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At least 883 records · Page 49

Multi-year Satellite and Surface Observations of AOD in support of Two-Column Aerosol Project (TCAP) Field Campaign

We use combined multi-year measurements from the surface and space for assessing the spatial and temporal distribution of aerosol properties within a large (~400x400 km) region centered on Cape Cod, Massachusetts, along the East Coast of the United States. The ground-based Aerosol Robotic Network (AERONET) measurements at Martha’s Vineyard Coastal Observatory (MVCO) site and Moderate Resolution Imaging Spectrometer (MODIS) sensors on board the Terra and Aqua satellites provide horizontal and temporal variations of aerosol optical depth, while the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) offers the altitudes of aerosol-layers. The combined ground-based and satellite measurements indicated several interesting features among which were the large differences in the aerosol properties observed in July and February. We applied the climatology of aerosol properties for designing the Two-Column Aerosol Project (TCAP), which is supported by the U.S. Department of Energy’s (DOE’s) Atmospheric Radiation Measurement (ARM) Program. The TCAP field campaign involves 12-month deployment (started July 1, 2012) of the ground-based ARM Mobile Facility (AMF) and Mobile Aerosol Observing System (MAOS) on Cape Cod and complimentary aerosol observations from two research aircraft: the DOE Gulfstream-1 (G-1) and the National Aeronautics and Space Administration (NASA) B200 King Air. Using results from the coordinated G-1 and B200 flights during the recent (July, 2012) Intensive Observation Period, we demonstrated that the G-1 in situ measurements and B200 active remote sensing can provide complementary information on the temporal and spatial changes of the aerosol properties off the coast of North America.

AOD↗

Back-Azimuth Estimation of Air-to-Ground Coupled Infrasound from Transverse Coherence Minimization

We present the transverse coherence minimization method (TCM)—an approach to estimate the back–azimuth of infrasound signals that are recorded on an infrasound microphone and a colocated three–component seismometer. Accurate back–azimuth information is important for a variety of monitoring efforts, but it is currently only available for infrasound arrays and for seismoacoustic sensor pairs separated by 10 s of meters. Our TCM method allows for the analysis of colocated sensor pairs, sensors located within a few meters of each other, which may extend the capabilities of existing seismoacoustic networks and supplement operating infrasound arrays. This approach minimizes the coherence of the transverse component of seismic displacement with the infrasound wave to estimate the infrasound back–azimuth. After developing an analytical model, we investigate seismoacoustic signals from the August 2012 Humming Roadrunner experiment and the 26 May 2021 eruption of Great Sitkin Volcano, Alaska, U.S.A., at the ranges of 6.5–185 km from the source. We discuss back–azimuth estimates and potential sources of deviation (1°–15°), such as local terrain effects or deviation from common analytical models. This practical method complements existing seismoacoustic tools and may be suitable for routine application to signals of interest.

58 GEOSCIENCES↗

Closing the Loop

Like all research, the concepts of exactly what a slicer should accomplish, and how, continue to evolve. The development of next-generation slicing is already underway, and this chapter introduces several related topics. This includes a new slicing paradigm driven by network connectivity, called “slice on demand.” This paradigm enables additional capabilities such as closing the loop with sensor feedback, experimental system support, and connectivity to simulation and visualization software, all of which are also discussed. Each of these concepts represents future opportunities for slicing software and supports the growing expectations of additive manufacturing technology.

Borish, Michael↗

Subsets of geostationary satellite data over international observing network sites for studying the diurnal dynamics of energy, carbon, and water cycles

The latest generation of geostationary satellites provide Earth observations similar to widely used polar-orbiting sensors but at intervals as frequently as every 5–10 min, making them ideal for studying the diurnal dynamics of land–atmosphere interactions. The NASA Earth Exchange (NEX) group created the GeoNEX datasets by collating data from several geostationary platforms, including GOES-16/17/18, Himawari-8/9, and GK-2A, and placing them on a common grid to facilitate use by the Earth science community. Here, we document the GeoNEX Coincident Ground Observations (GeCGO) dataset for terrestrial ecosystem studies and provide examples for its use. Currently, GeCGO provides GOES-16 Advanced Baseline Imager (ABI) data over a 10 km × 10 km area surrounding 1586 network sites across the Americas. GeCGO makes it easy to compare the time series of geostationary data with the diurnal ground observations, including carbon/water fluxes and aerosol optical depth, and is extensible to other regions. We also develop GeoNEXTools to facilitate analyses that require both GeoNEX data and other NASA satellite data. The objectives of this paper are to introduce GeCGO and GeoNEXTools and demonstrate their applications. First, we describe the details of GeCGO and GeoNEXTools. Second, we explain how GeCGO can be integrated with other satellite data. Finally, we showcase comparisons between GeCGO and observations from three ground-based networks. GeCGO is available at https://doi.org/10.25966/y5pe-xp41 (Hashimoto et al., 2025).

Hashimoto, Hirofumi [NASA Ames Research Center (AR↗

Steel Creek, Pen Branch, and D-Area Watershed Stream Gauging Stations

A network of stream gauging systems were installed in the Steel Creek, Pen Branch, D-Area Discharge Canal, and the D006 Stream in support of the groundwater modeling efforts for the P-Area Groundwater Operable Unit (OU); Chemical, Metals, and Pesticides (CMP) Pits OU; and the D-Area Watershed, respectively. Each location is monitored by a MACE Floseries3 FloPro data logger and a MACE doppler ultrasonic area/velocity sensor. Each stream gauging system is powered by an internal 12-volt battery supplied by a solar panel with a trickle charger. Information collected by each data logger is logged internally and telecommunicated via a cellular network to an online server for real time analysis and monitoring. The MACE doppler ultrasonic area/velocity sensor can measure stream depth and velocities to give output values of flow rates, total flow, net flow, and volumes. The water depth is measured by a ceramic pressure transducer located on the top of the sensor. The velocity is measured by a continuous wave doppler sensor to give an average velocity across the whole stream profile. This report discusses the equipment and methods used to install continuous stream gauging stations and provides a summary of data collected through FY2025.

54 ENVIRONMENTAL SCIENCES↗

Real-Time Xenon Sensor Analysis Report

Radiotracer release experiments were performed at the Nevada National Security Site in October 2022. The overall experiment was called the RElease ACTivity (REACT) experiment. Twenty-two real-time xenon sensors were deployed for each of four releases. Initial, quick-look analysis results were reported in December 2022. This report reviews the more comprehensive offline analysis effort that was conducted during the remainder of fiscal year 2023 by the Dynamic Networks venture. Improved energy stabilization routines were implemented along with an improved background subtraction routine compared to the original quicklook calculations. The relative detection efficiencies of all real-time sensors were examined. Finally, simulated detector response functions were coupled to two different meteorological models using the measured conditions for the final release (REACT-04) to compare simulated detections with measurements. While there is some agreement between the models and measured data on the detection locations and timing, there is less agreement on the magnitude of those detections. Future sensor and meteorological modeling work will be needed to improve the agreement and to examine the additional releases (REACT-01 through REACT-03).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Shortest path network interdiction with asymmetric uncertainty

Abstract This paper considers an extension of the shortest path network interdiction problem that incorporates robustness to account for parameter uncertainty. The shortest path interdiction problem is a game of two players with conflicting agendas and capabilities: an evader, who traverses the arcs of a network from a source node to a sink node using a path of shortest length, and an interdictor, who maximizes the length of the evader's shortest path by interdicting arcs on the network. It is usually assumed that the parameters defining the network are known exactly by both players. We consider the situation where the evader assumes the nominal parameter values while the interdictor uses robust optimization techniques to account for parameter uncertainty or sensor degradation. We formulate this problem as a nonlinear mixed‐integer semi‐infinite bilevel program and show that it can be converted into a mixed‐integer linear program with a second order cone constraint. We use random geometric networks and transportation networks to perform computational studies and demonstrate the unique decision strategies that our variant produces. Solving the shortest path interdiction problem with asymmetric uncertainty protects the interdictor from investing in a strategy that hinges on key interdictions performing as promised. It also provides an alternate strategy that mitigates the risk of these worst‐case possibilities.

Punla‐Green, She'ifa Z.↗

Data Quality Monitoring for the Hadron Calorimeters Using Transfer Learning for Anomaly Detection

The proliferation of sensors brings an immense volume of spatio-temporal (ST) data in many domains, including monitoring, diagnostics, and prognostics applications. Data curation is a time-consuming process for a large volume of data, making it challenging and expensive to deploy data analytics platforms in new environments. Transfer learning (TL) mechanisms promise to mitigate data sparsity and model complexity by utilizing pre-trained models for a new task. Despite the triumph of TL in fields like computer vision and natural language processing, efforts on complex ST models for anomaly detection (AD) applications are limited. In this study, we present the potential of TL within the context of high-dimensional ST AD with a hybrid autoencoder architecture, incorporating convolutional, graph, and recurrent neural networks. Motivated by the need for improved model accuracy and robustness, particularly in scenarios with limited training data on systems with thousands of sensors, this research investigates the transferability of models trained on different sections of the Hadron Calorimeter of the Compact Muon Solenoid experiment at CERN. The key contributions of the study include exploring TL’s potential and limitations within the context of encoder and decoder networks, revealing insights into model initialization and training configurations that enhance performance while substantially reducing trainable parameters and mitigating data contamination effects.

47 OTHER INSTRUMENTATION↗

Connecting the Dots: An Assessment of Cyber-risks in Networked Building and Municipal Infrastructure Systems

The buildings and city streets we walk down are changing. Driven by various data-driven use cases, there is increased interest in networking and integrating lighting and other building systems (e.g., heating, ventilation, and air conditioning (HVAC), security, scheduling) that were previously not internet-facing, and equipping them with sensors that collect information about their environment and the people that inhabit it. These data-enabled systems can potentially deliver improved occupant and resident experiences and help meet the U.S. Department of Energy (DOE) national energy and carbon reduction goals. Deploying connected devices new to being networked, however, is not without its challenges. This paper explores tools available to system designers and integrators that facilitate a cybersecurity landscape assessment – or more specifically the identification of threats, vulnerabilities, and adversarial behaviors that could be used against these networked systems. These assessments can help stakeholders shift security prioritization proactively toward the beginning of the development process.

cyber-risk assesment, adversarial behavior, MITRE ↗

The Use of Geomorphometrics for Geologic Site Characterization

The Problem: Developing an accurate geologic site characterization is difficult for denied-access sites. A good understanding of the geology (both in terms of the rock types and the fracture networks) is required for event evaluation (e.g., modulation of seismic signals from the source), planning of treaty monitoring sensors (fracture play a key role in the gas migration pathways), and evaluation of containment strategies. The Hypothesis: Quantitative analysis of terrain characteristics provides a way to relate the topography (easily obtained at high resolution) to surface geology. The Method: Integration of Terrain Complexity Index (TCI, derived from surface roughness) with drainage patterns and texture to produce a "predicted" geologic map. The viability of this method was evaluated by applying the algorithm to an area of know geology (Area 15 at the Nevada Test Site - NNSS). A 10-meter digital elevation model (DEM) was used for this evaluation. The Application: We have demonstrated the utility of this method by developing an improved surface geologic map for the North Korean Test Site using a 5-meter DEM. Why Now: Improved geologic characterization of potential nuclear test sites in a number of countries is needed for a number of Nonproliferation objectives. What's Needed Next: 1) A more robust and automated interpretation algorithm for the drainage analysis aspect; 2) improved data fusion of the TCI with drainage patterns; and 3) evaluation of the potential for fracture mapping in granite using a very high resolution DEM at the NNSS site (a 1-meter DEM in on order).

58 GEOSCIENCES↗

Performance analysis of Wald-statistic based network detection methods for radiation sources

There have been increasingly large deployments of radiation detection networks that require computationally fast algorithms to produce prompt results over ad-hoc sub-networks of mobile devices, such as smart-phones. These algorithms are in sharp contrast to complex network algorithms that necessitate all measurements to be sent to powerful central servers. In this work, at individual sensors, we employ Wald-statistic based detection algorithms which are computationally very fast, and are implemented as one of three Z-tests and four chi-square tests. At fusion center, we apply the K-out-of-N fusion to combine the sensors hard decisions. We characterize the performance of detection methods by deriving analytical expressions for the distributions of underlying test statistics, and by analyzing the fusion performances in terms of K, N, and the false-alarm rates of individual detectors. We experimentally validate our methods using measurements from indoor and outdoor characterization tests of the Intelligence Radiation Sensors Systems (IRSS) program. In particular, utilizing the outdoor measurements, we construct two important real-life scenarios, boundary surveillance and portal monitoring, and present the results of our algorithms.

Sen, Satyabrata↗

Physical Watermarking for Securing Cyber-Physical Systems via Packet Drop Injections

Physical watermarking is a well known solution for detecting integrity attacks on Cyber-Physical Systems (CPSs) such as the smart grid. Here, a random control input is injected into the system in order to authenticate physical dynamics and sensors which may have been corrupted by adversaries. Packet drops may naturally occur in a CPS due to network imperfections. To our knowledge, previous work has not considered the role of packet drops in detecting integrity attacks. In this paper, we investigate the merit of injecting Bernoulli packet drops into the control inputs sent to actuators as a new physical watermarking scheme. With the classical linear quadratic objective function and an independent and identically distributed packet drop injection sequence, we study the effect of packet drops on meeting security and control objectives. Our results indicate that the packet drops could act as a potential physical watermark for attack detection in CPSs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A Self-Sustained CPS Design for Reliable Wildfire Monitoring

Continuous monitoring of areas nearby the electric grid is critical for preventing and early detection of devastating wildfires. Existing wildfire monitoring systems are intermittent and oblivious to local ambient risk factors, resulting in poor wildfire awareness. Ambient sensor suites deployed near the gridlines can increase the monitoring granularity and detection accuracy. However, these sensors must address two challenging and competing objectives at the same time. First, they must remain powered for years without manual maintenance due to their remote locations. Second, they must provide and transmit reliable information if and when a wildfire starts. The first objective requires aggressive energy savings and ambient energy harvesting, while the second requires continuous operation of a range of sensors. To the best of our knowledge, this paper presents the first self-sustained cyber-physical system that dynamically co-optimizes the wildfire detection accuracy and active time of sensors. The proposed approach employs reinforcement learning to train a policy that controls the sensor operations as a function of the environment (i.e., current sensor readings), harvested energy, and battery level. Here, the proposed cyber-physical system is evaluated extensively using real-life temperature, wind, and solar energy harvesting datasets and an open-source wildfire simulator. In long-term (5 years) evaluations, the proposed framework achieves 89% uptime, which is 46% higher than a carefully tuned heuristic approach. At the same time, it averages a 2-minute initial response time, which is at least 2.5× faster than the same heuristic approach. Furthermore, the policy network consumes 0.6 mJ per day on the TI CC2652R microcontroller using TensorFlow Lite for Micro, which is negligible compared to the daily sensor suite energy consumption.

54 ENVIRONMENTAL SCIENCES↗

Energy-Efficient and Comfortable Buildings through Multivariate Integrated Control (ECoMIC)

This project aims to develop an integrated control solution for enhanced energy efficiency and user comfort in commercial buildings. The developed technology is a zone-based control framework that minimizes energy usage while maintaining occupants’ visual and thermal comfort through control of electric lights, motorized venetian blinds and thermostats. The control framework is designed following a modular, scalable and flexible architecture to facilitate easy integration with exiting building management systems. The control framework contains two key algorithms: 1) the lighting load balancing algorithm and 2) the thermostat control algorithm. The lighting load balancing algorithm adopts a model-based closed-loop control approach to determine the optimal electric light and venetian blind settings. It is formulated into an optimization problem with minimizing lighting-related energy consumptions as the objective and delivering adequate task light and preventing daylight glare as the constraints. The thermostat control algorithm is based on a well-established thermal comfort model and formulated as a root-finding problem to dynamically determine the optimal thermostat setpoint for both energy savings and improved thermal comfort. To address building-wide scalability, a system architecture was developed for the zone-based control technology. Three levels of services are defined in the architecture: external services, facility level services and zone level services. The zone-level service includes the control algorithms described above as well as the corresponding interfaces, profiles, sensors and actuators to realize the zone controller. The facility level services connect to the zones through a backbone network, handle supervisory level information and controls, and thus facilitate building-wide scalability. The external services provide communication capability to entities outside of the building for grid interaction and remote access. Various aspects of the developed control technology were evaluated and verified through both simulations and testbed implementations. Simulations coupling a DOE medium office reference building in EnergyPlus building simulation software and a prototype controller in Matlab were performed. During summer time in a mixed-humid climate zone, the simulations revealed reductions of 27% and 42% in electric lighting load and cooling load, respectively, when compared to an advanced base case with daylight dimming and blinds automatically tilted to block direct sun. Two single-room testbeds were established. The testbed at Philips Lighting business building (Rosemont, IL) was designed for quantifying energy performance of integrated controls. This particular implementation achieved 40% and 79% savings on lighting and HVAC energy, respectively, compared to a relatively simple base case operated on predefined schedules. While the resulting energy savings was very encouraging, it should be noted that there may be several caveats associated with it. 1) The test was run during late spring and early summer, and the savings numbers might not be directly used to extrapolate the annual energy savings. 2) Due to the needs for separate control and metering of the small-scale demonstrator within a large building, the HVAC system, hence the corresponding savings, did not represent a typical energy code-compliant design. 3) The light level in the control case was regulated at a particular setpoint, which was lower than then the full-on light level in the base case, and the savings resulted from tuning down the light level to the setpoint was not attributable to the contribution of the developed technology. The testbed at the Lawrence Berkeley National Laboratory (Berkeley, CA) specifically focused on glare control integration, and has demonstrated the feasibility and capability of the glare detection and prevention technique. While the short one-month test in this testbed provided a functional indication of the developed technology, and it would require at least a full solstice-to-solstice cycle to ruinously quantify the performance, which was not possible within the project timeframe. There are certain limitations inherited from the operational assumptions, which could potentially affect the effectiveness and applicability of the developed control technologies. The system takes a typical ceiling-mounting approach for the photosensor locations, and therefore, the control performance relies on proper commissioning or the built-in intelligence of the photosensor for pertinent task light level estimations. For spaces where daylight penetration diminishes significantly deeper into the zone, certain modification to the control algorithms is required to accommodate multiple lighting control subzones and the corresponding sensors for providing a more uniform light level across the entire zone. Integrated control of visual and thermal comfort requires the lighting control zone and thermal control zone to coincide with each other. In other words, the area illuminated by a lighting circuit needs to be the same area served by the thermostat. Thus, the original zoning will potentially constrain the applicability of this technology in retrofitting projects. This project demonstrated the technical feasibility of a zone-based integrated control technology. From the simulation results and testbed implementations, up to 60% lighting energy savings in daylit areas relative to a “no-controls” case can easily be achieved. A 20% reduction of whole building energy consumption is also attainable. In the aspect of occupant comfort, the testbed demonstrated the ability to maintain specified light level on the workplane while promptly mitigate daylight glare 90% of the time. The control system also managed to maintain the thermal environment at a comfortable level 90% of the time. The aspect of system scalability was guaranteed by the system architecture design, based on which the testbeds were instantiated. Analysis on the aspect of economic benefit has yielded an about 6-year payback time for a medium-sized building, including the installation of all hardware and software, such as motorized blinds and LED luminaires. The payback time can be significantly reduced if part of the hardware is already in place for retrofitting projects. It needs to be noted that since the payback analysis was partly based on the testbed performance results, it is constrained by the caveats associated with the testbed implementations. The main uncertainty lies in the contribution from the space conditioning energy savings as it was non-trivial to realistically configure a room-size HVAC system for directly extrapolating whole-building HVAC energy savings. It is recommended to further evaluate the developed technology at a larger scale, where the lighting and HVAC energy consumption can be realistically measured at the building level, to more rigorously quantify the performance potentials.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Real World Use Case Evaluation of Radar Retro-reflectors for Autonomous Vehicle Lane Detection Applications

Lane detection plays a critical role in autonomous vehicles for safe and reliable navigation. Lane detection is traditionally accomplished using a camera sensor and computer vision processing. The downside of this traditional technique is that it can be computationally intensive when high quality images at a fast frame rate are used and has reliability issues from occlusion such as, glare, shadows, active road construction, and more. This study addresses these issues by exploring alternative methods for lane detection in specific scenarios caused from road construction-induced lane shift and sun glare. Specifically, a U-Net, a convolutional network used for image segmentation, camera-based lane detection method is compared with a radar-based approach using a new type of sensor previously unused in the autonomous vehicle space: radar retro-reflectors. This evaluation is performed using ground truth data, obtained by measuring the lane positions and transforming them into pixel coordinates. The performance of each method is assessed using the statistical R2 score, indicating the correlation between the detected lane lines and the ground truth. The results show that the U-Net camera-based method exhibits limitations in accurately detecting and aligning the lane lines, particularly in challenging scenarios. However, the radar-based lane detection method demonstrates a strong correlation with the ground truth which implies that the use of this sensor may improve current reliability issues from conventional camera lane detection approach. Furthermore, the study highlights the limitations of the U-Net model for camera lane detection, especially in scenarios with sun glare. This study shows that infrastructure-based radar retro-reflectors can improve autonomous vehicle lane detection reliability. The integration of different sensor modalities and the development of advanced computer vision algorithms are crucial for improving the accuracy, reliability, and energy efficiency of lane detection systems. Addressing these challenges contributes to the advancement of autonomous vehicles and the realization of safer and more efficient transportation systems.

Brown, Nicolas E.↗

WellSTIC: A Cost-Effective Sensor for Performing Point Dilution Tests to Measure Groundwater Velocity in Shallow Aquifers

Many individual measurement points are required to characterize groundwater velocity within an aquifer. Groundwater velocity is most commonly measured using a network of >5 cm diameter monitoring wells, which, if not already present at a site, are expensive and labor-intensive to install. Drive-point piezometers—simple, cost-effective wells that can be installed by hand—are a common tool for sampling groundwater in shallow, alluvial aquifers, but most groundwater velocity measurement techniques require equipment that is too large for these narrow (usually <2 cm inside diameter) piezometers. In this technical note, we introduce a low-cost sensor and well packer system (<$90 USD) for performing point dilution tests in narrow piezometers. Field data show that the magnitude of groundwater velocity measured with this technique agrees with velocities computed from natural gradient tracer tests. Additionally, with proper calibration, these sensors can be used to continuously monitor in-well specific conductance, either during inter-well tracer tests with saline tracers or for water quality monitoring. Finally, this system is a viable tool for rapid assessment of the magnitude of groundwater velocity in shallow aquifers.

54 ENVIRONMENTAL SCIENCES↗

Neural network-based classification and regression of magnetohydrodynamic modes in tokamaks

We present a machine learning-based magnetohydrodynamic (MHD) classifier and regressor that utilizes real or complex-valued 3D magnetic sensor array data to determine neoclassical tearing mode (NTM) onset times in tokamaks with millisecond accuracy. The input dataset consists of poloidal profiles of complex Fourier amplitudes with an n = 1 toroidal mode number from 144 human-labeled ITER Baseline Scenario discharges in the DIII-D tokamak, spanning both tearing-dominated and sawtooth-dominated regimes. Since m, n = 2,1 NTMs frequently emerge alongside sawteeth at the same frequency in this scenario, the focus is on isolating the m = 1 and m = 2 components of the n = 1 MHD mode near the tearing onset. To improve model regularization and prediction stability, singular value decomposition was applied to balance the sawtooth and tearing datasets. The enriched datasets facilitated training neural networks that learn the key distinguishing features of sawtooth and tearing modes in the poloidal profiles of their magnetic amplitude and phase. When the modes occur independently, the networks achieve perfect classification due to the modes’ distinct characteristics and low measurement noise. In the more experimentally relevant case where both modes coexist, the networks maintain exceptional performance across key metrics. Tests on synthetic data with known ground truth demonstrate the superior accuracy of the neural network trained on complex-valued input compared to models using real amplitude, phase, or pseudo-complex data, achieving both a mean time delay and standard deviation below 1 ms. Notably, standard linear regression methods fitting the dominant singular modes to the data closely match the neural network’s performance. Applying these methods across a broad range of H-mode scenarios will enable future studies to systematically identify dominant NTM triggers as scenario-specific variables, paving the way for more effective tearing mode avoidance strategies in future fusion reactor designs.

machine learning↗

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve forward, inverse, and mixed stochastic problems in a unified manner based on a limited number of scattered measurements. Unlike standard GANs relying solely on data for training, here we encoded into the architecture of GANs the governing physical laws in the form of stochastic differential equations (SDEs) using automatic differentiation. In particular, we applied Wasserstein GANs with gradient penalty (WGAN-GP) for its enhanced stability compared to vanilla GANs. We first tested WGAN-GP in approximating Gaussian processes of different correlation lengths based on data realizations collected from simultaneous reads at sparsely placed sensors. We obtained good approximation of the generated stochastic processes to the target ones even if there is a mismatch between the input noise dimensionality and the effective dimensionality of the target stochastic processes. We also studied the overfitting issue for both the discriminator and the generator, and we found that overfitting occurs also in the generator in addition to the discriminator as previously reported. Subsequently, we considered the solution of elliptic SDEs requiring approximations of three stochastic processes, namely the solution, the forcing, and the diffusion coefficient. Here again, we assumed data collected from simultaneous reads at a limited number of sensors for the multiple stochastic processes. Furthermore, three generators were used for the PI-GANs: two of them were feed forward deep neural networks (DNNs), while the other one was the neural network induced by the SDE. For the case where we have one group of data, we employed one feed forward DNN as the discriminator, while for the case of multiple groups of data we employed multiple discriminators in PI-GANs. We solved forward, inverse, and mixed problems without changing the framework of PI-GANs, obtaining both the means and the standard deviations of the stochastic solution and the diffusion coefficient in good agreement with benchmarks. In this work, we have demonstrated the effectiveness of PI-GANs in solving SDEs for about 120 dimensions. In principle, PI-GANs could tackle very high dimensional problems given more sensor data with low-polynomial growth in computational cost.

97 MATHEMATICS AND COMPUTING↗