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At least 811 records · Page 45

Numerical Investigation of Fuel Property Effects on Mixed-Mode Combustion in a Spark-Ignition Engine

In this research, lean mixed-mode combustion is numerically investigated using computational fluid dynamics (CFD) in a spark-ignition engine. A new E30 fuel surrogate is developed using a neural network model with matched octane numbers. A skeletal mechanism is also developed by automated mechanism reduction and by incorporating a NO x submechanism. A hybrid approach that couples the G-equation model and the well-stirred reactor model is employed for turbulent combustion modeling. The developed CFD model is shown to well predict pressure and apparent heat release rate (AHRR) traces compared with experiment. Two types of combustion cycles (deflagration-only and mixed-mode cycles) are observed. The mixed-mode cycles feature early flame propagation and subsequent end-gas auto-ignition, leading to two distinctive AHRR peaks. The validated CFD model is then employed to investigate the effects of NO x chemistry. The NO x chemistry is found to promote auto-ignition through the residual gas, while the deflagration phase remains largely unaffected. Sensitivity analysis is finally performed to understand effects of fuel properties, including heat of vaporization (HoV) and laminar flame speed (S L ). An increased HoV tends to suppress auto-ignition through charge cooling, while the impact of HoV on flame propagation is insignificant. In contrast, an increased S L is found to significantly promote both flame propagation and end-gas auto-ignition. The promoting effect of S L on auto-ignition is not a direct chemical effect; it is rather caused by an advancement of the combustion phasing, which increases compression heating of the end-gas.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Large Eddy Simulation of Lean Mixed-Mode Combustion Assisted by Partial Fuel Stratification in a Spark-Ignition Engine

Partial fuel stratification (PFS) is a promising fuel injection strategy to improve the stability of lean combustion by applying a small amount of pilot injection right before spark timing. Mixed-mode combustion, which makes use of end-gas autoignition following conventional deflagration-based combustion, can be further utilized to speed up the overall combustion. In this study, PFS-assisted mixed-mode combustion in a lean-burn direct injection spark-ignition (DISI) engine is numerically investigated using multi-cycle large eddy simulation (LES). A previously developed hybrid G-equation/well-stirred reactor combustion model for the well-mixed operation is extended to the PFS-assisted operation. The experimental spray morphology is employed to derive spray model parameters for the pilot injection. The LES-based model is validated against experimental data and is further compared with the Reynolds-averaged Navier–Stokes (RANS)-based model. Overall, both RANS and LES predict the mean pressure and heat release rate traces well, while LES outperforms RANS in capturing the cycle-to-cycle variation (CCV) and the combustion phasing in the mass burned space. Liquid and vapor penetrations obtained from the simulations agree reasonably well with the experiment. Detailed flame structures predicted from the simulations reveal the transition from a sooting diffusion flame to a lean premixed flame, which is consistent with experimental findings. LES captures more wrinkled and stretched flames than RANS. Finally, the LES model is employed to investigate the impacts of fuel properties, including heat of vaporization (HoV) and laminar burning speed (SL). Combustion phasing is found more sensitive to SL than to HoV, with a larger fuel property sensitivity of the heat release rate from autoignition than that from deflagration. Moreover, the combustion phasing in the PFS-assisted operation is shown to be less sensitive to SL compared with the well-mixed operation.

fuel property sensitivity↗

Numerical Modeling of Atmospheric Rime Ice Accretion on an Airfoil Using an Eulerian Approach

This paper presents an approach to numerically simulate the inherently unsteady rime ice accretion problem on a two-dimensional airfoil and elucidate the associated variations under different icing conditions. The airflow field and the water impingement on the airfoil are obtained based on an Eulerian two-phase model. A dynamic mesh strategy is employed to unsteadily account for the changes in the ice profile and its impact on the air and droplet flow by continuously reconstructing the computational grid at each time-step through smoothing and layering mechanisms. All main icing modules including the airflow field, droplet trajectory, icing thickness profile, and mesh management are fully coupled within the same computational framework without resorting to any external tools. Classical icing theory is employed to model the rime ice roughness, and it is assumed that the ice accretes in a direction normal to the airfoil surface. The governing Reynolds-averaged Navier–Stokes (RANS) conservation equations along with the energy and continuity equations are solved to produce the velocity and temperature fields. A convective film heat transfer coefficient is computed based on the surface heat flux and a recovery temperature which takes into account the dissipative heat release in the boundary layer in the vicinity of the airfoil surface. With the implemented strategy and calculating the convective heat transfer coefficient, the water film thickness is also calculated along with the ice shape. Furthermore, the model is validated by comparing the local collection efficiency distribution and ice shape with experimental data, and the results show that the implemented approach provides acceptable predictions of ice accretion profiles and rates.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Direct Numerical Simulation of Transitional and Turbulent Flows Over Multi-Scale Surface Roughness—Part I: Methodology and Challenges

Abstract High-fidelity simulation of transitional and turbulent flows over multi-scale surface roughness presents several challenges. For instance, the complex and irregular geometrical nature of surface roughness makes it impractical to employ conforming structured grids, commonly adopted in large-scale numerical simulations due to their high computational efficiency. One possible solution to overcome this problem is offered by immersed boundary methods, which allow wall boundary conditions to be enforced on grids that do not conform to the geometry of the solid boundary. To this end, a three-dimensional, second-order accurate boundary data immersion method (BDIM) is adopted. A novel mapping algorithm that can be applied to general three-dimensional surfaces is presented, together with a newly developed data-capturing methodology to extract and analyze on-surface flow quantities of interest. A rigorous procedure to compute gradient quantities such as the wall shear stress and the heat flux on complex non-conforming geometries is also introduced. The new framework is validated by performing a direct numerical simulation (DNS) of fully developed turbulent channel flow over sinusoidal egg-carton roughness in a minimal-span domain. For this canonical case, the averaged streamwise velocity profiles are compared against results from the literature obtained with a body-fitted grid. General guidelines on the BDIM resolution requirements for multi-scale roughness simulation are given. Momentum and energy balance methods are used to validate the calculation of the overall skin friction and heat transfer at the wall. The BDIM is then employed to investigate the effect of irregular homogeneous surface roughness on the performance of an LS-89 high-pressure turbine blade at engine-relevant conditions using DNS. This is the first application of the BDIM to realize multi-scale roughness for transitional flow in transonic conditions in the context of high-pressure turbines. The methodology adopted to generate the desired roughness distribution and to apply it to the reference blade geometry is introduced. The results are compared to the case of an equivalent smooth blade.

Engineering↗

Iterative Stress Reconstruction Algorithm to Estimate Three-Dimensional Residual Stress Fields in Manufactured Components

Residual stress (RS) significantly impacts the mechanical performance of components. Measurement of RS often provides incomplete data in terms of components of stress and spatial density. Employing such fields in finite element simulations results in significant modification of the field to achieve equilibrium and compatibility among strains. To overcome this, an iterative stress reconstruction algorithm (ISRA) is developed to estimate 3D RS fields that satisfy equilibrium, are stress component-wise complete, and represent the characterized data sampled. An Al 7075-T651 plate and an additively manufactured (AM) A36 steel wall are considered for RS reconstruction using measurement data from the literature. A maximum variation of ~2.5 MPa in the Al plate, and ~10 MPa in the steel wall are observed between the reconstructed and measured stresses. Furthermore, unknown stress components emerge and reach significant magnitudes (upto ~2.3 MPa in the Al plate and ~45 MPa in the AM wall) during ISRA. Indeed, it is found that minor errors in measurement or data processing are eliminated through the physical requirements during ISRA. Employing a reconstructed RS field is hence not just more accurate given its compatibility, but it additionally corrects for minor errors in measurement. Furthermore, it is found that spatially dense measurement data result in convergence with fewer iterations. Finally, although ISRA yields a nonunique solution dependent on boundary conditions, measurement errors, fitting errors, and mesh density, it accommodates for uncertainties and inaccuracies in measurement, as opposed to failing to reach a physically realistic converged solution.

42 ENGINEERING↗

Multidimensional Modeling of Mixture Formation in a Hydrogen-Fueled Heavy-Duty Optical Engine With Direct Injection

Hydrogen (H 2 ), as a carbon-free fuel, is considered as one of the most promising solutions to reduce the carbon footprint of hard-to-decarbonize energy and transportation sectors. As such, hydrogen-fueled internal combustion engines (H 2 ICEs) have recently been receiving increasing attention, particularly in applications such as on-road/off-road heavy-duty transport and combined heat and power. The direct injection (DI) of gaseous hydrogen into the combustion chamber offers great potential for achieving high power density and high engine efficiency, while mitigating the risk of backfire and reducing pre-ignition. However, the numerical simulation of H 2 DI system remains a formidable challenge associated with the high computational cost of reproducing compressible supersonic flow and shocks in narrow injector passages and in near-nozzle regions. In general, there is a lack of well-established and validated practices for the modeling of high-pressure H 2 DI in large-bore engines. Here, to this end, this study focuses on computational fluid dynamics (CFD) modeling of the mixture formation process in a heavy-duty optical engine employing a medium-pressure H 2 DI system. Both large eddy simulations (LES) and Reynolds Averaged Navier–Stokes (RANS) simulations are performed and evaluated against optical data. Gaseous hydrogen is injected into the combustion chamber via a centrally located outward opening hollow-cone injector at a pressure of 40 bar. Simulations are carried out for two injection timings, namely, −120 and −60 °CA. The numerical predictions for H 2 distribution in different horizontal and vertical planes during the compression stroke are systematically compared against optical data obtained through planar laser-induced fluorescence (PLIF) measurements. Overall, the LES approach using the Dynamic Structure model is found to have good predictive capabilities for the early jet penetration in terms of length and shape, as well as the later H 2 distributions. However, the unsteady RANS approach with the renormalization group $k - ϵ$ model, which is widely used by industry to model heavy-duty ICEs, significantly underpredicts the H 2 mixing, even at similar mesh resolution to that used in LES. These results indicate that there is a need for the improvement of mixing submodels within the RANS approach when applied to H 2 DI simulations.

LES↗

System Design of a 2.0 MWth Sodium/Molten Salt Pilot System

Nitrate molten salt concentrating solar power (CSP) systems are currently deployed globally and are considered state-of the art heat transfer fluids (HTFs) for present day high-temperature operation. Although slightly higher limits may be possible with molten salt, to fully realize SunShot efficiency goals of $15/kWhth HTFs and an LCOE of 6¢/kWh, HTF technologies working at higher temperatures (e.g., 650 °C to 750 °C) will require an alternative to molten salts, such as with alkali metal systems. This investigation explores the development of a 2.0 MWth sodium receiver system that employs a sodium receiver as the HTF, as well as with a ternary chloride (20%NaCl/40%MgCl/40%KCl by mol wt.%) salt as a thermal energy storage (TES) medium to facilitate a 6-hr. storage duration. A sodium-to-salt heat exchanger model as well as a salt-to-sCO2 primary heat exchanger model are employed and evaluated in this investigation. A thermodynamic system design model was developed using Engineering Equation Solver (EES) where state properties were calculated at inlets and outlets along both hot and cold legs of the pilot-scale plant. This investigation assesses receiver performance as well as system efficiency studies for the pump and system operational ranges. Results found that high efficiency sodium receivers were found to have higher heat transfer coefficients and required far less spreading of incident flux. The system performance model results suggest that for a pump speed of 2400 RPM, respective hot and cold pump TDH values were determined to be 260.1–307 ft. and 260.1–307 ft for pump flow rates of 90–120 GPM.

41 EE - Solar Energy Technologies Office (EE-4S)↗

Deep Learning for Intelligent Bubble Size Detection in the Spallation Neutron Source Visual Target

The Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL) will undergo proton power upgrade (PPU), increasing the proton beam power from 1.4 MW to 2.8 MW. From 2.8 MW, 2.0 MW will go to the current First Target Station and the rest will go to the future Second Target Station (STS). The First Target Station uses a liquid mercury target that is contained in a 316L stainless steel vessel. The proton beam is pulsed at 60 Hz, with a pulse of about 0.7μs. When the proton beam hits the target, the intense energy deposition leads to a rapid rise in temperature in the mercury. This temperature rise creates pressure waves that propagate through the mercury and cause cavitation erosion. The power upgrade will cause stronger pressure waves that will further increase damage because of cavitation. Injecting small helium bubbles in the mercury has been an efficient method of mitigating the pressure wave at 1.4 MW. However, at higher power, additional mitigation is necessary. Therefore, the 2 MW target vessel will be equipped with swirl bubblers and an additional gas injection port near the nose to inject more gas in the target. To develop a gas injection strategy and design, flow visualization in water with a transparent prototypical target (“visual target”) was performed. Bubble sizes and their spatial distribution in the flow loop are crucial to understanding the effectiveness of the bubbles in mitigating pressure waves. Bubbles were generated in the visual target under varied conditions of input pressures with helium and air. Images were captured using a high-speed camera at varied frame rates at different positions away from the swirl bubbler and different depths in the flow loop under varying lighting conditions. Initially, methods such as circular Hough transforms were applied after a series of images processing to obtain a general distribution of bubble sizes. Bubbles smaller than 500 μm are preferred to effectively mitigate the effect of pressure waves, which demands an accurate bubble detection and sizing system. Intelligent detection and identification of bubble sizes alleviate misdetection and improves accuracies. Employing neural networks, intelligent detection of bubble sizes and their distribution was developed and provides a robust alternative to traditional techniques. Human intervention was employed to label in-focus and out-of-focus bubbles in the set of training images. An object detection network using a pretrained convolutional neural network was created that extracted the features from the training images. Data augmentation was used to improve network accuracy through a random transformation of the original data.

Rasheed, Fayaz↗

Investigation of Theoretical Solutions to a Bottom-Raised Oscillating Surge Wave Energy Converter (OSWEC) Through Experimental and Parametric Studies

Experiments were conducted on a wave tank model of a bottom raised oscillating surge wave energy converter (OSWEC) model in regular waves. The OSWEC model shape was a thin rectangular flap, which was allowed to pitch in response to incident waves about a hinge located at the intersection of the flap and the top of the supporting foundation. Torsion springs were added to the hinge in order to position the pitch natural frequency at the center of the wave frequency range of the wave maker. The flap motion as well as the loads at the base of the foundation were measured. The OSWEC was modeled analytically using elliptic functions in order to obtain closed form expressions for added mass and radiation damping coefficients, along with the excitation force and torque. These formulations were derived and reported in a previous publication by the authors. While analytical predictions of the foundation loads agree very well with experiments, large discrepancies are seen in the pitch response close to resonance. These differences are analyzed by conducting a sensitivity study, in which system parameters, including damping and added mass values, are varied. The likely contributors to the differences between predictions and experiments are attributed to tank reflections, standing waves that can occur in long, narrow wave tanks, as well as the thin plate assumption employed in the analytical approach.

analytical↗

High-capacity rotary drum for atomic layer deposition onto powders and small mechanical parts in a hot-walled viscous flow reactor

Atomic layer deposition (ALD) is uniquely capable of providing uniform thin-film coatings on powder substrates, but powder processing has historically required an ALD reactor designed specifically for powders-e.g., a fluidized bed. Tubular hot-walled viscous-flow reactors commonly employed in laboratory-scale ALD research for coating planar substrates such as silicon have been employed previously to coat gram quantities of powder spread out in a thin layer on a tray, but larger quantities of powder introduce long diffusion pathways where reactants are unable to percolate to the bottom of the powder bed to provide uniform coating in reasonable time periods. In this work, we report a rotary drum with a capacity of 100s of grams that is compatible with conventional tubular hot-walled ALD reactors and provides uniform coatings on powders in viscous flow operation. We benchmark this system using Al 2 O 3 ALD with trimethylaluminum and water. We examine the effect of rotation speed and powder quantity on saturation time via in situ quadrupole mass spectroscopy measurements and gravimetric analysis. Finally, the rotary drum we report is able to provide homogenous coating of up to 75g of silica gel powder with a total surface area of similar to 1500m 2 in viscous flow operation with precursor utilization as high as 70%.

47 OTHER INSTRUMENTATION↗

Evolution of Metastable Phases During Mg Metal Corrosion: An In Situ Cryogenic X-ray Photoelectron Spectroscopy Study

Magnesium and its alloys are potential structural materials candidates for a wide variety of applications due to their high strength-to-weight ratio. However, ductility and poor corrosion resistance under ambient environmental conditions are the bottleneck for industrial deployment. Designing passivation layers and/or corrosion resistant alloys requires fundamental understanding of the corrosion process. The traditional ex-situ spectroscopic measurements of polycrystalline metal surface with ubiquitous surface impurities and grain boundaries only provided an indistinct view of the corrosion process. To clearly distinguish the mechanism and sequence of corrosion process, we employed in-situ cryo-based x-ray photoelectron spectroscopy (XPS) measurements on Mg single crystal surface exposed to aqueous salt solution. Clean Mg (0001) surfaces were exposed to pure D2O and NaCl aqueous solution (5 wt% NaCl+95 wt% D2O). The interfacial reactions were studied using multimodal analysis including XPS, x-ray diffraction (XRD) and scanning electron microscopy (SEM). In contrast to previous studies, our experiments demonstrated the formation of magnesium chloride hydroxide hydrate during aqueous salt corrosion processes. Evidence of metastable ClO* radicals were also found during the initial aqueous salt solution exposure.

Shutthanandan, Vaithiyalingam↗

Attosecond probing and control of charge migration in carbon-chain molecule

In quantum mechanics, when an electron is quickly ripped off from a molecule, a superposition of new eigenstates of the cation creates an electron wave packet that governs the charge flow inside, which has been called charge migration (CM). Experimentally, extracting such dynamics at its natural (attosecond) timescale is quite difficult. We report the first such experiment in a linear carbon-chain molecule, butadiyne (C 4 H 2 ), via high-harmonic spectroscopy (HHS). By employing advanced theoretical and computational tools, we showed that the wave packet and the CM of a single molecule are reconstructed from the harmonic spectra for each fixed-in-space angle of the molecule. For this one-dimensional molecule, we calculate the center of charge $\langle$ x $\rangle$ ( t ) to obtain v cm , to quantify the migration speed and how it depends on the orientation angle. The findings also uncover how the electron dynamics at the first few tens to hundreds of attoseconds depends on molecular structure. The method can be extended to other molecules where the HHS technique can be employed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Photon Doppler velocimetry surface return study for common surface preparations

Photon Doppler velocimetry (PDV) is a ubiquitous diagnostic method in dynamic compression experiments. It typically requires the roughening of the test surface to ensure scattering of the probe light back into the PDV probe at non-normal angles of incidence. Although surface scattering plays an essential role in the quality of PDV data, surface scattering properties for common materials and preparations have not previously been studied with specific relevance to PDV. Here, we present detailed measurements of the bidirectional reflectance distribution function for four different surface preparations (Scotch-Brite hand and drill roughened, ball-rolled, and grit blasted) and four different materials (copper, aluminum, stainless steel, and tantalum). These measurements employ a conventional PDV probe and obtain a diffraction limited angular resolution with 10 pW accuracy and 2.6% repeatability. In addition to scattering data, we employ scattering theory and simulations to accurately emulate the measured data. We also present a straightforward method to derive the average scattering distribution from surface profilometry and observe several qualitative aspects of the scattering data that may help to optimize PDV signals.

42 ENGINEERING↗

Design and pre-flight performance of SPIDER 280 GHz receivers

In this work we describe upgrades to the Spider balloon-borne telescope in preparation for its second flight, currently planned for December 2021. The Spider instrument is optimized to search for a primordial B-mode polarization signature in the cosmic microwave background at degree angular scales. During its first flight in 2015, Spider mapped ~10% of the sky at 95 and 150 GHz. The payload for the second Antarctic flight will incorporate three new 280 GHz receivers alongside three refurbished 95- and 150 GHz receivers from Spider's first flight. In this work we discuss the design and characterization of these new receivers, which employ over 1500 feedhorn-coupled transition-edge sensors. We describe pre-flight laboratory measurements of detector properties, and the optical performance of completed receivers. These receivers will map a wide area of the sky at 280 GHz, providing new information on polarized Galactic dust emission that will help to separate it from the cosmological signal.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Robust measurement of microbial reduction of graphene oxide nanoparticles using image analysis

ABSTRACT Shewanella oneidensis ( S. oneidensis ) has the capacity to reduce electron acceptors within a medium and is thus used frequently in microbial fuel generation, pollutant breakdown, and nanoparticle fabrication. Microbial fuel setups, however, often require costly or labor-intensive components, thus making optimization of their performance onerous. For rapid optimization of setup conditions, a model reduction assay can be employed to allow simultaneous, large-scale experiments at lower cost and effort. Since S. oneidensis uses different extracellular electron transfer pathways depending on the electron acceptor, it is essential to use a reduction assay that mirrors the pathways employed in the microbial fuel system. For microbial fuel setups that use nanoparticles to stimulate electron transfer, reduction of graphene oxide provides a more accurate model than other commonly used assays as it is a bulk material that forms flocculates in solutions with a large ionic component. However, graphene oxide flocculates can interfere with traditional absorbance-based measurement techniques. This study introduces a novel image analysis method for quantifying graphene oxide reduction, showing improved performance and statistical accuracy over traditional methods. A comparative analysis shows that the image analysis method produces smaller errors between replicates and reveals more statistically significant differences between samples than traditional plate reader measurements under conditions causing graphene oxide flocculation. Image analysis can also detect reduction activity at earlier time points due to its use of larger solution volumes, enhancing color detection. These improvements in accuracy make image analysis a promising method for optimizing microbial fuel cells that use nanoparticles or bulk substrates. IMPORTANCE Shewanella oneidensis ( S. oneidensis ) is widely used in reduction processes such as microbial fuel generation due to its capacity to reduce electron acceptors. Often, these setups are labor-intensive to operate and require days to produce results, so use of a model assay would reduce the time and expenses needed for optimization. Our research developed a novel digital analysis method for analysis of graphene oxide flocculates that may be utilized as a model assay for reduction platforms featuring nanoparticles. Use of this model reduction assay will enable rapid optimization and drive improvements in the microbial fuel generation sector.

Bennett, Danielle T. (ORCID:0009000188748827)↗

Identification of recG genetic interactions in Escherichia coli by transposon sequencing

ABSTRACT Maintaining the integrity of the genome is of utmost importance for cell division and propagation. In Escherichia coli , the RecG protein has been implicated in processing branched recombination intermediates during DNA repair processes, but the primary cellular role(s) of RecG and the repair pathways in which it acts have been difficult to define. To gain additional insight into RecG function, we employed transposon sequencing to identify recG genetic interactions and reveal complementary or redundant functions. The strongest hits from the screen were the dam , uvrD , rnhA , radA , and rep genes. The conditional importance of these five genes in cells lacking recG was confirmed using a plasmid-based assay, revealing synthetic lethal interactions for most double deletion strains. Several of the synthetic lethal gene combinations (with uvrD, rep, and radA , but not rnhA or dam ) were suppressed by deletion of recF or recO , indicating that their genetic relationships involved roles in post-replication gap repair. Additionally, loss of the RecG/SSB interaction phenocopied a recG deletion when combined with dam , uvrD , radA , or rnhA deletions but not with rep . The results reinforce the idea of RecG as a general genome guardian. RecG has at least two functions. It plays an important role in the resolution of joint molecules behind the fork, formed during post-replication gap repair. RecG is also required to suppress genome over-replication caused by unscheduled replication initiation at R-loops, at double-strand breaks caused by dam inactivation, and during replication termination. IMPORTANCE DNA damage and subsequent DNA repair processes are mutagenic in nature and an important driver of evolution in prokaryotes, including antibiotic resistance development. Genetic screening approaches, such as transposon sequencing (Tn-seq), have provided important new insights into gene function and genetic relationships. Here, we employed Tn-seq to gain insight into the function of the recG gene, which renders Escherichia coli cells moderately sensitive to a variety of DNA-damaging agents when they are absent. The reported recG genetic interactions can be used in combination with future screens to aid in a more complete reconstruction of DNA repair pathways in bacteria.

59 BASIC BIOLOGICAL SCIENCES↗

Utility of Human In Vitro Data in Risk Assessments of Influenza A Virus Using the Ferret Model

Both in vitro and in vivo models are employed for assessing the pandemic potential of novel and emerging influenza A viruses in laboratory settings, but systematic examinations of how well viral titer measurements obtained in vitro align with results from in vivo experimentation are not frequently performed. We show that certain viral titer measurements following infection of a human bronchial epithelial cell line are positively correlated with viral titers in specimens collected from virus-inoculated ferrets and employ mathematical modeling to identify commonalities between viral infection progression between both models.

60 APPLIED LIFE SCIENCES↗

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↗