate existing ice sheet models at a fraction of their cost. Our approach consists of replacing the finite element model for the momentum equations for the ice velocity, the most expensive part of an ice sheet model, with a Deep Operator Network, while we retain a classic finite element discretization for the evolution of the ice thickness. We show that the resulting hybrid model is very accurate and it is an order of magnitude faster than the traditional finite element model. Further, a distinctive feature of the proposed model, compared to other neural network approaches, is that it can handle high-dimensional parameter spaces (parameter fields) such as the basal friction at the bed of the glacier and can therefore be used for generating samples for uncertainty quantification. Further, we study the impact of hyper-parameters, number of unknowns and correlation length of the parameter distribution on the training and accuracy of the Deep Operator Network on a synthetic ice sheet model. We then target the evolution of the Humboldt glacier in Greenland and show that our hybrid model can provide accurate statistics of the glacier mass loss and can be effectively used to accelerate the quantification of uncertainty.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗