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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Gradient sensing via cell communication

Experimental evidence lends support to the conjecture that cell-to-cell communication plays a role in the gradient sensing of chemical species by certain chains of cells. Models have been formulated to explore this idea. For cells with no identifiable sensing structure, Mugler et al. [Proc. Natl. Acad. Sci. (U.S.A.) 113, E689 (2016)] have defined a particular local excitation, global inhibition (LEGI) model that pits nearest-neighbor communication against local reactions in a noisy environment to suggest how this sensing capability might arise in a physical system. In this study, we generalize the nearest-neighbor communication mechanism in the aforementioned LEGI model in order to explore the extent to which the gradient sensing characteristics depend on the parametrization of the communication itself, as well as on the cell size, the radius of influence of neighboring cells, and the influence of the background noise. Using our generalization and a collection of particular candidate communication models, we find that the precision of gradient sensing is indeed sensitive to the particular communication model, and we derive physical and analytic explanations for these results. The framework established and the associated results should prove useful in understanding the appropriateness of particular cell-to-cell communication models in gradient sensing studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Thermal Effects on Far-Field Distributed Acoustic Strain-Rate Sensors

Summary Fiber-optic cables cemented outside of the casing of an unconventional well measure crosswell strain changes during fracturing of neighboring wells with low-frequency distributed acoustic sensing (LF-DAS). As a hydraulic fracture intersects an observation well instrumented with fiber-optic cables, the fracture fluid injected at ambient temperatures can cool a section of the sensing fiber. Often, LF-DAS and distributed temperature sensing (DTS) cables are run in tandem, enabling the detection of such cooling events. The increasing use of LF-DAS for characterizing unconventional hydraulic fracture completions demands an investigation of the effects of temperature on the measured strain response by LF-DAS. Researchers have demonstrated that LF-DAS can be used to extract the temporal derivative of temperature for use as a differential-temperature-gradient sensor. However, differential-temperature-gradient sensing is predicated on the ability to filter strain components out of the optical signal. In this work, beginning with an equation for optical phase shift of LF-DAS signals, a model relating strain, temperature, and optical phase shift is explicitly developed. The formula provides insights into the relative strength of strain and temperature effects on the phase shift. The uncertainty in the strain-rate measurements due to thermal effects is estimated. The relationship can also be used to quantify uncertainties in differential-temperature-gradient sensors due to strain perturbations. Additionally, a workflow is presented to simulate the LF-DAS response accounting for both strain and temperature effects. Hydraulic fracture geometries are generated with a 3D fracture simulator for a multistage unconventional completion. The fracture width distributions are imported by a displacement discontinuity method (DDM) program to compute the strain rates along an observation well. An analytic model is used to approximate the temperature in the fracture. Using the derived formulae for optical phase shift, the model outputs are then used to compute the LF-DAS response at a fiber-optic cable, enabling the generation of waterfall plots including both strain and thermal effects. The model results suggest that before, during, and immediately following a fracture intersecting a well instrumented with fiber, the strain on the fiber drives the LF-DAS signal. However, at later times, as completion fluid cools the observation well, the temperature component of the LF-DAS signal can be equal to or exceed the strain component. The modeled results are compared to a published field case in an attempt to enhance the interpretation of LF-DAS waterfall plots. Finally, we propose a sensing configuration to identify the events when “wet fractures” (fractures with fluids) intersect the observation well.

Engineering↗
DOE OSTI2026

Nanoscale Compositional and Strain Gradients Enable High‐Speed and Amplitude‐Resolved Pyroelectric Sensing

The frequency response of pyroelectric sensors is fundamentally governed by thermal time constant (τth, determined by thermal mass and thermal conductance) and electrical impedance arising from film capacitance and readout circuit. Conventional bulk LiTaO3 detectors are optimized for high responsivity at low modulation frequencies (0.1-10 Hz), possessing a large τth that thermally averages rapid temperature oscillations at elevated modulation frequencies, limiting fidelity in resolving dynamic varying thermal signals. Here, compositional and strain gradients are introduced into 100-nm-thick relaxor-ferroelectric films reducing τth to ≈2 µs and producing built-in potentials (≈1.45 V or 145 kV cm-1) that enhance the pyroelectric coefficient and suppress the dielectric constant. This enables complementary dual-mode operation by enhancing current-mode electrical responsivity and improving the voltage-mode figure of merit - advantageous for superior temperature resolution (ΔTmin ≈ 30 µK). The responsivity peak shifts to near 1 kHz (>2500-times higher than conventional bulk sensors), with measurable responsivity extending to a carrier frequency of 100 kHz and amplitude-resolved detection at modulation frequencies up to 15 kHz. These results establish nanoscale internal-field engineering can reshape electro-thermal trade-off in pyroelectric thin films toward zero-bias, high-thermal-sensitivity, and amplitude-resolved thermal sensing across a wide frequency bandwidth.

Lin, Ching‐Che↗
DOE OSTI2021

Fiber Optic Sensing Technologies for Battery Management Systems and Energy Storage Applications

Applications of fiber optic sensors to battery monitoring have been increasing due to the growing need of enhanced battery management systems with accurate state estimations. The goal of this review is to discuss the advancements enabling the practical implementation of battery internal parameter measurements including local temperature, strain, pressure, and refractive index for general operation, as well as the external measurements such as temperature gradients and vent gas sensing for thermal runaway imminent detection. A reasonable matching is discussed between fiber optic sensors of different range capabilities with battery systems of three levels of scales, namely electric vehicle and heavy-duty electric truck battery packs, and grid-scale battery systems. The advantages of fiber optic sensors over electrical sensors are discussed, while electrochemical stability issues of fiber-implanted batteries are critically assessed. This review also includes the estimated sensing system costs for typical fiber optic sensors and identifies the high interrogation cost as one of the limitations in their practical deployment into batteries. Finally, future perspectives are considered in the implementation of fiber optics into high-value battery applications such as grid-scale energy storage fault detection and prediction systems.

25 ENERGY STORAGE↗
DOE OSTI2026

Sedimentation and Nonlinear Trapping in Texas Reservoirs Identified Using Remote Sensing and Bathymetric Survey Records

Decreasing reservoir storage capacity due to sedimentation poses great challenges to aging U.S. reservoirs, as it reduces the efficacy and reliability of their socio‐economic services. However, systematic assessments of reservoir sedimentation rates and associated issues remain limited because of sparse and infrequent bathymetry survey data. In this study, we use remote sensing‐driven estimates of sediment concentrations to identify regions experiencing rapid reservoir capacity loss, as observed in repeated bathymetry surveys. Our analysis focuses on Texas, where one of the most reliable state‐level reservoir capacity loss data sets is available through a unique long‐term monitoring program by the Texas Water Development Board. We find that reservoirs with large storage capacities and high sedimentation rate are concentrated in Northeast Texas. We also show that reduced forest, increased barren land, and erosive soil properties are co‐varying with high reservoir sedimentation rates. Temporal changes in the longitudinal gradient of the remotely sensed sediment flux highlight the nonlinear nature of sediment trapping processes, and can be used to estimate the reservoir storage capacity loss over time. In combination with standard bathymetry surveys, our approach shows potential for more cost‐effective and frequent assessment of reservoir storage loss.

Lee, Jiyong [ORNL] (ORCID:0000000198957406)↗
DOE OSTI2020

Diversity in Photoprotection and Energy Balancing in Terrestrial and Aquatic Phototrophs

The evolution of oxygenic photosynthesis enabled organisms to use sunlight as an energy source, allowing them to colonize new niches. At the same time, life (as we know it) places severe constraints on photosynthesis. For example, the initial reactions of photosynthesis involve highly energetic intermediates that, if not controlled, can generate highly toxic side products (especially reactive oxygen species, ROS), that can damage other essential components of the organisms it powers. Photosynthesis must therefore be tightly regulated to balance the need for efficient energy conversion with the necessity of avoiding photodamage (Gust D, Kramer D, Moore A, Moore T, Vermaas W, Mater Res Bull 33:383–389, 2008). A related constraint on photosynthesis is the need to precisely balance how much energy is stored in ATP and NADPH to precisely meet biochemical demands. If this balancing does not occur, the system will fail, leading to photodamage (Kramer DM, Evans JR, Plant Physiol 155:70–78, 2011). Consideration of these requirements is essential for efforts to improve the efficiency of photosynthesis by introducing CO 2 concentrating mechanisms, altering metabolism or biosynthetic pathways to shunt energy to alternative products (Kramer DM, Evans JR, Plant Physiol 155:70–78, 2011). These balancing processes must be extremely robust to contend with the rapid and unpredictable fluctuations in environmental conditions and metabolic demands that occur in nature. A large body of work has come from model systems, especially terrestrial higher plants and the green alga Chlamydomonas reinhardtii, leading to a model for the regulation of light reactions that involves 1) sensing of the pH gradient component of the thylakoid proton motive force (pmf), and 2) the redox state of the plastoquinone- and stromal pools. Over the short term, these sensors trigger regulation of light capture by altering the activity of ATP synthase leading to adjustments in lumen pH, which fine tunes light capture through nonphotochemical quenching (NPQ) and control of electron flow by adjusting the rate of PQH 2 oxidation at the b 6 f complex. Simultaneously, this system controls the balance of ATP/NADPH by adjusting electron flux to linear and cyclic electron flow pathways to balance ATP/NADPH. This integrated “pmf paradigm” model explains much of the existing data on plants and green algae, but may not extend to other diverse organisms. This review considers how advances in our understanding of photosynthesis over the past 7–8 years, particularly in the discoveries of diverse biochemical/biophysical mechanisms in aquatic photosynthetic species, affects the view of energy balance, including the shunting of electrons to O 2 through the flavodiiron proteins (FLV), the plastid terminal oxidase, the dissipation of electric field by ion movements, and the activation of alternative electron sinks. Furthermore, we will introduce the basic model that has been developed for higher plant chloroplasts, then contrast these with selected aquatic systems, focusing on how the differences impact the needs to re-balance both energy input and its partitioning into energy currencies.

Kanazawa, Atsuko↗
DOE OSTI2024

Carbon-13 Radiofrequency Amplification by Stimulated Emission of Radiation of the Hyperpolarized Ketone and Hemiketal Forms of Allyl [1- 13 C]Pyruvate

13 C hyperpolarized pyruvate is an emerging MRI contrast agent for sensing molecular events in cancer and other diseases with aberrant metabolic pathways. This metabolic contrast agent can be produced via several hyperpolarization techniques. Despite remarkable success in research settings, widespread clinical adoption faces substantial roadblocks because the current sensing technology utilized to sense this contrast agent requires the excitation of 13 C nuclear spins that also need to be synchronized with MRI field gradient pulses. Here, we demonstrate sensing of hyperpolarized allyl [1- 13 C]pyruvate via the stimulated emission of radiation that mitigates the requirements currently blocking broader adoption. Specifically, 13 C Radiofrequency Amplification by Stimulated Emission of Radiation ( 13 C RASER) was obtained after pairwise addition of parahydrogen to a pyruvate precursor, detected in a commercial inductive detector with a quality factor (Q) of 32 for sample concentrations as low as 0.125 M with 13 C polarization of 4%. Moreover, parahydrogen-induced polarization allowed for the preparation of a mixture of ketone and hemiketal forms of hyperpolarized allyl [1- 13 C]pyruvate, which are separated by 10 ppm in 13 C NMR spectra. This is a good model system to study the simultaneous 13 C RASER signals of multiple 13 C species. This system models the metabolic production of hyperpolarized [1- 13 C]lactate from hyperpolarized [1- 13 C]pyruvate, which has a similar chemical shift difference. Our results show that 13 C RASER signals can be obtained from both species simultaneously when the emission threshold is exceeded for both species. On the other hand, when the emission threshold is exceeded only for one of the hyperpolarized species, 13 C stimulated emission is confined to this species only, therefore enabling the background-free detection of individual hyperpolarized 13 C signals. Furthermore, the reported results pave the way to novel sensing approaches of 13 C hyperpolarized pyruvate, potentially unlocking hyperpolarized 13 C MRI on virtually any MRI system–an attractive vision for the future molecular imaging and diagnostics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Optically pumped gradient magnetometer

A method is provided for sensing a magnetic field in a magnetic gradiometer of the kind in which pump light and light constituting an optical carrier traverse first and second atomic vapor cells that contain host atoms and that are separated from each other by a known distance. According to such method, the host atoms are prepared in a coherent superposition of two quantum states that differ in energy by an amount that is sensitive to an ambient magnetic field. Modulation of the optical carrier in the respective cells gives rise to sidebands that interfere to generate a beat frequency indicative of the magnetic field gradient. The host atoms are prepared at least in a mode that allows measurement of ambient magnetic field components perpendicular to the axis of the pump light. In such mode, the host atoms are spin-polarized by pump light while subjected to a controlled magnetic field directed parallel to the pump beam, and then the controlled magnetic field is adiabatically extinguished.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Increased accuracy and signal-to-noise ratio through recent improvements in infra-red video bolometer fabrication and calibration

The infra-red video bolometer (IRVB) is a diagnostic equipped with an infra-red camera that measures the total radiated power in thousands of lines of sight within a large field of view. Recently validated in MAST-U [Fderici et al., Rev. Sci. Instrum. 94, 033502 (2023)], it offers a high spatial resolution map of the radiated power in the divertor region, where large gradients are expected. The IRVB’s sensing element comprises a thin layer of high Z absorbing material, typically platinum, usually coated with carbon to reduce reflections [Peterson et al., Rev. Sci. Instrum. 79, 10E301 (2008)].Here, the possibility of using a relatively inert material such as titanium, is explored that can be produced in layers up to 1 μm compared to 2.5 μm for Pt and then coat it with Pt of the desired thickness (0.3 μm per side here) and carbon. This leads to a higher temperature signal (about 3 times) and better spatial resolution (about 4 times), resulting in higher accuracy in the measured power [Peterson et al., Rev. Sci. Instrum. 79, 10E301 (2008)]. This assembly is also expected to improve foil uniformity, as the Pt layer is obtained via deposition rather than mechanical processes [Mukai et al., Rev. Sci. Instrum. 87, 2014 (2016)].Given its multi-material composition, measuring the thermal properties of the foil assembly is vital. Various methods using a calibrated laser as a heat source have been developed, analyzing the temperature profile shape [Sano et al., Plasma and Fusion Res. 7, 2405039 (2012)] and [Mukai et al., Rev. Sci. Instrum. 89, 10E114 (2018)] or fitting the calculated laser power for different intensities and frequencies [Fderici et al., Rev. Sci. Instrum. 94, 033502 (2023)]. Here, a simpler approach is presented, which relies on analyzing the separate components of the foil heat equation for a single laser exposure in a given area. This can then be iterated over the entire foil to capture local deviations.

Magnetic Fusion Energy↗
DOE OSTI2024

Highly cascaded first-order fiber Bragg gratings in highly multimode optical fibers for distributed temperature sensing under harsh environment conditions

This study presents a pioneering technique for fabricating highly cascaded first-order fiber Bragg gratings (FBGs) using a femtosecond laser-assisted point-by-point inscription method in highly multimode optical fibers, specifically Sapphire crystalline fiber, and pure silica coreless fiber. Notably, it marks the first successful demonstration of a distributed array comprising 10 FBGs within highly multimode fibers. This achievement is facilitated by a high-power laser technique that yields larger reflectors characterized by a Gaussian intensity profile. These first-order FBGs offer various advantages, including enhanced reflectivity, reduced fabrication time, and simplified spectral characteristics, enhancing their accessibility for interpretation when contrasted with higher-order FBGs. In addition to that it encompasses a comprehensive analysis of the robustness and efficacy of these FBGs, with particular emphasis on their ability to endure extreme temperatures. These FBGs demonstrate an advantageous capability for localized multi-point temperature monitoring, reaching temperatures up to 1500°C with sapphire crystalline fiber and 1100°C with pure silica coreless fiber. This resilience makes them suitable for deployment in harsh environmental conditions. This innovative approach substantially broadens the potential applications of highly multimode optical fibers, particularly in the arena of sensing and communication, where challenges related to thermal gradients and harsh environments prevail. Furthermore, these groundbreaking first-order FBGs signify a substantial advancement in the realm of distributed temperature sensing, offering supreme capabilities for temperature monitoring and signal stability. As such, our work holds the promise of a substantial impact on industries and applications that demand unwavering reliability under extreme conditions.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Extracting energy from ocean thermal and salinity gradients to power unmanned underwater vehicles: State of the art, current limitations, and future outlook

Thermal gradient energy-generation technologies for powering unmanned underwater vehicles (UUVs) or autonomous sensing systems in the ocean are mainly in the research development phase or commercially available at a limited scale, and salinity-gradient energy-generation technologies have not been adequately researched yet. The demand for self-powered UUVs suitable for long-term deployments has been growing, and further research related to small-scale ocean gradient energy systems is needed. In this study, we conducted a comprehensive review about harvesting energy from ocean thermal or salinity gradients for powering UUVs, focusing on gliders and profiling floats. Thermal gradient energy systems for UUVs based on phase change materials (PCM) cannot provide the energy required for powering autonomous sensing systems because of the systems' low energy conversion efficiency. Besides reducing energy consumption by developing more efficient electrical-mechanical systems, enhancing the thermal conductivity of the PCMs may help address this challenge by increasing the power generation rate of the UUVs. Several other emerging technologies, such as thermoelectric generators, shape memory alloys, and small-scale thermodynamic cycle systems, have shown potential for powering UUVs, but they are still only at the laboratory testing or conceptual design phase. The most advanced power generation technologies based on salinity gradients, reverse electrodialysis and pressure-retarded osmosis, are still not economically viable for large-scale deployment, mainly because of the high cost of the components required to operate in harsh saline environments. Our feasibility evaluation showed that existing salinity gradient power generation technologies are not directly feasible for powering UUVs in the open ocean.

16 TIDAL AND WAVE POWER↗
DOE OSTI2022

The Thermal Response of a Packed Bed Thermal Energy Storage System upon Saturated Steam Injection Using Distributed Temperature Sensing

The effectiveness of a thermal energy storage (TES) system is typically characterized with the help of thermal stratification or temperature gradients along the direction of heat injection, which is typically the flow direction of heat transfer fluid. The steepness of temperature gradients are a direct indicator of the effectiveness or efficiency of the heat storage or dispatch process. The temperature gradient evolution along the packed bed of ceramic particles upon saturated steam injection is presented in this work. Distributed temperature sensing based on optical frequency domain reflectometry was deployed in a packed bed of ceramic particles to capture the thermal front evolution in the axial direction. The physical processes accompanying steam injection in packed beds are complex due to phase change, transitioning two-phase flow, and changes in condensate accumulation. Therefore, the variation of thermal response of the TES system for various steam injection flow rates was experimentally studied using a high-resolution distributed temperature sensing system in a chemically inert alumina particle-packed bed. Distinct zones of different heat transfer modes were observed during the steam injection experiments. A distinct conduction zone, evident from diffuse thermal fronts, was observed at low flow rates, and these thermal gradients became sharper as the flow rate increased. The diffuse thermal fronts in the heat storage media suggest a low exergy efficiency of the TES system, as energy losses started initiating before a significant fraction of the bed was saturated with steam.

25 ENERGY STORAGE↗
DOE OSTI2023

Evidence of Abrupt Transitions Between Sea Ice Dynamical Regimes in the East Greenland Marginal Ice Zone

Sea ice modulates the energy exchange between the atmosphere and the ocean through its kinematics. Marginal ice zone (MIZ) dynamics are complex and are not well resolved in routine observations. Here, we investigate sea ice dynamics in the Greenland Sea MIZ using in situ and remote sensing Lagrangian drift datasets. These datasets provide a unique view into ice dynamics spanning spatial scales. We find evidence of tidal currents strongly affecting sub-daily ice motion. Velocity anomalies show abrupt transitions aligned with gradients in seafloor topography, indicating changes in ocean currents. Remote-sensed ice floe trajectories derived from moderate resolution satellite imagery provide a view of small-scale variability across the Greenland continental shelf. Ice floe trajectories reveal a west-east increasing velocity gradient imposed by the East Greenland Current, with maximum velocities aligned along the continental shelf edge. These results highlight the importance of small scale ocean variability for ice dynamics in the MIZ.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Dairy Methane Emissions in California's San Joaquin Valley Inferred With Ground‐Based Remote Sensing Observations in the Summer and Winter

Abstract The dairy industry in the San Joaquin Valley (SJV) is one of California’s largest methane (CH 4 ) sources. Reducing dairy emissions is a priority for the state’s climate change plans. Observations of current dairy CH 4 emissions are key to monitoring actions taken toward this goal. To help support this, we present new ground‐based measurements of atmospheric column‐averaged CH 4 mixing ratio (XCH 4 ) gradients across a group of 600 dairies in the central SJV using EM27/SUN solar spectrometers. We used measurements from the 2019 summer and 2020 winter seasons for a top‐down emission inversion based on the WRF‐STILT model. Our top‐down estimates of the region’s dairy emissions range from 90% to 183% of the current CALGEM inventory’s emissions of 277 Gg/yr. In contrast to the strong temperature dependence found by earlier dairy CH 4 emission studies, we also find that our top‐down emissions during the winter measurement days are comparable to the summer measurement days, possibly due to seasonal changes in dairy management practices and meteorological conditions. Furthermore, we find significant interday variability in our measurements and find that our emission estimates overlap with earlier top‐down studies and bottom‐up inventories in this region. Our study demonstrates how analysis of ground‐based remotely sensed CH 4 gradient observations can help improve our understanding of CH 4 sources at scales relevant to mitigation policy. It also reflects the need for long‐term monitoring of CH 4 emissions in the region and at individual facilities to better understand their emissions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Running Primal-Dual Gradient Method for Time-Varying Nonconvex Problems

This paper focuses on a time-varying constrained nonconvex optimization problem, and considers the synthesis and analysis of online regularized primal-dual gradient methods to track a Karush-Kuhn-Tucker (KKT) trajectory. The proposed regularized primal-dual gradient method is implemented in a running fashion, in the sense that the underlying optimization problem changes during the execution of the algorithms. In order to study its performance, we first derive its continuous-time limit as a system of differential inclusions. We then study sufficient conditions for tracking a KKT trajectory, and also derive asymptotic bounds for the tracking error (as a function of the time-variability of a KKT trajectory). Further, we provide a set of sufficient conditions for the KKT trajectories not to bifurcate or merge, and also investigate the optimal choice of the parameters of the algorithm. Illustrative numerical results for a time-varying nonconvex problem are provided.

differential inclusion↗
DOE OSTI2020

Field-gradient measurement using a Stern-Gerlach atomic interferometer with butterfly geometry

Atomic interferometers have been studied as a promising device for precise sensing of external fields. Among various configurations, a particular configuration with a butterfly-shaped geometry has been designed to sensitively probe field gradients. Here, we introduce a Stern-Gerlach (SG) butterfly interferometer by incorporating magnetic field in the conventional butterfly-shaped configuration. Atomic trajectories of the interferometer can be flexibly adjusted by controlling magnetic fields to increase the sensitivity of the interferometer, while the conventional butterfly interferometer using Raman transitions can be understood as a special case. We also show that the SG interferometer can keep high contrast against a misalignment in position and momentum caused by the field gradient.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Explicit physics-informed neural networks for nonlinear closure: The case of transport in tissues

In upscaling methods, closures for nonlinear problems present a well-known challenge. While a number of theoretical methods have been proposed for handling such closures, nonlinearities still remain a significant obstacle for many problems. In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in multiscale tissues. The classical effectiveness factor model is used to formulate the macroscale reaction kinetics. We train a multilayer perceptron network using training data generated by direct numerical simulations over microscale examples. Once trained, the network is used in an algorithm for numerically solving the upscaled (coarse-grained) differential equation describing mass transport and reaction in two example tissues. The network is described as being explicit in the sense that the network is trained using macroscale concentrations and gradients of concentration as components of the feature space rather than incorporating them as part of a constraint in the optimization process. Network training and solutions to the macroscale transport equations were computed for two different tissues. The two tissue types (brain and liver) exhibit markedly different geometrical complexity and spatial scale (cell size and sample size). The upscaled solutions for the average concentration are compared with numerical solutions derived from the microscale concentration fields by a posteriori averaging. There are three outcomes of this work of particular note. 1) Our overall approach results in an upscaled nonlinear PDE. The PDE is closed using a neural network, and our approach results in the definition of the classical effectiveness factor for effecting closure. 2) We identify particular source terms for the closure problem that are important for representing the structure of the closure. These source terms involve macroscale concentrations and their gradients. We adopt these source terms to use as explicit features in the learning algorithm. We find the trained networks that include the macroscale source terms generate models that are able to predict the correction factor with increased fidelity over those that do not. 3) We find that the trained network exhibits good generalizability, and it is able to predict the effectiveness factor with high fidelity for realistically-structured tissues despite the significantly different scale and geometrical complexity of the two example tissue types. This latter result emphasizes our purposeful connection between conventional averaging methods with the use of machine learning for closure; this contrasts with some machine learning methods for upscaling where the exact form of the macroscale equation remains unknown.

97 MATHEMATICS AND COMPUTING↗