Bayesian Optimization for E3SM climate model surrogate hyperparameter selection
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Richards-Dinger, Maia Katherine↗
SEARCH · Engineering Papers
Results for “Hyperparameter optimization”
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Reward Driven Workflows for Unsupervised Explainable Analysis of Phases and Ferroic Variants From Atomically Resolved Imaging Data
Rapid progress in aberration corrected electron microscopy necessitates development of robust methods for the identification of phases, ferroic variants, and other pertinent aspects of materials structure from imaging data. While unsupervised methods for clustering and classification are widely used for these tasks, their performance can be sensitive to hyperparameter selection in the analysis workflow. In this study, the effects of descriptors and hyperparameters are explored on the capability of unsupervised ML methods to distill local structural information, exemplified by the discovery of polarization and lattice distortion in Sm − dopped BiFeO 3 (BFO) thin films. It is demonstrated that a reward-driven approach can be used to optimize these key hyperparameters across the full workflow, where rewards are designed to reflect domain wall continuity and straightness, ensuring that the analysis aligns with the material's physical behavior. This approach allows the discovery of local descriptors that are best aligned with the specific physical behavior, providing insight into the fundamental physics of materials. The reward driven workflow is further extended to disentangle structural factors of variation via an optimized variational autoencoder (VAE). Lastly, the importance of well-defined rewards is explored as a quantifiable measure of the success of the workflow.
Barakati, Kamyar [University of Tennessee, Knoxvil↗
Optimization of Water-Alternating-CO2 Injection Field Operations Using a Machine-Learning-Assisted Workflow
Summary This paper will present a robust workflow to address multiobjective optimization (MOO) of carbon dioxide (CO2)-enhanced oil recovery (EOR)-sequestration projects with a large number of operational control parameters. Farnsworth unit (FWU) field, a mature oil reservoir undergoing CO2 alternating water injection (CO2-WAG) EOR, will be used as a field case to validate the proposed optimization protocol. The expected outcome of this work would be a repository of Pareto-optimal solutions of multiple objective functions, including oil recovery, carbon storage volume, and project economics. FWU’s numerical model is used to demonstrate the proposed optimization workflow. Because using MOO requires computationally intensive procedures, machine-learning-based proxies are introduced to substitute for the high-fidelity model, thus reducing the total computation overhead. The vector machine regression combined with the Gaussian kernel (Gaussian-SVR) is used to construct proxies. An iterative self-adjusting process prepares the training knowledge base to develop robust proxies and minimizes computational time. The proxies’ hyperparameters will be optimally designed using Bayesian optimization to achieve better generalization performance. Trained proxies will be coupled with multiobjective particle swarm Optimization (MOPSO) protocol to construct the Pareto-front solution repository. The outcomes of this workflow will be a repository containing Pareto-optimal solutions of multiple objectives considered in the CO2-WAG project. The proposed optimization workflow will be compared with another established methodology using a multilayer neural network (MLNN) to validate its feasibility in handling MOO with a large number of parameters to control. Optimization parameters used include operational variables that might be used to control the CO2-WAG process, such as the duration of the water/gas injection period, producer bottomhole pressure (BHP) control, and water injection rate of each well included in the numerical model. It is proved that the workflow coupling Gaussian-SVR proxies and the iterative self-adjusting protocol is more computationally efficient. The MOO process is made more rapid by squeezing the size of the required training knowledge base while maintaining the high accuracy of the optimized results. The outcomes of the optimization study show promising results in successfully establishing the solution repository considering multiple objective functions. Results are also verified by validating the Pareto fronts with simulation results using obtained optimized control parameters. The outcome from this work could provide field operators an opportunity to design a CO2-WAG project using as many inputs as possible from the reservoir models. The proposed work introduces a novel concept that couples Gaussian-SVR proxies with a self-adjusting protocol to increase the computational efficiency of the proposed workflow and to guarantee the high accuracy of the obtained optimized results. More importantly, the workflow can optimize a large number of control parameters used in a complex CO2-WAG process, which greatly extends its utility in solving large-scale MOO problems in various projects with similar desired outcomes.
Energy & Fuels↗
Practical Hamiltonian learning with unitary dynamics and Gibbs states
We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. In this work, we build upon recent approaches to Hamiltonian learning via derivative estimation. We propose a protocol that improves the scaling dependence of prior works, particularly with respect to parameters relating to the structure of the Hamiltonian (e.g., its locality k). Furthermore, by deriving exact bounds on the performance of our protocol, we are able to provide a precise numerical prescription for theoretically optimal settings of hyperparameters in our learning protocol, such as the maximum evolution time (when learning with unitary dynamics) or minimum temperature (when learning with Gibbs states). Thanks to these improvements, our protocol has practical scaling for large problems: we demonstrate this with a numerical simulation of our protocol on an 80-qubit system.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A Machine Learning–Based Tire Life Prediction Framework for Increasing Life of Commercial Vehicle Tires
In the commercial freight industry, tire retreading decisions are often conservative due to limited knowledge of a tire’s remaining service life. This practice leads to increased costs and material waste. This paper proposes a machine learning–based approach for estimating tire casing life and retreadability, focusing on usage data rather than wear information. This approach could extend the tire’s lifespan and reduce landfill waste. Data integration from diverse tire casing measurement sources presents challenges, including imbalanced removal data. Our methodology addresses these challenges by using historical inspection, telematics, and finite element modeling (FEM) datasets. We introduce “Tire Casing Energy” as a comprehensive usage input and apply a Variance-Reduction Synthetic Minority Oversampling Technique (VR-SMOTE) for data imbalance rectification. A random forest model is used to estimate the state of the tire casing and the casing removal probability, with Bayesian optimization applied for hyperparameter tuning, enhancing model accuracy. Here, the proposed prediction framework is able to differentiate different truck fleets and tire locations based on their usage parameters. With the aid of this machine learning model, the importance and sensitivity of different tire usage parameters can be obtained, which is beneficial to maximize tire life.
Data balancing↗
Deep Learning Image Segmentation for Atmospheric Rivers
Abstract The identification of atmospheric rivers (ARs) is crucial for weather and climate predictions as they are often associated with severe storm systems and extreme precipitation, which can cause large impacts on society. This study presents a deep learning model, termed ARDetect, for image segmentation of ARs using ERA5 data from 1960 to 2020 with labels obtained from the TempestExtremes tracking algorithm. ARDetect is a convolutional neural network (CNN)-based U-Net model, with its structure having been optimized using automatic hyperparameter tuning. Inputs to ARDetect were selected to be the integrated water vapor transport (IVT) and total column water (TCW) fields, as well as the AR mask from TempestExtremes from the previous time step to the one being considered. ARDetect achieved a mean intersection-over-union (mIoU) rate of 89.04% for ARs, indicating its high accuracy in identifying these weather patterns and a superior performance than most deep learning–based models for AR detection. In addition, ARDetect can be executed faster than the TempestExtremes method (seconds vs minutes) for the same period. This provides a significant benefit for online AR detection, especially for high-resolution global models. An ensemble of 10 models, each trained on the same dataset but having different starting weights, was used to further improve on the performance produced by ARDetect, thus demonstrating the importance of model diversity in improving performance. ARDetect provides an effective and fast deep learning–based model for researchers and weather forecasters to better detect and understand ARs, which have significant impacts on weather-related events such as floods and droughts.
Galea, Daniel↗
Optimizing training trajectories in variational autoencoders via latent Bayesian optimization approach *
Unsupervised and semi-supervised ML methods such as variational autoencoders (VAE) have become widely adopted across multiple areas of physics, chemistry, and materials sciences due to their capability in disentangling representations and ability to find latent manifolds for classification and/or regression of complex experimental data. Like other ML problems, VAEs require hyperparameter tuning, e.g. balancing the Kullback–Leibler and reconstruction terms. However, the training process and resulting manifold topology and connectivity depend not only on hyperparameters, but also their evolution during training. Because of the inefficiency of exhaustive search in a high-dimensional hyperparameter space for the expensive-to-train models, here we have explored a latent Bayesian optimization (zBO) approach for the hyperparameter trajectory optimization for the unsupervised and semi-supervised ML and demonstrated for joint-VAE with rotational invariances. We have demonstrated an application of this method for finding joint discrete and continuous rotationally invariant representations for modified national institute of standards and technology database (MNIST) and experimental data of a plasmonic nanoparticles material system. The performance of the proposed approach has been discussed extensively, where it allows for any high dimensional hyperparameter trajectory optimization of other ML models.
42 ENGINEERING↗
Robust Design Under Uncertainty in Quantum Error Mitigation
Error mitigation techniques are crucial to achieving near-term quantum advantage. Classical postprocessing of quantum computation outcomes is a popular approach for error mitigation, which includes methods, such as zero noise extrapolation, virtual distillation, and learning-based error mitigation. However, these techniques have limitations due to the propagation of uncertainty resulting from the finite shot number of a quantum measurement. In this work, we introduce general and unbiased methods for quantifying the uncertainty and error of error-mitigated observables based on the strategic sampling of error mitigation outcomes. We then extend our approach to demonstrate the optimization of performance and robustness of error mitigation under uncertainty. To illustrate our methods, we apply them to zero noise extrapolation and Clifford date regression in the ground state of the XY model simulated using depolarizing and International Business Machines Corporation (IBM) Toronto noise models, respectively. In particular, we optimize the choice of noise levels and the allocation of shots for zero noise extrapolation and the distribution of the training circuits for Clifford data regression. While our methods are readily applicable to any postprocessing-based error mitigation approach, in practice they must not be prohibitively expensive—even though they perform optimizations of the error mitigation hyperparameters requiring sampling of a statistical distribution of error mitigation outcomes. By leveraging surrogate-based optimization, we show that our methods can efficiently perform optimal design for a zero noise extrapolation implementation. We then further demonstrate the transferability of learned zero noise extrapolation hyperparameters to other similar circuits.
97 MATHEMATICS AND COMPUTING↗
Scaling and merging time-resolved pink-beam diffraction with variational inference
Time-resolved x-ray crystallography (TR-X) at synchrotrons and free electron lasers is a promising technique for recording dynamics of molecules at atomic resolution. While experimental methods for TR-X have proliferated and matured, data analysis is often difficult. Extracting small, time-dependent changes in signal is frequently a bottleneck for practitioners. Recent work demonstrated this challenge can be addressed when merging redundant observations by a statistical technique known as variational inference (VI). However, the variational approach to time-resolved data analysis requires identification of successful hyperparameters in order to optimally extract signal. In this case study, we present a successful application of VI to time-resolved changes in an enzyme, DJ-1, upon mixing with a substrate molecule, methylglyoxal. We present a strategy to extract high signal-to-noise changes in electron density from these data. Furthermore, we conduct an ablation study, in which we systematically remove one hyperparameter at a time to demonstrate the impact of each hyperparameter choice on the success of our model. We expect this case study will serve as a practical example for how others may deploy VI in order to analyze their time-resolved diffraction data.
47 OTHER INSTRUMENTATION↗
Deep learning to estimate permeability using geophysical data
Time-lapse electrical resistivity tomography (ERT) is a popular geophysical method to estimate three-dimensional (3D) permeability fields from electrical potential difference measurements. Traditional inversion and data assimilation methods are used to ingest this ERT data into hydrogeophysical models to estimate permeability. Due to ill-posedness and the curse of dimensionality, existing inversion strategies provide poor estimates and low resolution of the 3D permeability field. Recent advances in deep learning provide us with powerful algorithms to overcome this challenge. This paper presents a deep learning (DL) framework to estimate the 3D subsurface permeability from time-lapse ERT data. To test the feasibility of the proposed framework, we train DL-enabled inverse models on simulation data. Each measurement in both synthetic and field data is standardized by removing the mean and scaling the time-series to unit variance. This pre-processing step is necessary to bring simulation data closer to field observations. Subsurface process models based on hydrogeophysics are used to generate this synthetic data. Training performed on limited simulation data resulted in the DL model over-fitting. An advanced data augmentation based on mixup is implemented to generate additional training samples to overcome this issue. This mixup technique creates weakly labeled (low-fidelity) samples from strongly labeled (high-fidelity) data. The weakly labeled training data is then used to develop DL-enabled inverse models and reduce over-fitting. As both time-lapse ERT (1133048 features/realization) and 3D permeability (585453 features/realization) data samples are from a high-dimensional space, principal component analysis (PCA) is employed to reduce dimensionality. Encoded ERT and encoded permeability are generated using the trained PCA estimators. A deep neural network is then trained to map the encoded ERT to encoded permeability. This mixup training and unsupervised learning allowed us to build a fast and reasonably accurate DL-based inverse model under limited simulation data. Results show that proposed weak supervised learning can capture salient spatial features in the 3D permeability field. Quantitatively, the average mean squared error (in terms of the natural log) on the strongly labeled training, validation, and test datasets is less than 0.5. The R 2 -score (global metric) is greater than 0.75, and the percent error in each cell (local metric) is less than 10%. Finally, an added benefit in terms of computational cost is that the proposed DL-based inverse model is at least O(10 4 ) times faster than running a forward model once it is trained. Data generation, DL model training, and hyperparameter tuning to identify optimal neural network architectures utilized high-performance computing resources while the DL inference is performed on a standard laptop. Approximately, O(10 5 ) processor hours are used for generating data and DL tuning and training. We acknowledge that the data generation and DL model development are expensive. But once a DL model is trained, it can be re-used for inversion rapidly for the given system, with set physics and domain. Note that traditional inversion may require multiple forward model simulations (e.g., in the order of 10 to 1000), which are very expensive. This computational savings ≈ O(10 5 ) – O(10 7 )) makes the proposed DL-based inverse model attractive for subsurface imaging and real-time ERT monitoring applications due to fast and yet reasonably accurate estimations of permeability field.
58 GEOSCIENCES↗
The expressivity of classical and quantum neural networks on entanglement entropy
Abstract Analytically continuing the von Neumann entropy from Rényi entropies is a challenging task in quantum field theory. While then-th Rényi entropy can be computed using the replica method in the path integral representation of quantum field theory, the analytic continuation can only be achieved for some simple systems on a case-by-case basis. In this work, we propose a general framework to tackle this problem using classical and quantum neural networks with supervised learning. We begin by studying several examples with known von Neumann entropy, where the input data is generated by representing$${\text {Tr}}\rho _A^n$$ Tr ρ A n with a generating function. We adopt KerasTuner to determine the optimal network architecture and hyperparameters with limited data. In addition, we frame a similar problem in terms of quantum machine learning models, where the expressivity of the quantum models for the entanglement entropy as a partial Fourier series is established. Our proposed methods can accurately predict the von Neumann and Rényi entropies numerically, highlighting the potential of deep learning techniques for solving problems in quantum information theory.
Physics↗
Surrogate Model Based Optimization for Finding Robust Deep Learning Model Architectures
Deep Learning (DL) models are increasingly used throughout the sciences. However, their performance and usefulness depend greatly on their architecture which is defined by hyperparameters such as the number of nodes, layers, the learning rate, etc. Tuning these hyperparameters is time-consuming because evaluating their performance requires a lengthy training step. Stochastic optimizers used in training lead to performance variability and potentially prediction reliability issues. In this talk, we will describe an automated optimization method based on surrogate models and active learning strategies for tuning DL model architectures. We take into account the prediction variability with the goal to identify architectures that make reliable and robust predictions. We demonstrate our developments on an application arising in particle physics.
deep learning↗
Exploring Applications of Machine Learning for Wildfire Monitoring and Detection using Unmanned Aerial Vehicles
Wildfires are increasing in frequency and severity around the world, including the United States. The losses caused by wildfires could be mitigated if high-risk areas, hotspots, and flare-ups could be monitored continuously, such as through the use of Unmanned Aerial Vehicles (UAVs). This paper documents exploratory efforts using machine learning to determine efficient flight paths for UAVs and to detect wildfires using image classification. On path planning, three machine learning techniques—Genetic Algorithm, Simulated Annealing, and Dynamic Programming—were explored. Genetic Algorithm was found to be an effective approach for path planning for wildfire monitoring and surveillance by UAVs. For a scenario of 25 locations in a circular arrangement, the algorithm was able to return the optimal path. The accuracy and execution time was found to be sensitive to the algorithm hyperparameters selected, which was especially evident in scenarios with hundreds or thousands of locations. Simulated Annealing was also found to be an effective approach for UAV path planning, with a major benefit of avoiding getting trapped in local minima and being straightforward to implement. Like Genetic Algorithm, the performance of Simulated Annealing was also found to be sensitive to the algorithm hyperparameters selected. By comparison, Dynamic Programming guarantees optimality for any number of locations, but it was found to be less practical in terms of execution time for scenarios with more than about a couple dozen locations. On wildfire detection, image classification using deep learning with a convolutional neural network was explored. Transfer learning was found to be a useful technique to efficiently train deep learning models. Also, it was determined that GPU processing can increase training speed by an order of magnitude, which enables significantly faster development. For a validation test set of 500 images, there were only two false negatives and zero false positives. These results demonstrate that detecting wildfires in static cameras using machine learning is feasible and establish a baseline for using images captured by UAVs in flight for wildfire detection.
Wildfire management↗
Towards an Aviation Large Language Model by Fine-tuning and Evaluating Transformers
In the aviation domain, there are many applications for machine learning and artificial intelligence tools that utilize natural language. For example, there is a desire to know the commonalities in written safety reports such as voluntary post incidents reports or aerial wildfire operations reports to better understand the risks present. Another use-case is the possibility of extracting airspace procedures and constraints currently written in documents such as Letters of Agreement. These applications can benefit from the use of state-of-the-art natural language processing techniques when adapted to the language/phraseology specific to the aviation domain. This paper evaluates the viability of adaptation of NLP tools to the aviation domain by fine-tuning transformer based models using aviation data sets. In 2018, a novel language model based on neural units (also called transformers) was created and became known as “Bidirectional Encoder Representations from Transformers” or BERT. This architecture combined with large amounts of English training data and innovative semi-supervised training tasks set the standard for what would later emerge as Large Language Models. The performance of these models was further improved by hyperparameter tuning and refinement of the semi-supervised training task and resulted in “Robustly Optimized BERT Pre-training Approach through hyperparameter tuning” or RoBERTa models. These pre-trained Large Language Models proved to be useful for a wide variety of natural language processing tasks such as text classification and question answering through a process called fine-tuning. The transformer architecture with pre-trained weights served as the basis with the last few layers replaced with layers fine-tuned to perform a new task e.g., a layer that provides a label for the entire input text. This process of fine-tuning can also be used to adapt the models to new domains; e.g., BioBERT started with the pre-trained BERT model and was completed by additional fine-tuning and training on biomedical documents. Transformer-based architectures can also be used to create rich representations of text called embeddings which can serve as the input to other machine learning models. This allows simpler algorithms such as logistic regression to use context-rich representations of the text while still remaining quick to train and evaluate. In the world of aviation, there is a growing demand for natural language processing and understanding but the domain presents unique challenges. Due to the technical content (and specialized language) of most aviation documents, fine-tuning pre-trained Large Language Models to specific tasks has not met the benchmark on natural language processing tasks set by simpler models trained from scratch on the data. To address this deficiency, this paper evaluates the improvements from fine-tuning a Large Language Model on a large set of aviation documents using the original semi-supervised training tasks before performing specific natural language tasks. In fine-tuning, a domain-specific dataset is used on the original training task but with the pre-trained Large Language Model instead of starting from a random initialization. This approach allows the model to be adapted to the specific domain language without discarding the information gained from training on general English data. This paper utilized two major dataset types to train and assess the RoBERTa fine-tuning performance. The first are 7,057 Letters of Agreement which are Federal Aviation Administration (FAA) documents that formalize airspace operations across the national airspace system. They contain many examples of ‘aviation English’ using domain specific terminology and phrasing which serves as a representative basis to perform the semi-supervised fine-tuning. The second type is the 494 document classification labels to be used for evaluation. This down-stream evaluation aims to show the performance of the fine-tuned model, better understand how much data is needed for an effective fine-tuning, and how fine-tuning can be adapted for different applications in-the domain. After semi-supervised training, evaluation begins by encoding the documents for classification using the fine-tuned RoBERTa model. Then a logistic regression classifier is trained to label the document type and compared against our ground truth labels. This currently leads to a 82.8% accuracy on 10-fold cross validation showing improvement over baseline RoBERTa which achieved 81.0%. We plan to measure the improvements on additional tasks and it is expected that these improvements will lead to more robust models that can tackle the natural language processing challenges present in aviation datasets.
ATM↗
Predicting Unreinforced Fabric Mechanical Behavior with Recurrent Neural Networks
Unreinforced woven fabrics are widely employed in various high-performance applications, including parachute deployment systems, airbags, and ballistic armor. The analysis of such materials is inherently complex due to the multiscale structure of these materials, and the dependence of macroscale behavior on changes that occur at lower scales. Previously, NASA’s Multiscale Analysis Tool (NASMAT) showed its capability in predicting unreinforced fabric behavior at the macroscale by capturing finite rotations that occur at the mesoscale. Though effective, the tool can face high computational cost for large, complex problems, motivating the need for the development of a surrogate model that can capture the same behavior. A recurrent neural network (RNN) was developed and trained on virtual NASMAT data to mimic the physics-based solutions while improving the computational runtime. The architecture of the RNN to best simulate the fabric behavior was carefully crafted based on heuristic knowledge of predicting physics-based temporal data, manual hyperparameter case studies, and Hyperband optimization.. The resultant model was able to predict a variety of stress-strain curves for fabrics with different mesoscale geometries, and was further validated by comparing to experimental data for the K706 style Kevlar plain-weave fabric, demonstrating the ability of the model to effectively capture the geometric changes in the fabric without explicitly calculating them, as is done in NASMAT. Furthermore, the tool showed its ability to improve on the runtime by a factor of 10 for fabric solutions compared to the multiscale tool, which would further enable the simulation of complex loading scenarios on unreinforced fabrics.
Fabric↗
Bayesian optimization of the beam injection process into a storage ring
We have evaluated the data-efficient Bayesian optimization method for the specific task of injection tuning in a circular accelerator. In this paper, we describe the implementation of this method at the Karlsruhe Research Accelerator with up to nine tuning parameters, including the determination of the associated hyperparameters. We show that the Bayesian optimization method outperforms manual tuning and the commonly used Nelder-Mead optimization algorithm in both simulation and experiment. The algorithm was also successfully used to ease the commissioning phase after the installation of new injection magnets and is regularly used during accelerator operations. We demonstrate that the introduction of context variables that include intrabunch scattering effects, such as the Touschek effect, further improves the control and robustness of the injection process.
43 PARTICLE ACCELERATORS↗
Gradient-Informed Design Optimization of Select Nuclear Systems
In this work, we present a gradient-informed design optimization of nuclear reactor core components based on neutronics objectives with both continuous and discrete materials. The main argument in favor of using gradient-informed design optimization is that it scales well with increasing dimensionality of the design space. First, a challenge problem with 121 free parameters is solved with a gradient-informed method and then with a genetic algorithm. Then, a challenge problem to optimize the flux profile of a simplified assembly with eight axial zones is solved. Both challenge problems are solved using directly calculated derivatives from Tools for Sensitivity and Uncertainty Analysis Methodology Implementation (TSUNAMI) in the SCALE package. Furthermore, we demonstrate how a discrete optimization problem—selection of materials for 121 voxels—can be lifted into a continuous problem with mixed materials. In the continuous space, adjoint-based gradients are well-defined, and gradient descent is applicable. Then, a forcing function is introduced that with the selection of an appropriately sized hyperparameter can be used to guide the optimized continuous solution back into a discrete solution. This paper presents an account of the challenges that were faced when applying a gradient-informed optimization algorithm using a Monte Carlo calculation to estimate the gradient information and compares a gradient descent optimization method to a genetic algorithm optimization of the same geometry. Overall, this work demonstrates the potential use of adjoint-based gradient calculations in design optimization of nuclear systems.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
A Generalized Approach to Aircraft Trajectory Prediction via Supervised Deep Learning
As research advances diverse forms and missions of aircraft, the National Airspace System (NAS) will become increasingly crowded, limiting current communications resources to accommodate aviation operations. Ongoing research proposes a paradigm of airspace communications, such that resources are autonomously and dynamically allocated via intelligent agents; this allocation requires accurate representations of the NAS, including the predicted positions of aircraft. State-of-the-art research emphasizes the importance of a hybrid-recurrent framework for trajectory prediction and compares the impact of commonly considered weather data on prediction accuracy. However, current research has been limited in its scope of efforts, frequently utilizing a unique flight route, architecture, set of weather data, and date range. This article considers the challenges of generalizing hybrid-recurrent predictive models for flight trajectories. Results illustrate an increase in error variance when identical models are trained over a generalized set of flights; this may be mitigated with careful tuning of hyperparameters, both in the network structure and optimization algorithms. Even so, an irreducible vertical error was identified, resulting from the complex takeoff and landing procedures which can not be correlated to functions of weather or additional assumptions of aircraft behavior. Finally, the use of a test route indicates that generalized models still do not possess sufficient knowledge for general aircraft predictions, with mean error increases ranging from 70-500%. These results illustrate the need for continued efforts on improving model versatility, as well as potential limitations for spectrum allocation near airports and other centers.
Nathan Schimpf↗