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

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Application of machine learning to discover new intermetallic catalysts for the hydrogen evolution and the oxygen reduction reactions

The adsorption energies for hydrogen, oxygen, and hydroxyl were calculated by means of density functional theory on the lowest energy surface of 24 pure metals and 332 binary intermetallic compounds with stoichiometries AB, A 2 B, and A 3 B taking into account the effect of biaxial elastic strains. This information was used to train two random forest regression models, one for the hydrogen adsorption and another for the oxygen and hydroxyl adsorption, based on 9 descriptors that characterized the geometrical and chemical features of the adsorption site as well as the applied strain. All the descriptors for each compound in the models could be obtained from physico-chemical databases. The random forest models were used to predict the adsorption energy for hydrogen, oxygen, and hydroxyl of ≈2700 binary intermetallic compounds with stoichiometries AB, A 2 B, and A 3 B made of metallic elements, excluding those that were environmentally hazardous, radioactive, or toxic. This information was used to search for potential good catalysts for the HER and ORR from the criteria that their adsorption energy for H and O/OH, respectively, should be close to that of Pt. Further, this investigation shows that the suitably trained machine learning models can predict adsorption energies with an accuracy not far away from density functional theory calculations with minimum computational cost from descriptors that are readily available in physico-chemical databases for any compound. Moreover, the strategy presented in this paper can be easily extended to other compounds and catalytic reactions, and is expected to foster the use of ML methods in catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Group-Invariant Quantum Machine Learning

Quantum machine learning (QML) models are aimed at learning from data encoded in quantum states. Recently, it has been shown that models with little to no inductive biases (i.e., with no assumptions about the problem embedded in the model) are likely to have trainability and generalization issues, especially for large problem sizes. As such, it is fundamental to develop schemes that encode as much information as available about the problem at hand. In this work we present a simple, yet powerful, framework where the underlying invariances in the data are used to build QML models that, by construction, respect those symmetries. These so-called group-invariant models produce outputs that remain invariant under the action of any element of the symmetry group $\mathfrak{G}$ associated with the dataset. We present theoretical results underpinning the design of $\mathfrak{G}$-invariant models, and exemplify their application through several paradigmatic QML classification tasks, including cases when $\mathfrak{G}$ is a continuous Lie group and also when it is a discrete symmetry group. Notably, our framework allows us to recover, in an elegant way, several well-known algorithms for the literature, as well as to discover new ones. Taken together, we expect that our results will help pave the way towards a more geometric and group-theoretic approach to QML model design.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2007

A Parametric Geometry Computational Fluid Dynamics (CFD) Study Utilizing Design of Experiments (DOE)

Design of Experiments (DOE) was applied to the LAS geometric parameter study to efficiently identify and rank primary contributors to integrated drag over the vehicles ascent trajectory in an order of magnitude fewer CFD configurations thereby reducing computational resources and solution time. SME s were able to gain a better understanding on the underlying flowphysics of different geometric parameter configurations through the identification of interaction effects. An interaction effect, which describes how the effect of one factor changes with respect to the levels of other factors, is often the key to product optimization. A DOE approach emphasizes a sequential approach to learning through successive experimentation to continuously build on previous knowledge. These studies represent a starting point for expanded experimental activities that will eventually cover the entire design space of the vehicle and flight trajectory.

Rhew, Ray D.↗
DOE OSTI2015

SU-E-J-254: Evaluating the Role of Mid-Treatment and Post-Treatment FDG-PET/CT in Predicting Progression-Free Survival and Distant Metastasis of Anal Cancer Patients Treated with Chemoradiotherapy

Purpose: To evaluate the role of mid-treatment and post-treatment FDG-PET/CT in predicting progression-free survival (PFS) and distant metastasis (DM) of anal cancer patients treated with chemoradiotherapy (CRT). Methods: 17 anal cancer patients treated with CRT were retrospectively studied. The median prescription dose was 56 Gy (range, 50–62.5 Gy). All patients underwent FDG-PET/CT scans before and after CRT. 16 of the 17 patients had an additional FDG-PET/CT image at 3–5 weeks into the treatment (denoted as mid-treatment FDG-PET/CT). 750 features were extracted from these three sets of scans, which included both traditional PET/CT measures (SUVmax, SUVpeak, tumor diameters, etc.) and spatialtemporal PET/CT features (comprehensively quantify a tumor’s FDG uptake intensity and distribution, spatial variation (texture), geometric property and their temporal changes relative to baseline). 26 clinical parameters (age, gender, TNM stage, histology, GTV dose, etc.) were also analyzed. Advanced analytics including methods to select an optimal set of predictors and a model selection engine, which identifies the most accurate machine learning algorithm for predictive analysis was developed. Results: Comparing baseline + mid-treatment PET/CT set to baseline + posttreatment PET/CT set, 14 predictors were selected from each feature group. Same three clinical parameters (tumor size, T stage and whether 5-FU was held during any cycle of chemotherapy) and two traditional measures (pre- CRT SUVmin and SUVmedian) were selected by both predictor groups. Different mix of spatial-temporal PET/CT features was selected. Using the 14 predictors and Naive Bayes, mid-treatment PET/CT set achieved 87.5% accuracy (2 PFS patients misclassified, all local recurrence and DM patients correctly classified). Post-treatment PET/CT set achieved 94.0% accuracy (all PFS and DM patients correctly predicted, 1 local recurrence patient misclassified) with logistic regression, neural network or support vector machine model. Conclusion: Applying radiomics approach to either midtreatment or post-treatment PET/CT could achieve high accuracy in predicting anal cancer treatment outcomes. This work was supported in part by the National Cancer Institute Grant R01CA172638.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Comparative study of machine learning techniques for post-combustion carbon capture systems

Computational analysis of countercurrent flows in packed absorption columns, often used in solvent-based post-combustion carbon capture systems (CCSs), is challenging. Typically, computational fluid dynamics (CFD) approaches are used to simulate the interactions between a solvent, gas, and column's packing geometry while accounting for the thermodynamics, kinetics, heat, and mass transfer effects of the absorption process. These simulations can then be used explain a column's hydrodynamic characteristics and evaluate its CO 2 -capture efficiency. However, these approaches are computationally expensive, making it difficult to evaluate numerous designs and operating conditions to improve efficiency at industrial scales. In this work, we comprehensively explore the application of statistical ML methods, convolutional neural networks (CNNs), and graph neural networks (GNNs) to aid and accelerate the scale-up and design optimization of solvent-based post-combustion CCSs. We apply these methods to CFD datasets of countercurrent flows in absorption columns with structured packings characterized by several geometric parameters. We train models to use these parameters, inlet velocity conditions, and other model-specific representations of the column to estimate key determinants of CO 2 -capture efficiency without having to simulate additional CFD datasets. We also evaluate the impact of different input types on the accuracy and generalizability of each model. We discuss the strengths and limitations of each approach to further elucidate the role of CNNs, GNNs, and other machine learning approaches for CO 2 -capture property prediction and design optimization.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2010

Vehicle Sketch Pad: a Parametric Geometry Modeler for Conceptual Aircraft Design

The conceptual aircraft designer is faced with a dilemma, how to strike the best balance between productivity and fidelity? Historically, handbook methods have required only the coarsest of geometric parameterizations in order to perform analysis. Increasingly, there has been a drive to upgrade analysis methods, but these require considerably more precise and detailed geometry. Attempts have been made to use computer-aided design packages to fill this void, but their cost and steep learning curve have made them unwieldy at best. Vehicle Sketch Pad (VSP) has been developed over several years to better fill this void. While no substitute for the full feature set of computer-aided design packages, VSP allows even novices to quickly become proficient in defining three-dimensional, watertight aircraft geometries that are adequate for producing multi-disciplinary meta-models for higher order analysis methods, wind tunnel and display models, as well as a starting point for animation models. This paper will give an overview of the development and future course of VSP.

Hahn, Andrew S.↗
NASA NTRSDate not supplied

Machine Learning Algorithms for Aerosol and Cloud Detection Using CATS on the ISS

Clouds and aerosols are one of the largest uncertainties in understanding and forecasting the Earth’s changing climate system. The type and height of aerosols are important factors in determining the top-of-atmosphere (TOA) radiation budget, either direct reflection of solar radiation back to space and/or absorption of solar radiation. In addition to their impact on the Earth’s climate system, aerosols near the surface from wildfires, man-made pollution events, and dust storms are hazardous to human health. The phase and height of clouds also play a critical role in determining the role of clouds in the Earth’s climate system. Cirrus clouds in the upper troposphere can induce a significant daytime TOA warming effect, while liquid water clouds near the surface cause a large corresponding cooling effect. Lidar measurements provide accurate vertically resolved information about clouds and aerosols, including complex multi-layer scenes where passive sensors are challenged and at night, when passive sensors are unable to measure cloud and aerosol properties. The Cloud-Aerosol Transport System (CATS) is a lidar instrument that operated for 33 months on the International Space Station (ISS) at the 1064 nm wavelength to measure attenuated total backscatter and depolarization ratio. These fundamental measurements are used to derive “vertical feature mask” cloud and aerosol products, including layer top/base heights, layer geometrical thickness, aerosol type, and cloud phase. While space-based lidar systems like CATS provide cloud and aerosol vertical distributions that improve our understanding of the climate system, averaging of the daytime data from these sensors is required, at the expense of spatial resolution, to improve the daytime signal-to noise (SNR) and thus atmospheric layer detection. This presentation shows results from machine learning (ML) techniques that, when applied to CATS data: 1. improve the 1064 nm SNR 2. enable detection of atmospheric features during daytime with a horizontal resolution of 350 m or 5 km (compared to the 60 km required for standard CATS data products) 3. increase the number of atmospheric layers detected in the CATS data. A Convolutional Neural Network (CNN) trained using CATS standard data products also demonstrated the potential for improved cloud-aerosol discrimination, cloud phase, and aerosol typing compared to the operational CATS algorithms for cloud edges and complex near-surface scenes during daytime. The ML tools described in this paper can facilitate the development of smaller, low-cost lidar systems in the future and enable real-time accessibility of lidar data products from future lidar systems for monitoring and forecasting of hazardous events.

John Yorks↗
NASA NTRS2003

Historical Review of Uncommanded Lateral-Directional Motions at Transonic Conditions

This paper presents the results of a survey of past experiences with uncommanded lateral-directional motions at transonic speeds during specific military aircraft programs. The effort was undertaken to provide qualitative and quantitative information on past airplane programs that might be of use to the participants in the joint NASA/Navy/Air Force Abrupt Wing Stall (AWS) Program. The AWS Program was initiated because of the experiences of the F/A-l8E/F development program, during which unexpected, severe wing-drop motions were encountered by preproduction aircraft at transonic conditions. These motions were judged to be significantly degrading to the primary mission requirements of the aircraft. Although the problem was subsequently solved for the production version of the F/A-l8E/F, a high-level review panel emphasized the poor understanding of such phenomena and issued a strong recommendation to: "Initiate a national research effort to thoroughly and systematically study the wing drop phenomena." A comprehensive, cooperative NASA/Navy/Air Force AWS Program was designed to respond to provide the required technology requirements. As part of the AWS Program, a work element was directed at a historical review of wing-drop experiences in past aircraft development programs at high subsonic and transonic speeds. In particular, information was requested regarding: specific aircraft configurations that exhibited uncommanded motions and the nature of the motions; geometric characteristics of the air- planes; flight conditions involved in occurrences; relevant data, including wind-tunnel, computational, and flight sources; figures of merit used for analyses; and approaches used to alleviate the problem. An attempt was also made to summarize some of the more important lessons learned from past experiences, and to recommend specific research efforts. In addition to providing technical information to assist the AWS research objectives, the study produced fundamental information regarding the historical challenge of uncommanded lateral-directional motions at transonic conditions and the associated aerodynamic phenomena.

Chambers, Joseph R.↗
NASA NTRS2003

Historical Review of Uncommanded Lateral-Directional Motions At Transonic Conditions (Invited)

This paper presents the results of a survey of past experiences with uncommanded lateral-directional motions at transonic speeds during specific military aircraft programs. The effort was undertaken to provide qualitative and quantitative information on past airplane programs that might be of use to the participants in the joint NASA/Navy/Air Force Abrupt Wing Stall (AWS) Program. The AWS Program was initiated because of the experiences of the F/A-18E/F development program, during which unexpected, severe wing-drop motions were encountered by preproduction aircraft at transonic conditions. These motions were judged to be significantly degrading to the primary mission requirements of the aircraft. Although the problem was subsequently solved for the production version of the F/A-l8E/F, a high-level review panel emphasized the poor understanding of such phenomena and issued a strong recommendation to: Initiate a national research effort to thoroughly and systematically study the wing drop phenomena. A comprehensive, cooperative NASA/Navy/Air Force AWS Program was designed to respond to provide the required technology requirements. As part of the AWS Program, a work element was directed at a historical review of wing-drop experiences in past aircraft development programs at high subsonic and transonic speeds. In particular, information was requested regarding: specific aircraft configurations that exhibited uncommanded motions and the nature of the motions; geometric characteristics of the air- planes; flight conditions involved in occurrences; relevant data, including wind-tunnel, computational, and flight sources; figures of merit used for analyses; and approaches used to alleviate the problem. An attempt was also made to summarize some of the more important lessons learned from past experiences, and to recommend specific research efforts. In addition to providing technical information to assist the AWS research objectives, the study produced fundamental information regarding the historical challenge of uncommanded lateral-directional motions at transonic conditions and the associated aerodynamic phenomena.

Chambers, Joseph R.↗
DOE OSTI2021

Attribute-Guided Adversarial Training for Robustness to Natural Perturbations

We report while existing work in robust deep learning has focused on small pixel-level norm-based perturbations, this may not account for perturbations encountered in several real world settings. In many such cases although test data might not be available, broad specifications about the types of perturbations (such as an unknown degree of rotation) may be known. We consider a setup where robustness is expected over an unseen test domain that is not i.i.d. but deviates from the training domain. While this deviation may not be exactly known, its broad characterization is specified a priori, in terms of attributes. We propose an adversarial training approach which learns to generate new samples so as to maximize exposure of the classifier to the attributes-space, without having access to the data from the test domain. Our adversarial training solves a min-max optimization problem, with the inner maximization generating adversarial perturbations, and the outer minimization finding model parameters by optimizing the loss on adversarial perturbations generated from the inner maximization. We demonstrate the applicability of our approach on three types of naturally occurring perturbations --- object-related shifts, geometric transformations, and common image corruptions. Our approach enables deep neural networks to be robust against a wide range of naturally occurring perturbations. We demonstrate the usefulness of the proposed approach by showing the robustness gains of deep neural networks trained using our adversarial training on MNIST, CIFAR-10, and a new variant of the CLEVR dataset.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Physics-informed machine learning assisted uncertainty quantification for the corrosion of dissimilar material joints

Jointing techniques like the Self-Piercing Riveting (SPR), Resistance Spot Welding (RSW) and Rivet-Weld (RW) joints are used for mass production of dissimilar material joints due to their high performance, short cycle time, and adaptability. However, the service life and safety usage of these joints can be largely impacted by the galvanic corrosion due to the difference in equilibrium potentials between the metals with the presence of electrolyte. Here, in this paper, we focus on Al-Fe galvanic corrosion and develop physics-informed machine learning based surrogate model for statistical corrosion analysis, which enables the reliability analysis of dissimilar material joints under corrosion environment. In this study, a physics-based finite element (FE) corrosion model has been developed to simulate the galvanic corrosion between a Fe cathode and an Al anode. Geometric and environmental factors including crevice gap, roughness of anode, conductivity, and the temperature of the electrolyte are investigated. Further, a thorough Uncertainty Quantification (UQ) analysis is conducted for the overall corrosion behavior of the Fe-Al joints. It is found that the electrolyte conductivity has the largest effects on the material loss and needs to be managed closely for better corrosion control. This will help in designing and manufacturing joints with improved corrosion performance.

42 ENGINEERING↗
DOE OSTI2019

Dynamical nonlinear memory capacitance in biomimetic membranes

Two-terminal memory elements, or memelements, capable of co-locating signal processing and memory via history-dependent reconfigurability at the nanoscale are vital for next-generation computing materials striving to match the brain’s efficiency and flexible cognitive capabilities. While memory resistors, or memristors, have been widely reported, other types of memelements remain underexplored or undiscovered. Here we report the first example of a volatile, voltage-controlled memcapacitor in which capacitive memory arises from reversible and hysteretic geometrical changes in a lipid bilayer that mimics the composition and structure of biomembranes. We demonstrate that the nonlinear dynamics and memory are governed by two implicitly-coupled, voltage-dependent state variables—membrane radius and thickness. Further, our system is capable of tuneable signal processing and learning via synapse-like, short-term capacitive plasticity. These findings will accelerate the development of low-energy, biomolecular neuromorphic memelements, which, in turn, could also serve as models to study capacitive memory and signal processing in neuronal membranes.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Neural network–based pore flow field prediction in porous media using super resolution

Direct pore-scale simulations of fluid flow through porous media are computationally expensive to perform for realistic systems. Previous works have demonstrated using the geometry of the microstructure of porous media to predict the velocity fields therein based on neural networks. However, such trained neural networks do not perform well for unseen porous media with a large degree of heterogeneity. In this study we propose that incorporating a coarse velocity field in the input of neural networks is an effective way to improve the prediction performance. The coarse velocity field can be simulated with a low computational cost and provides global information to regularize the ill-posedness of the learning problem, which is usually caused by the use of local geometries due to the computational resource constraints. We show that incorporating the coarse-mesh velocity field significantly improves the prediction accuracy of the fine-mesh velocity field by comparison to the prediction that relies on geometric information alone, especially for the porous medium with a large interior vuggy pore space. We also show the flexibility of training the network in using coarse velocity fields with various resolutions. The results suggest that even using coarse velocity field with a very low resolution, the predictions are still enhanced and close to the ground truths. The feasibility of the method is further demonstrated by testing the trained network on real rocks. This study highlights the merits of incorporating a coarse-mesh velocity field into the input for neural networks, which provides global, physics-based information for the model, thereby improving the model's generalization capability.

42 ENGINEERING↗
DOE OSTI2021

Significant DBSCAN+: Statistically Robust Density-based Clustering

Cluster detection is important and widely used in a variety of applications, including public health, public safety, transportation, and so on. Given a collection of data points, we aim to detect density-connected spatial clusters with varying geometric shapes and densities, under the constraint that the clusters are statistically significant. The problem is challenging, because many societal applications and domain science studies have low tolerance for spurious results, and clusters may have arbitrary shapes and varying densities. As a classical topic in data mining and learning, a myriad of techniques have been developed to detect clusters with both varying shapes and densities (e.g., density-based, hierarchical, spectral, or deep clustering methods). However, the vast majority of these techniques do not consider statistical rigor and are susceptible to detecting spurious clusters formed as a result of natural randomness. On the other hand, scan statistic approaches explicitly control the rate of spurious results, but they typically assume a single “hotspot” of over-density and many rely on further assumptions such as a tessellated input space. To unite the strengths of both lines of work, we propose a statistically robust formulation of a multi-scale DBSCAN, namely Significant DBSCAN+, to identify significant clusters that are density connected. As we will show, incorporation of statistical rigor is a powerful mechanism that allows the new Significant DBSCAN+ to outperform state-of-the-art clustering techniques in various scenarios. We also propose computational enhancements to speed-up the proposed approach. Experiment results show that Significant DBSCAN+ can simultaneously improve the success rate of true cluster detection (e.g., 10–20% increases in absolute F1 scores) and substantially reduce the rate of spurious results (e.g., from thousands/hundreds of spurious detections to none or just a few across 100 datasets), and the acceleration methods can improve the efficiency for both clustered and non-clustered data.

Computer Science↗
DOE OSTI2014

The development of poly(vinyl chloride) [PVC] extrusions for a 14,000-ton self-supporting structure for the detection of neutrinos

The NOvA Neutrino Experiment has built a one of a kind self-supporting plastic structure, potentially the largest ever built. The PVC structure serves as a neutrino detector and is composed of 28 individual blocks that measure 15.5 m (51 feet) high by 15.5 m (51 feet) wide by 2.1 m (7 feet) deep. The primary parts in the detector construction are 15.5m (51 foot), 15-cell PVC extrusions. These extrusions from the basis of the detector modules which are laminated together in a crossed pattern to form the individual blocks and then filled with mineral oil based liquid scintillator. The self-supporting nature of the detector places important structural requirements on both the PVC formulation and the extrusions. Block assembly requirements impose narrow geometric tolerances. Due to the method of detecting neutrinos, the extrusions must possess exceptionally high reflectivity over a particular wavelength range. The requirement places additional restrictions on the components of the PVC formulation. Altogether, the PVC extrusions have to maintain important reflectivity characteristics, provide structural support to the detector, and meet relatively tight geometric requirements for assembly. In order to meet these constraints, a custom PVC formulation had to be created and extruded. Here, we describe the purpose and requirements of the NOvA detector leading to the production of our unique PVC extrusion, summarize the R&D process, and discuss the lessons learned.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

SU-F-J-199: Predictive Models for Cone Beam CT-Based Online Verification of Pencil Beam Scanning Proton Therapy

Purpose: To utilize online CBCT scans to develop models for predicting DVH metrics in proton therapy of head and neck tumors. Methods: Nine patients with locally advanced oropharyngeal cancer were retrospectively selected in this study. Deformable image registration was applied to the simulation CT, target volumes, and organs at risk (OARs) contours onto each weekly CBCT scan. Intensity modulated proton therapy (IMPT) treatment plans were created on the simulation CT and forward calculated onto each corrected CBCT scan. Thirty six potentially predictive metrics were extracted from each corrected CBCT. These features include minimum/maximum/mean over and under-ranges at the proximal and distal surface of PTV volumes, and geometrical and water equivalent distance between PTV and each OARs. Principal component analysis (PCA) was used to reduce the dimension of the extracted features. Three principal components were found to account for over 90% of variances in those features. Datasets from eight patients were used to train a machine learning model to fit these principal components with DVH metrics (dose to 95% and 5% of PTV, mean dose or max dose to OARs) from the forward calculated dose on each corrected CBCT. The accuracy of this model was verified on the datasets from the 9th patient. Results: The predicted changes of DVH metrics from the model were in good agreement with actual values calculated on corrected CBCT images. Median differences were within 1 Gy for most DVH metrics except for larynx and constrictor mean dose. However, a large spread of the differences was observed, indicating additional training datasets and predictive features are needed to improve the model. Conclusion: Intensity corrected CBCT scans hold the potential to be used for online verification of proton therapy and prediction of delivered dose distributions.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Manifold Learning: What, How, and Why

Manifold learning (ML), also known as nonlinear dimension reduction, is a set of methods to find the low-dimensional structure of data. Dimension reduction for large, high-dimensional data is not merely a way to reduce the data; the new representations and descriptors obtained by ML reveal the geometric shape of high-dimensional point clouds and allow one to visualize, denoise, and interpret them. This review presents the underlying principles of ML, its representative methods, and their statistical foundations, all from a practicing statistician's perspective. It describes the trade-offs and what theory tells us about the parameter and algorithmic choices we make in order to obtain reliable conclusions.

Mathematics↗
DOE OSTI2021

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019; Lee et al., 2020). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.

60 APPLIED LIFE SCIENCES↗