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At least 487 records · Page 27

Sensor Reduction for Diversion Detection in a Realistic Heat Pipe Microreactor Using Supervised Machine Learning

Microreactors are designed as a smaller, cheaper, and safer alternative to traditional nuclear power plants. Their non-traditional characteristics and prospect of mass production and deployment will likely require new approaches to nuclear safeguards. The primary proliferation concern with microreactors is the diversion of fuel material. Such diversion may produce measurable defects in key physical attributes like neutron flux, which may in turn be detectable using machine learning models. Preliminary work has demonstrated this ability for modeled nominal and diversion scenarios using large quantities of energy integrated neutron flux data. In practice, the number of available sensors for such measurements will be limited and energy integrated flux information will not be available. This work explores the ability of tree-based gradient boosted ensemble models to classify a given microreactor core is nominal or diversion, and determine the number of fuel pins diverted in the case of diversion with reduced numbers of sensors and more realistic detector responses. Classification accuracy of greater than 98% and regression errors as low as 5% of the total number of fuel pins were achieved with as few as 15 sensors, compared to 99% and 4.1% with a maximum of 240 sensors.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Deep-Learning-derived Boundary Layer Height from Meteorological Data over the SGP, GOAMAZON, CACTI

The planetary boundary-layer (PBL) height (PBLH) is an important parameter for various meteorological and climate studies. This study presents a multi-structure deep neural network (DNN) model, designed to estimate PBLH by integrating morning temperature profiles with surface meteorological observations. The DNN model is developed by leveraging a rich data set of PBLH derived from long-standing radiosonde records and augmented with high-resolution micropulse lidar and Doppler lidar observations. We access the performance of the DNN with an ensemble of 10 members, each featuring distinct hidden layer structures, which collectively yield a robust 27-year PBLH data set over the Southern Great Plains from 1994 to 2020. The influence of various meteorological factors on PBLH is rigorously analyzed through the importance test. Moreover, the DNN model's accuracy is evaluated against radiosonde observations and juxtaposed with conventional remote-sensing methodologies, including Doppler lidar, ceilometer, Raman lidar, and micropulse lidar. The DNN model exhibits reliable performance across diverse conditions and demonstrates lower biases relative to remote-sensing methods. In addition, the DNN model, originally trained over a plain region, demonstrates remarkable adaptability when applied to the heterogeneous terrains and climates encountered during the GoAmazon (tropical rainforest) and CACTI (middle-latitude mountain) campaigns. These findings demonstrate the effectiveness of deep learning models in estimating PBLH, enhancing our understanding of boundary-layer dynamics with implications for enhancing the representation of PBL in weather forecasting and climate modeling.

54 ENVIRONMENTAL SCIENCES↗

Dimensionally Reduced Model for Rapid and Accurate Prediction of Gas Saturation, Pressure, and Brine Production in a CO 2 Storage Application: Case Study Using the SACROC Field as Part of SMART Task 5

This technical report presents work conducted by the sub surface analysis team of the Strategic Systems Analysis & Engineering group at NETL for Task 5 of SMART Phase 1. This study involved the development of deep learning models for CO 2 geologic storage that are capable of accurate prediction of spatio-temporal outputs of CO 2 saturation, pressure, and brine production in three dimensional space over a storage operation's injection and post-injection timeframes. The model framework involves ensembling multi-layer encoder networks that provide dimesionality reduction of geologic inputs with fully connected long short-term memory (LSTM) neural networks that generate time-series prediction This approach offers a means to maximize training time efficiency, reduce computational memory burden, and minimize prediction turnaround.

54 ENVIRONMENTAL SCIENCES↗

Development and Implementation of a Comprehensive Radiometric Validation Protocol for the CERES Earth Radiation Budget Climate Record Sensors

The CERES Flight Models 1 through 4 instruments were launched aboard NASA's Earth Observing System (EOS) Terra and Aqua Spacecraft into 705 Km sun-synchronous orbits with 10:30 a.m. and 1:30 p.m. equatorial crossing times. These instruments supplement measurements made by the CERES Proto Flight Model (PFM) instrument launched aboard NASA's Tropical Rainfall Measuring Mission (TRMM) into a 350 Km, 38-degree mid-inclined orbit. CERES Climate Data Records consist of geolocated and calibrated instantaneous filtered and unfiltered radiances through temporally and spatially averaged TOA, Surface and Atmospheric fluxes. CERES filtered radiance measurements cover three spectral bands including shortwave (0.3 to 5 microns), total (0.3 to 100 microns) and an atmospheric window channel (8 to 12 microns). The CERES Earth Radiation Budget measurements represent a new era in radiation climate data, realizing a factor of 2 to 4 improvement in calibration accuracy and stability over the previous ERBE climate records, while striving for the next goal of 0.3-percent per decade absolute stability. The current improvement is derived from two sources: the incorporation of lessons learned from the ERBE mission in the design of the CERES instruments and the development of a rigorous and comprehensive radiometric validation protocol consisting of individual studies covering different spatial, spectral and temporal time scales on data collected both pre and post launch. Once this ensemble of individual perspectives is collected and organized, a cohesive and highly rigorous picture of the overall end-to-end performance of the CERES instrument's and data processing algorithms may be clearly established. This approach has resulted in unprecedented levels of accuracy for radiation budget instruments and data products with calibration stability of better than 0.2-percent and calibration traceability from ground to flight of 0.25-percent. The current work summarizes the development, philosophy and implementation of the protocol designed to rigorously quantify the quality of the data products as well as the level of agreement between the CERES TRMM, Terra and Aqua climate data records.

Priestley, K. J.↗

Disentangling Rotational Dynamics and Ordering Transitions in a System of Self-Organizing Protein Nanorods via Rotationally Invariant Latent Representations

The dynamics of complex ordering systems with active rotational degrees of freedom exemplified by protein self-assembly is explored using a machine learning workflow that combines deep learning-based semantic segmentation and rotationally invariant variational autoencoder-based analysis of orientation and shape evolution. The latter allows for disentanglement of the particle orientation from other degrees of freedom and compensates for lateral shifts. The disentangled representations in the latent space encode the rich spectrum of local transitions that can now be visualized and explored via continuous variables. The time dependence of ensemble averages allows insight into the time dynamics of the system and, in particular, illustrates the presence of the potential ordering transition. Finally, analysis of the latent variables along the single-particle trajectory allows tracing these parameters on a single-particle level. The proposed approach is expected to be universally applicable for the description of the imaging data in optical, scanning probe, and electron microscopy seeking to understand the dynamics of complex systems where rotations are a significant part of the process.

representation learning↗

Deep-learning-derived planetary boundary layer height from conventional meteorological measurements

Abstract. The planetary boundary layer (PBL) height (PBLH) is an important parameter for various meteorological and climate studies. This study presents a multi-structure deep neural network (DNN) model, which can estimate PBLH by integrating the morning temperature profiles and surface meteorological observations. The DNN model is developed by leveraging a rich dataset of PBLH derived from long-standing radiosonde records augmented with high-resolution micro-pulse lidar and Doppler lidar observations. We access the performance of the DNN with an ensemble of 10 members, each featuring distinct hidden-layer structures, which collectively yield a robust 27-year PBLH dataset over the southern Great Plains from 1994 to 2020. The influence of various meteorological factors on PBLH is rigorously analyzed through the importance test. Moreover, the DNN model's accuracy is evaluated against radiosonde observations and juxtaposed with conventional remote sensing methodologies, including Doppler lidar, ceilometer, Raman lidar, and micro-pulse lidar. The DNN model exhibits reliable performance across diverse conditions and demonstrates lower biases relative to remote sensing methods. In addition, the DNN model, originally trained over a plain region, demonstrates remarkable adaptability when applied to the heterogeneous terrains and climates encountered during the GoAmazon (Green Ocean Amazon; tropical rainforest) and CACTI (Cloud, Aerosol, and Complex Terrain Interactions; middle-latitude mountain) campaigns. These findings demonstrate the effectiveness of deep learning models in estimating PBLH, enhancing our understanding of boundary layer processes with implications for improving the representation of PBL in weather forecasting and climate modeling.

54 ENVIRONMENTAL SCIENCES↗

A multi-dimensional parametric study of variability in multi-phase flow dynamics during geologic CO 2 sequestration accelerated with machine learning

Successful geologic CO 2 storage projects depend on numerical simulations to predict reservoir performance during site selection, injection verification, and post-injection monitoring phases of the project. These numerical simulations solve non-linear sets of coupled partial differential equations, while accounting for multi-phase fluid dynamics on the basis of constitutive equations that are embedded into the solution scheme. As a consequence, individual simulations often require tens to hundreds of hours to complete on high-performance computing clusters. Moreover, laboratory experiments reveal that parametric functions for capillary pressure and relative permeability exhibit substantial variability, even within the same rock type. This combination of computational expense and wide-ranging parametric variability means that there remains substantial uncertainty in the behavior of multi-phase CO 2 -water systems, particularly in the context of feedbacks between relative permeability and capillary pressure. To bridge this knowledge gap, here we develop a novel workflow that utilizes physics-based numerical simulation to train an artificial neural network (ANN) emulator for interrogating the multivariate parameter space that governs both capillary pressure and relative permeability. With this approach, the ANN is trained to emulate both fluid pressure distribution and CO 2 saturation, which are then interrogated quantitatively to generate parametric response surface mappings with high-fidelity resolution. Results from this study initially show that capillary entry pressure is the dominant control on both CO 2 plume geometry and fluid pressure propagation when considering the combined effects of capillary pressure and relative permeability, particularly when phase interference is low and residual CO 2 saturation is high. Moreover, the ANN emulator provides tremendous computational speed-up by computing 2691 individual simulations in several minutes; whereas, the same simulation ensemble would have required ~3 years of simulation time using only physics-based simulation methods (25,000 times speed up).

58 GEOSCIENCES↗

FY21 Progress Report: SRNL Analysis of ICCWR LCM and WAMS data for Corrosion and Cracking

The development of algorithms for machine learning and data analysis for the 3013 Surveillance Program is a collaborative effort by the Savannah River National Laboratory (SRNL) and the University of South Carolina (USC). For corrosion detection, Laser Confocal Microscope (LCM) or Wide Area 3D Measurement System (WAMS) data is extracted from large binary files, with software written to convert the data to physical attributes (e.g., height, color and grayscale values; all as functions of a location in a plane projection). A user-friendly Matlab Graphical User Interface (GUI) that reads data from either LCM or WAMS files was developed to integrate input data with software developed for processing and evaluation. The GUI can selectively download binary data, interrogate data attributes, label data, flag significant features, execute Machine Learning (ML) algorithms, output parameters for trained ML algorithms, report ML model accuracy with respect to labeled data, and generate graphical representations for various analyses. Features can be called out by user-specified thresholds, manual labeling or machine learning algorithms when they have been completed. The ability to rapidly label data is important because of the volume of data required for training machine learning algorithms. The GUI has the flexibility to allow addition of improved ML algorithms, methods for data visualization, and statistical computations. Statistical analyses via the GUI include areas of pits within a defined range of pit depths, correlations between Red-Green-Blue (RGB) or grayscale intensity and relative surface height, covariances between values associated with features, and feature histograms. The development of supervised machine learning algorithms, however, has been hindered by a lack of training data. The machine learning algorithms for crack identification are being refined but require improvements to the true positive rate for crack detection. This shortcoming is an artifact of the limited training data currently available, perhaps more so than the structure of the neural networks. At present, the best results are had from a consensus over an ensemble of randomly generated Deep Neural Network (DNN) or Convolutional Neural Network (CNN) algorithms. Although the consensus accuracy method has yielded optimum true positive and true negative rates in excess of 80%, additional validation testing is necessary. In addition to the suite of LCM data that was initially used, and which represents the majority of the work presented in this report, WAMS image data was also reviewed at a preliminary level. The review included a comparison between image resolution and dynamic range for each method. WAMS (ZON file) image data was found to have a pixel pitch of 3.69μm compared to 1 μm for the LCM (vk4 file) data, which implies a lower resolution for the WAMS images. Conversely, the ratio of dynamic range of the WAMS data to the LCM data was approximately 41:20 for height data, suggesting that information from WAMS should more accurately determine the depth of pits. At present, the significance of the greater dynamic range of the WAMS data relative to the LCM data has not yet been evaluated.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Revealing the evolution of order in materials microstructures using multi-modal computer vision

The development of high-performance materials for microelectronics, energy storage, and extreme environments depends on our ability to describe and direct property-defining microstructural order. Our present understanding is typically derived from laborious manual analysis of imaging and spectroscopy data, which is difficult to scale, challenging to reproduce, and lacks the ability to reveal latent associations needed for mechanistic models. Here, we demonstrate a multi-modal machine learning (ML) approach to describe order from electron microscopy analysis of the complex oxide La 1−x Sr x FeO 3 . We construct a hybrid pipeline based on fully and semi-supervised classification, allowing us to evaluate both the characteristics of each data modality and the value each modality adds to the ensemble. We observe distinct differences in the performance of uni- and multi-modal models, from which we draw general lessons in describing crystal order using computer vision.

36 MATERIALS SCIENCE↗

Maximum Entropy Theory of Multiscale Coarse-Graining via Matching Thermodynamic Forces: Application to a Molecular Crystal (TATB)

The MSCG/FM (multiscale coarse-graining via force-matching) approach is an efficient supervised machine learning method to develop microscopically informed coarse-grained (CG) models. Here we present a theory based on the principle of maximum entropy (PME) enveloping the existing MSCG/FM approaches. This theory views the MSCG/FM method as a special case of matching the thermodynamic forces from the extended ensemble described by the set of thermodynamic (relevant) system coordinates. This set may include CG coordinates, the stress tensor, applied external fields, and so forth, and may be characterized by nonequilibrium conditions. Following the presentation of the theory, we discuss the consistent matching of both bonded and nonbonded interactions. The proposed PME formulation is used as a starting point to extend the MSCG/FM method to the constant strain ensemble, which together with the explicit matching of the bonded forces is better suited for coarse-graining anisotropic media at a submolecular resolution. The theory is demonstrated by performing the fine coarse-graining of crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a well-known insensitive molecular energetic material, which exhibits highly anisotropic mechanical properties.

1,3,5-triamino-2,4,6-trinitrobenzene↗

Detection of Diversion in a Realistic Heat Pipe Microreactor Using Supervised Machine Learning

Microreactors (MRs) pose new challenges for international safeguards. Here, their small size and mass reproducibility make them ideal for deployment in greater numbers and in remote locations, making the job of safeguards inspectors more challenging. Machine learning (ML) is currently being applied to many fields to augment human performance and increase automation; in particular, ML could be used to provide insight for international inspectors to help detect the diversion of nuclear fuel from MR cores. Four ML model types (k-nearest neighbors, decision tree, random forest, and histogram-based gradient boosted ensemble) were trained on integrated flux and critical control drum angle data generated with Serpent 2 for a realistic heat pipe MR design, achieving nearly 100% binary classification accuracy of nominal and diversion core configurations by the end of 1 full power year for three of the four model types. Regression model variants were also trained, using the same input data, for predicting the number of fuel pins diverted. Root-mean-square errors below 5% of the total number of fuel pins were achieved by the 1 full power year mark for all models.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Prediction of Distributed River Sediment Respiration Rates Using Community-Generated Data and Machine Learning

River sediment microbial respiration is a key indicator of ecosystem functioning and the biogeochemical fluxes across this critical zone link surface and subsurface waters. As such, there is tremendous interest in measuring and mapping these respiration rates. Respiration observations are expensive and labor intensive; there is limited data available to the community. An open science, collaborative initiative is collecting samples for respiration rate analysis and multi-scale metadata; this evolving data set is being used for making machine learning (ML) predictions at unsampled sites to help inform continued community engagement. However, it is a challenge to find an optimum configuration for ML models to work with this feature-rich (i.e., 100+ possible input variables) data set. Here, we present results from a two-tiered approach to managing the analysis of this complex data set: (a) a stacked ensemble of models that automatically optimizes hyperparameters and manages the training of many models and (b) feature permutation importance to detect the most important features in the models. The major elements of this workflow are modular, portable, open, and cloud-based thus making this implementation a potential template for other applications. The models developed here predict that sediment organic matter chemistry is one of the most important features for predicting sediment respiration rate. Other larger-scale, important features fall into the categories of climatic, ecological, geological, and fluvial settings. Leveraging these larger-scale features to generate data-driven estimates of river sediment respiration rates reveals spatially consistent but heterogeneous patterns across the river network of the Columbia River Basin.

54 ENVIRONMENTAL SCIENCES↗

Internal variability and forcing influence model–satellite differences in the rate of tropical tropospheric warming

Climate-model simulations exhibit approximately two times more tropical tropospheric warming than satellite observations since 1979. The causes of this difference are not fully understood and are poorly quantified. Here, we apply machine learning to relate the patterns of surface-temperature change to the forced and unforced components of tropical tropospheric warming. This approach allows us to disentangle the forced and unforced change in the model-simulated temperature of the midtroposphere (TMT). In applying the climate-model-trained machine-learning framework to observations, we estimate that external forcing has produced a tropical TMT trend of 0.25 ± 0.08 K⋅decade −1 between 1979 and 2014, but internal variability has offset this warming by 0.07 ± 0.07 K⋅decade −1 . Using the Community Earth System Model version 2 (CESM2) large ensemble, we also find that a discontinuity in the variability of prescribed biomass-burning aerosol emissions artificially enhances simulated tropical TMT change by 0.04 K⋅decade −1 . The magnitude of this aerosol-forcing bias will vary across climate models, but since the latest generation of climate models all use the same emissions dataset, the bias may systematically enhance climate-model trends over the satellite era. Our results indicate that internal variability and forcing uncertainties largely explain differences in satellite-versus-model warming and are important considerations when evaluating climate models.

54 ENVIRONMENTAL SCIENCES↗

gRASPA

GPU Monte Carlo Simulation Code with a taste of RASPA We present enhancements in Monte Carlo simulation speed and functionality within an open-source code, gRASPA, which uses graphical processing units (GPUs) to achieve significant performance improvements compared to serial, CPU implementations of Monte Carlo. The code supports a wide range of Monte Carlo simulations, including canonical ensemble (NVT), grand canonical, NVT Gibbs, Widom test particle insertions, and continuous-fractional component Monte Carlo. Implementation of grand canonical transition matrix Monte Carlo (GC-TMMC) and a novel feature to allow different moves for the different components of metal-organic framework (MOF) structures exemplify the capabilities of gRASPA for precise free energy calculations and enhanced adsorption studies, respectively. The introduction of a High-Throughput Computing (HTC) mode permits many Monte Carlo simulations on a single GPU device for accelerated materials discovery. The code can incorporate machine learning (ML) potentials. The open-source nature of gRASPA promotes reproducibility and openness in science, and users may add features to the code and optimize it for their own purposes. The code is written in CUDA/C++ and SYCL/C++ to support different GPU vendors. The gRASPA code is publicly available at https://github.com/snurr-group/gRASPA.

Li, Zhao [Purdue/Northwestern/Notre Dame Universit↗

Spectral Data Fusion From Handheld Laser-Induced Breakdown Spectroscopy (LIBS) and X-ray Fluorescence (XRF) Analyzers for Improved Detection of Cerium in a Simulated Dispersal Accident

Here, this work implements a mid-level data fusion methodology on spectral data from handheld X-ray fluorescence and laser-induced breakdown spectroscopy analyzers to quantify plutonium surrogate (CeO 2 ) contamination in soil samples for the first time. Spectral data from each analyzer were used independently to train supervised machine learning regressions to predict Ce concentration. Fused features from both data sets were then used to train the same models, comparing prediction performance by evaluating model precision and sensitivity. Fusing principal component scores from the two sensors yielded an order of magnitude improvement in precision and sensitivity of predictions made with an artificial neural network, compared to predictions made by models trained on independent sensor data. As a result, a boosted ensemble trained on the fused spectral features yielded an ideal predictor with root-mean-squared error on the order of 10 –6 and calculated limit of detection order 10 –5 wt %.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Active Learning A Neural Network Model For Gold Clusters & Bulk From Sparse First Principles Training Data

Small metal clusters are of fundamental scientific interest and of tremendous significance in catalysis. These nanoscale clusters display diverse geometries and structural motifs depending on the cluster size; a knowledge of this size-dependent structural motifs and their dynamical evolution has been of longstanding interest. Given the high computational cost of first-principles calculations, molecular modeling and atomistic simulations such as molecular dynamics (MD) has proven to be an important complementary tool to aid this understanding. Classical MD typically employ predefined functional forms which limits their ability to capture such complex size-dependent structural and dynamical transformation. Neural Network (NN) based potentials represent flexible alternatives and in principle, well-trained NN potentials can provide high level of flexibility, transferability and accuracy on-par with the reference model used for training. A major challenge, however, is that NN models are interpolative and requires large quantities (similar to 10 4 or greater) of training data to ensure that the model adequately samples the energy landscape both near and far-from-equilibrium. A highly desirable goal is minimize the number of training data, especially if the underlying reference model is first-principles based and hence expensive. In this work, we introduce an active learning (AL) scheme that trains a NN model on-the-fly with minimal amount of first-principles based training data. Our AL workflow is initiated with a sparse training dataset (similar to 1 to 5 data points) and is updated on-the-fly via a Nested Ensemble Monte Carlo scheme that iteratively queries the energy landscape in regions of failure and updates the training pool to improve the network performance. Using a representative system of gold clusters, we demonstrate that our AL workflow can train a NN with similar to 500 total reference calculations. Using an extensive DFT test set of similar to 1100 configurations, we show that our AL-NN is able to accurately predict both the DFT energies and the forces for clusters of a myriad of different sizes. Our NN predictions are within 30 meV/atom and 40 meV/angstrom of the reference DFT calculations. Moreover, our AL-NN model also adequately captures the various size-dependent structural and dynamical properties of gold clusters in excellent agreement with DFT calculations and available experiments. We finally show that our AL-NN model also captures bulk properties reasonably well, even though they were not included in the training data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

deeprob/ThioesteraseEnzymeSpecificity: EnZymClass-first-release

Characterizing the functional properties of plant acyl-ACP thioesterases (TEs), a key enzyme class used in the production of renewable oleochemicals in microbial hosts, experimentally, can be an expensive and time consuming process since it requires manual screening of thousands of candidates in a database. Using amino acid sequence to computationally predict an enzyme’s function might accelerate this process; however obtaining the necessary amount of information on previously characterized enzymes and their respective sequences required by standard Machine Learning (ML) based approaches to accurately infer sequence-function relationships can be prohibitive, especially with a low-throughput testing cycle. Experimental noise, unbalanced dataset where high sequence similarity does not always imply identical functional properties will further prevent robust prediction performance. Herein we present a ML method, Ensemble method for enZyme Classification (EnZymClass), that is specifically designed to address these issues. We used EnZymClass to classify TEs into short, long and mixed free fatty acid substrate specificity categories. While general guidelines for inferring substrate specificity have been proposed before, prediction of chain-length preference from primary sequence has remained elusive for plant acyl-ACP TEs. By applying EnZymClass to a subset of TEs in the ThYme database, we identified two medium chain TEs, ClFatB3 and CwFatB2, with previously uncharacterized activity in E. coli fatty acid production hosts.

Banerjee, Deepro↗

Inverse Mapping of the Collision Kernel and Wall Flux Scaling in a Tall Convection‐Cloud Chamber Using Local Sensors and Knowledge‐Informed Deep Learning

Droplet collision–coalescence is a crucial process in cloud physics, but accurately representing this process under different dynamical conditions remains challenging. A proposed future convective‐cloud chamber aims to investigate this key process, but the method for observing it remains unclear, even though it is theoretically established that collision‐coalescence will occur. This study serves as a proof‐of‐concept demonstration of how knowledge‐informed deep learning, combined with measurement data from local sensors in the chamber, can be used to estimate the collision kernels, which determine how the droplet size distribution evolves during collision‐coalescence. In addition to estimating the collision kernel, we also address wall fluxes, another uncertain but important process that acts as a source of heat and moisture in the chamber. Ensemble runs of large‐eddy simulations are conducted by scaling the wall fluxes and the collision kernel, while the measured flow and cloud properties are used as inputs for a neural network. Results indicate that this approach successfully maps the scaling of wall fluxes and the collision kernel with biases of approximately 1% or less relative to the range of the target data. This proof‐of‐concept lays the groundwork for future applications; when the real measurements are available, real sensor data combined with the trained model presented in this work will enable estimation of the actual wall fluxes and collision kernel.

cloud chamber↗