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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.

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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Scaling Deep Learning workloads: NVIDIA DGX-1/Pascal and Intel Knights Landing

Deep Learning (DL) algorithms have become ubiquitous in data analytics. As a result, major computing vendors—including NVIDIA, Intel, AMD, and IBM—have architectural road maps influenced by DL workloads. Furthermore, several vendors have recently advertised new computing products as accelerating large DL workloads. Unfortunately, it is difficult for data scientists to quantify the potential of these different products. Here, this article provides a performance and power analysis of important DL workloads on two major parallel architectures: NVIDIA DGX-1 (eight Pascal P100 GPUs interconnected with NVLink) and Intel Knights Landing (KNL) CPUs interconnected with Intel Omni-Path or Cray Aries. Our evaluation consists of a cross section of convolutional neural net workloads: CifarNet, AlexNet, GoogLeNet, and ResNet50 topologies using the Cifar10 and ImageNet datasets. The workloads are vendor-optimized for each architecture. We use sequentially equivalent implementations to maintain iso-accuracy between parallel and sequential DL models. Our analysis indicates that although GPUs provide the highest overall performance, the gap can close for some convolutional networks; and the KNL can be competitive in performance/watt. We find that NVLink facilitates scaling efficiency on GPUs. However, its importance is heavily dependent on neural network architecture. Furthermore, for weak-scaling—sometimes encouraged by restricted GPU memory—NVLink is less important.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Range and Performance Optimized Version of the Computer-Aided Speckle Interferometry Algorithm for Real-Time Displacement-Strain Field Monitoring

Abstract This work presents an optimized implementation of the Computer-Aided Speckle Interferometry algorithm which enables full-field determination of displacements and strains on commodity Graphics Processing Units at high resolution and frame rates. By combining careful control of the average speckle size in a laser speckle pattern with a simple sampling rate conversion scheme, a compact representation of the optical speckle is achieved. This allows for optimal use of Graphics Processing Unit architecture with robust range extension. The optimal mapping of the Computer-Aided Speckle Interferometry algorithm to Graphics Processing Unit architecture is shown in detail, and a straightforward method for disambiguating large displacements is illustrated. Lastly, this paper demonstrates a two-step subimage-tapering modification to the original algorithm that enables robust range enhancement while maintaining resolution. Results from numerical simulations on synthetic speckle patterns are shown, and runtime performance metrics are provided, with performance ranging up to 60 frames per second in some cases. The method is suitable for interactive experimental mechanics research, process and testing or any application where real-time high-resolution displacement-strain monitoring is needed. A .NET Framework class library enabling the incorporation of the algorithm into 3rd -party applications is available for download.

42 ENGINEERING↗
NASA NTRS2025

Assessment of Model Outcomes Between the Integrated Medical Model (IMM) and the Medical Extensible Dynamic Probabilistic Risk Assessment Tool (MEDPRAT)

The Medical Extensible Dynamic Probabilistic Risk Assessment Tool (MEDPRAT) is a computational model that provides human health and medical risk predictions for crewed spaceflight missions. MEDPRAT utilizes discrete event modeling and dynamic probabilistic simulation to predict critical mission outcomes (total medical events, crew health index, quality time lost, loss of crew life, removal to definitive care), condition occurrences, and resource consumption. Input parameters for MEDPRAT include crew attributes (e.g., sex), types of mission activities (e.g., whether and where crew members perform an extravehicular activity (EVA)), available resources, treatment information, and probability distributions for medical conditions. As an evolution of the Integrated Medical Model (IMM), MEDPRAT provides enhanced capabilities and higher fidelity, and incorporates more appropriate assumptions for long-duration spaceflight. IMM is the currently accepted standard for quantifying spaceflight mission medical risk in NASA operations that uses a probabilistic risk assessment (PRA) approach. MEDPRAT builds on the same logical foundation as IMM but implements the model architecture through highly optimized Monte Carlo sampling methods. An analysis is performed comparing the outputs from IMM with those from MEDPRAT V1.0 and V2.0 for the same reference missions in order to quantify similarities and differences in the model outcomes. The juxtaposition between IMM and MEDPRAT V1.0 and 2.0 shown in this report demonstrates that these two models generate very similar results; where differences in outcomes are shown, these are in accordance with the underlying assumptions and differences in the model architectures. This validation effort further establishes the credibility and reliability of the MEDPRAT software.

Matthew T Prelich↗
DOE OSTI2022

Scalable deep learning for watershed model calibration

Watershed models such as the Soil and Water Assessment Tool (SWAT) consist of high-dimensional physical and empirical parameters. These parameters often need to be estimated/calibrated through inverse modeling to produce reliable predictions on hydrological fluxes and states. Existing parameter estimation methods can be time consuming, inefficient, and computationally expensive for high-dimensional problems. In this paper, we present an accurate and robust method to calibrate the SWAT model (i.e., 20 parameters) using scalable deep learning (DL). We developed inverse models based on convolutional neural networks (CNN) to assimilate observed streamflow data and estimate the SWAT model parameters. Scalable hyperparameter tuning is performed using high-performance computing resources to identify the top 50 optimal neural network architectures. We used ensemble SWAT simulations to train, validate, and test the CNN models. We estimated the parameters of the SWAT model using observed streamflow data and assessed the impact of measurement errors on SWAT model calibration. We tested and validated the proposed scalable DL methodology on the American River Watershed, located in the Pacific Northwest-based Yakima River basin. Our results show that the CNN-based calibration is better than two popular parameter estimation methods (i.e., the generalized likelihood uncertainty estimation [GLUE] and the dynamically dimensioned search [DDS], which is a global optimization algorithm). For the set of parameters that are sensitive to the observations, our proposed method yields narrower ranges than the GLUE method but broader ranges than values produced using the DDS method within the sampling range even under high relative observational errors. The SWAT model calibration performance using the CNNs, GLUE, and DDS methods are compared using R 2 and a set of efficiency metrics, including Nash-Sutcliffe, logarithmic Nash-Sutcliffe, Kling-Gupta, modified Kling-Gupta, and non-parametric Kling-Gupta scores, computed on the observed and simulated watershed responses. The best CNN-based calibrated set has scores of 0.71, 0.75, 0.85, 0.85, 0.86, and 0.91. The best DDS-based calibrated set has scores of 0.62, 0.69, 0.8, 0.77, 0.79, and 0.82. The best GLUE-based calibrated set has scores of 0.56, 0.58, 0.71, 0.7, 0.71, and 0.8. The scores above show that the CNN-based calibration leads to more accurate low and high streamflow predictions than the GLUE and DDS sets. Our research demonstrates that the proposed method has high potential to improve our current practice in calibrating large-scale integrated hydrologic models.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2016

Model-Based Engine Control Architecture with an Extended Kalman Filter

This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The nonlinear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.

engine control↗
NASA NTRS2016

Model-Based Engine Control Architecture with an Extended Kalman Filter

This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The non-linear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.

engine control↗
DOE OSTI2021

Porting the Nonlinear Optimization Library HiOp to Accelerator-Based Hardware Architectures

While interior point method has been the centerpiece of nonlinear programming tools used in science and engineering, its reliance on linear solvers that can tackle sparse symmetric indefinite and highly ill-conditioned problems made it difficult to implement it effectively on hardware accelerators. HiOp optimization package attempts to provide an implementation of the interior point method suitable for hardware accelerators by compressing the original sparse problem to produce an underlying linear problem that is dense and of manageable size. Implementations of dense linear solvers are more mature and utilize hardware accelerators better than their sparse counterparts. There is a number of important domain problems, such as optimal power flow analysis for power grids, where the sparse problem can be effectively compressed and deploying dense linear solver within the interior point method can improve performance. Here we describe a portable implementation of HiOp optimization engine, which uses a linear solver from Magma library and runs entirely on hardware accelerators. To compress the problem, HiOp uses customized mixed dense-sparse linear algebra. All HiOp kernels are implemented using Umpire and RAJA portability libraries. We describe details of the implementation and discuss trade-offs between performance, portability and development cost.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Parallel algorithms for mapping pipelined and parallel computations

Many computational problems in image processing, signal processing, and scientific computing are naturally structured for either pipelined or parallel computation. When mapping such problems onto a parallel architecture it is often necessary to aggregate an obvious problem decomposition. Even in this context the general mapping problem is known to be computationally intractable, but recent advances have been made in identifying classes of problems and architectures for which optimal solutions can be found in polynomial time. Among these, the mapping of pipelined or parallel computations onto linear array, shared memory, and host-satellite systems figures prominently. This paper extends that work first by showing how to improve existing serial mapping algorithms. These improvements have significantly lower time and space complexities: in one case a published O(nm sup 3) time algorithm for mapping m modules onto n processors is reduced to an O(nm log m) time complexity, and its space requirements reduced from O(nm sup 2) to O(m). Run time complexity is further reduced with parallel mapping algorithms based on these improvements, which run on the architecture for which they create the mappings.

Nicol, David M.↗
NASA NTRS1995

CFD research, parallel computation and aerodynamic optimization

Over five years of research in Computational Fluid Dynamics and its applications are covered in this report. Using CFD as an established tool, aerodynamic optimization on parallel architectures is explored. The objective of this work is to provide better tools to vehicle designers. Submarine design requires accurate force and moment calculations in flow with thick boundary layers and large separated vortices. Low noise production is critical, so flow into the propulsor region must be predicted accurately. The High Speed Civil Transport (HSCT) has been the subject of recent work. This vehicle is to be a passenger vehicle with the capability of cutting overseas flight times by more than half. A successful design must surpass the performance of comparable planes. Fuel economy, other operational costs, environmental impact, and range must all be improved substantially. For all these reasons, improved design tools are required, and these tools must eventually integrate optimization, external aerodynamics, propulsion, structures, heat transfer and other disciplines.

Ryan, James S.↗
DOE OSTI2022

Hypothesis testing via AI: Generating physically interpretable models of scientific data with machine learning (Full Technical Report)

Deep learning has demonstrated an exceptional ability to solve complex tasks (an engineering success); however, it has done so at the expense of the ability to generate new knowledge (a scientific failure). We propose an alternative framework—entitled Deep Symbolic Regression (DSR)—in which artificial neural networks (NNs) rapidly generate hypotheses about physical relationships among inputs. This framework bypasses the need to interpret an NN altogether, while still leveraging the representational power of deep learning. The resulting models are tractable mathematical expressions, which are inherently and readily human interpretable and can provide insights into underlying physical phenomena. Further, we fold this methodology into the scientific process by allowing the scientist to directly integrate a priori knowledge and beliefs to accelerate learning. We demonstrate this methodology on symbolic regression—the problem of rediscovering underlying expressions describing a dataset—and achieve state-of-the-art performance across a wide variety of symbolic regression problems. Further, we generalize our DSR framework to apply to the more general class of symbolic optimization problems, in which one seeks to optimize a sequence of symbols or “tokens” under a black-box reward function. Examples of other symbolic optimization problems include neural architecture search and computational antibody design. Our generalized tool, Deep Symbolic Optimization (DSO), has been demonstrated on the task of learning symbolic control policies for reinforcement learning environments, and has been adopted as an enabling capability for computational antibody design.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

TH-AB-BRA-07: PENELOPE-Based GPU-Accelerated Dose Calculation System Applied to MRI-Guided Radiation Therapy

Purpose: The clinical commissioning of IMRT subject to a magnetic field is challenging. The purpose of this work is to develop a GPU-accelerated Monte Carlo dose calculation platform based on PENELOPE and then use the platform to validate a vendor-provided MRIdian head model toward quality assurance of clinical IMRT treatment plans subject to a 0.35 T magnetic field. Methods: We first translated PENELOPE from FORTRAN to C++ and validated that the translation produced equivalent results. Then we adapted the C++ code to CUDA in a workflow optimized for GPU architecture. We expanded upon the original code to include voxelized transport boosted by Woodcock tracking, faster electron/positron propagation in a magnetic field, and several features that make gPENELOPE highly user-friendly. Moreover, we incorporated the vendor-provided MRIdian head model into the code. We performed a set of experimental measurements on MRIdian to examine the accuracy of both the head model and gPENELOPE, and then applied gPENELOPE toward independent validation of patient doses calculated by MRIdian’s KMC. Results: We achieve an average acceleration factor of 152 compared to the original single-thread FORTRAN implementation with the original accuracy preserved. For 16 treatment plans including stomach (4), lung (2), liver (3), adrenal gland (2), pancreas (2), spleen (1), mediastinum (1) and breast (1), the MRIdian dose calculation engine agrees with gPENELOPE with a mean gamma passing rate of 99.1% ± 0.6% (2%/2 mm). Conclusions: We developed a Monte Carlo simulation platform based on a GPU-accelerated version of PENELOPE. We validated that both the vendor provided head model and fast Monte Carlo engine used by the MRIdian system are accurate in modeling radiation transport in a patient using 2%/2 mm gamma criteria. Future applications of this platform will include dose validation and accumulation, IMRT optimization, and dosimetry system modeling for next generation MR-IGRT systems.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Best Practices for Grid Communications

As the grid evolves, the communications architecture will need to evolve with it. That architecture affords a structured means by which the evolving complexities of the modern electric grid can be managed. This document provides best practices that can be implemented in the grid of today and evolve towards the grid and grid architecture of the future. The evolving grid and its control communications increasingly rely on commercial communications providers and a variety of technologies, from wireless (e.g., 5G, microwave, Wi-Fi) to wireline (fiber, copper) to radio communications (P25, other repeater-based systems), and all these communications systems rely on electric power. A reliable and resilient grid must account for this complex set of interdependencies in its planning activities, especially those involving restoration and recovery. The participation of all relevant parties in both planning and exercising of plans can prevent unexpected conditions that impede the reliable operation and recovery of the grid. Best practices for grid communications include using a Network Management System to document the operational state, define and monitor baselines, detect changes, and accelerate response to abnormalities. If transitioning from SONET to IP/packet-based systems, translating grid requirements into communications requirements for latency, bandwidth and throughput, IP packet delay variation, packet loss, and availability should inform and drive technology planning and selection as well as that communication system’s Quality of Service (QoS) policies and Service Level Agreements (SLAs). Secure and reliable timing is another key component of a reliable and resilient grid that can operate through adverse events. A trusted internal NTP configuration, an integrated and diverse timing delivery system, optimizing the timing architecture based on the transport technologies of the communications system, and using established standards can deliver the level of timing accuracy required by a range of time-sensitive power system applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2016

A GPU-accelerated Monte Carlo dose calculation platform and its application toward validating an MRI-guided radiation therapy beam model

Purpose: The clinical commissioning of IMRT subject to a magnetic field is challenging. The purpose of this work is to develop a GPU-accelerated Monte Carlo dose calculation platform based on PENELOPE and then use the platform to validate a vendor-provided MRIdian head model toward quality assurance of clinical IMRT treatment plans subject to a 0.35 T magnetic field. Methods: PENELOPE was first translated from FORTRAN to C++ and the result was confirmed to produce equivalent results to the original code. The C++ code was then adapted to CUDA in a workflow optimized for GPU architecture. The original code was expanded to include voxelized transport with Woodcock tracking, faster electron/positron propagation in a magnetic field, and several features that make gPENELOPE highly user-friendly. Moreover, the vendor-provided MRIdian head model was incorporated into the code in an effort to apply gPENELOPE as both an accurate and rapid dose validation system. A set of experimental measurements were performed on the MRIdian system to examine the accuracy of both the head model and gPENELOPE. Ultimately, gPENELOPE was applied toward independent validation of patient doses calculated by MRIdian’s KMC. Results: An acceleration factor of 152 was achieved in comparison to the original single-thread FORTRAN implementation with the original accuracy being preserved. For 16 treatment plans including stomach (4), lung (2), liver (3), adrenal gland (2), pancreas (2), spleen(1), mediastinum (1), and breast (1), the MRIdian dose calculation engine agrees with gPENELOPE with a mean gamma passing rate of 99.1% ± 0.6% (2%/2 mm). Conclusions: A Monte Carlo simulation platform was developed based on a GPU- accelerated version of PENELOPE. This platform was used to validate that both the vendor-provided head model and fast Monte Carlo engine used by the MRIdian system are accurate in modeling radiation transport in a patient using 2%/2 mm gamma criteria. Future applications of this platform will include dose validation and accumulation, IMRT optimization, and dosimetry system modeling for next generation MR-IGRT systems.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Soft Core/Shell Packages for Stretchable Electronics

This paper presents materials and core/shell architectures that provide optimized mechanical properties in packages for stretchable electronic systems. Detailed experimental and theoretical studies quantitatively connect the geometries and elastic properties of the constituent materials to the overall mechanical responses of the integrated systems, with a focus on interfacial stresses, effective modulus, and maximum extent of elongation. Specific results include core/shell designs that lead to peak values of the shear and normal stresses on the skin that remain less than 10 kPa even for applied strains of up to 20%, thereby inducing minimal somatosensory perception of the device on the human skin. Additional, strain-limiting mesh structures embedded in the shell improve mechanical robustness by protecting the active components from strains that would otherwise exceed the fracture point. Demonstrations in precommercial stretchable electronic systems illustrate the utility of these concepts.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Impacts of the Conductive Networks on Solid‐State Battery Operation

The micromorphology of composite cathodes is known to play a vital role in determining all-solid-state battery (ASSB) performance. However, much of our current understanding is derived from empirical observations, lacking a deeper mechanistic foundation. The “rocking chair” concept of battery chemistry requires maintaining charge neutrality, emphasizing the necessity of examining electrode micromorphology from the perspective of conductive networks. This study systematically investigates the microscopic electrochemical impacts of conductive network micromorphology by varying the Li + -to-e − channel ratio in cathodes comprising LiNbO 3 -coated LiNi 0.8 Co 0.1 Mn 0.1 O 2 , Li 6 PS 5 Cl, and carbon fibers. Utilizing multiscale synchrotron-based spectro-microscopy, we unravel that unbalanced Li + and e − conducting channels intensify charge polarization within active cathode particles and accelerate their degradation. A further model system with X-ray nano-tomography resolved e − and Li + channels indicates that spatially uniform and well-paired Li + and e − conducting channels are highly desirable as they could promote more uniform lithiation/delithiation, mitigating microscopic electrochemical polarization. Electrode-scale X-ray holotomography analysis reveals that the impact of conductive networks is particle-size-dependent, with smaller cathode particles being more significantly affected. These findings provide mechanistic insights into the interplay between conductive networks and all-solid-state battery operation, laying the groundwork for rational design and optimization of cathode architectures in future solid-state battery technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Advances in Machine and Deep Learning for Modeling and Real-time Detection of Multi-Messenger Sources

We live in momentous times. The science community is empowered with an arsenal of cosmic messengers to study the universe in unprecedented detail. Gravitational waves, electromagnetic waves, neutrinos, and cosmic rays cover a wide range of wavelengths and timescales. Combining and processing these datasets that vary in volume, speed, and dimensionality requires new modes of instrument coordination, funding, and international collaboration with a specialized human and technological infrastructure. In tandem with the advent of large-scale scientific facilities, the last decade has experienced an unprecedented transformation in computing and signal-processing algorithms. The combination of graphics processing units, deep learning, and the availability of open source, high-quality datasets has powered the rise of artificial intelligence. This digital revolution now powers a multibillion dollar industry, with far-reaching implications in technology and society. In this chapter, we describe pioneering efforts to adapt artificial intelligence algorithms to address computational grand challenges in multi-messenger astrophysics. We review the rapid evolution of these disruptive algorithms, from the first class of algorithms introduced in early 2017 to the sophisticated algorithms that now incorporate domain expertise in their architectural design and optimization schemes. We discuss the importance of scientific visualization and extreme-scale computing in reducing time-to-insight and obtaining new knowledge from the interplay between models and data.

Artificial Intelligence↗
DOE OSTI2018

An Artificial Neural Network Model to Predict the Bainite Plate Thickness of Nanostructured Bainitic Steels Using an Efficient Network-Learning Algorithm

Nanostructured bainitic steel has an extraordinary ultrahigh strength of about 2.0 GPa along with good toughness of 30 MPa m{sup 1/2}. The finer thickness of plate 20-80 nm is largely responsible for achieving such a large hardness of 690-720 HV. In this work, a multilayer perceptron-based artificial neural network (ANN) model has been developed to predict the thickness of bainite plate pertaining to nanostructured bainitic steels. The inputs of the ANN model are, namely, Gibbs free energy for bainitic transformation, austenite strength, transformation temperature for bainite and carbon concentration in the steel. The model prediction revealed that the bainite plate thickness critically depends on austenite strength and Gibbs free energy. From the neural prediction, it is concluded that formation of nanostructured bainitic steel is feasible only if sufficient austenite strength (above 165 MPa) has been achieved. This can be accomplished with a minimum carbon content of 0.5 wt.% in steel and transformation temperature below 300 °C. Higher driving force (Gibbs free energy) below − 1800 J/mol is another prerequisite condition of formation of nanostructured bainite steel. The network-learning architecture has been optimized using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to minimize the network training error within eight training cycles. The algorithm facilitates a faster convergence of network training and testing errors.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Deep learning to estimate permeability using geophysical data

Time-lapse electrical resistivity tomography (ERT) is a popular geophysical method to estimate three-dimensional (3D) permeability fields from electrical potential difference measurements. Traditional inversion and data assimilation methods are used to ingest this ERT data into hydrogeophysical models to estimate permeability. Due to ill-posedness and the curse of dimensionality, existing inversion strategies provide poor estimates and low resolution of the 3D permeability field. Recent advances in deep learning provide us with powerful algorithms to overcome this challenge. This paper presents a deep learning (DL) framework to estimate the 3D subsurface permeability from time-lapse ERT data. To test the feasibility of the proposed framework, we train DL-enabled inverse models on simulation data. Each measurement in both synthetic and field data is standardized by removing the mean and scaling the time-series to unit variance. This pre-processing step is necessary to bring simulation data closer to field observations. Subsurface process models based on hydrogeophysics are used to generate this synthetic data. Training performed on limited simulation data resulted in the DL model over-fitting. An advanced data augmentation based on mixup is implemented to generate additional training samples to overcome this issue. This mixup technique creates weakly labeled (low-fidelity) samples from strongly labeled (high-fidelity) data. The weakly labeled training data is then used to develop DL-enabled inverse models and reduce over-fitting. As both time-lapse ERT (1133048 features/realization) and 3D permeability (585453 features/realization) data samples are from a high-dimensional space, principal component analysis (PCA) is employed to reduce dimensionality. Encoded ERT and encoded permeability are generated using the trained PCA estimators. A deep neural network is then trained to map the encoded ERT to encoded permeability. This mixup training and unsupervised learning allowed us to build a fast and reasonably accurate DL-based inverse model under limited simulation data. Results show that proposed weak supervised learning can capture salient spatial features in the 3D permeability field. Quantitatively, the average mean squared error (in terms of the natural log) on the strongly labeled training, validation, and test datasets is less than 0.5. The R 2 -score (global metric) is greater than 0.75, and the percent error in each cell (local metric) is less than 10%. Finally, an added benefit in terms of computational cost is that the proposed DL-based inverse model is at least O(10 4 ) times faster than running a forward model once it is trained. Data generation, DL model training, and hyperparameter tuning to identify optimal neural network architectures utilized high-performance computing resources while the DL inference is performed on a standard laptop. Approximately, O(10 5 ) processor hours are used for generating data and DL tuning and training. We acknowledge that the data generation and DL model development are expensive. But once a DL model is trained, it can be re-used for inversion rapidly for the given system, with set physics and domain. Note that traditional inversion may require multiple forward model simulations (e.g., in the order of 10 to 1000), which are very expensive. This computational savings ≈ O(10 5 ) – O(10 7 )) makes the proposed DL-based inverse model attractive for subsurface imaging and real-time ERT monitoring applications due to fast and yet reasonably accurate estimations of permeability field.

58 GEOSCIENCES↗