Layer Artificial Neural Network Research Articles

Deep-time neural networks: An efficient approach for solving high-dimensional PDEs

This paper presents the Deep-Time Neural Network (DTNN), an efficient and novel deep-learning approach for solving partial differential equations (PDEs). DTNN leverages the power of deep neural networks to approximate the solution for a class of quasi-linear parabolic PDEs. We demonstrate that DTNN significantly reduces the computational cost and speeds up the training process compared to other models in the literature. The results of our study indicate that DTNN architecture is promising for the fast and accurate solution of time-dependent PDEs in various scientific and engineering applications. The DTNN architecture addresses the pressing need for enhanced time considerations in the deeper layers of Artificial Neural Networks (ANNs), thereby improving convergence time for high-dimensional PDE solutions. This is achieved by integrating time into the hidden layers of the DTNN, demonstrating a marked improvement over existing ANN-based solutions regarding efficiency and speed.

An artificial neural network visible mathematical model for predicting slug liquid holdup in low to high viscosity multiphase flow for horizontal to vertical pipes

AbstractSlug liquid holdup (SLH) is a critical requirement for accurate pressure drop prediction during multiphase pipe flows and by extension optimal gas lift design and production optimization in wellbores. Existing empirical correlations provide inaccurate predictions because they were developed with regression analysis and data measured for limited ranges of flow conditions. Existing SLH machine learning models provide accurate predictions but are published without any equations making their use by other researchers difficult. The only existing ML model published with actual equations cannot be considered optimum because it was selected by considering artificial neural network (ANN) structures with only one hidden layer. In this study, an ANN-based model for SLH prediction with actual equations is presented. A total of 2699 data points randomly divided into 70%, 15%, and 15% for training, validation, and testing was used in constructing 71 different network structures with 1, 2, and 3 hidden layers respectively. Sensitivity analysis revealed that the optimum network structure has 3 hidden layers with 20, 5, and 15 neurons in the first, second, and third hidden layers, respectively. The optimum network structure was translated into actual equations with the aid of the weights, biases, and activation functions. Trend analysis revealed that this study’s model reproduced the expected effects of inputs on SLH. Test against measured data revealed that this study’s model is in agreement with measured data with coefficient of determinations of 0.9791, 0.9727, 0.9756, and 0.9776 for training, testing, validation, and entire datasets, respectively. Comparative study revealed that this study’s model outperformed existing models with a relative performance factor of 0.002. The present model is presented with visible mathematical equations making its implementation by any user easy and without the need for any ML framework. Unlike existing ANN-based models developed with one hidden layered ANN structures, the present model was developed by considering ANN structures with one, two, and three hidden layers, respectively.

A comprehensive analysis of the artificial neural networks model for predicting monkeypox outbreaks

Monkeypox is a viral disease that causes outbreaks in various countries, significantly impacting public health and healthcare systems. Effective preparedness and response efforts require accurately predicting the severity of these outbreaks. Currently, there are no publicly released studies for nations like Chile and Mexico on monkeypox, leading to this study's creation. We use a neural network model with a time series dataset of monkeypox cases from multiple countries, including Argentina, Brazil, France, Germany, Chile, and Mexico. The Levenberg-Marquardt learning technique is employed to develop and validate single and two hidden layers artificial neural network models. We train various model architectures with different numbers of hidden layer neurons using the K-fold cross-validation early stopping method. Additionally, we use long short-term memory and gated recurrent unit models, commonly employed for time series data processing, to compare the performance of our artificial neural network model.

Hebbian Descent: A Unified View on Log-Likelihood Learning.

This study discusses the negative impact of the derivative of the activation functions in the output layer of artificial neural networks, in particular in continual learning. We propose Hebbian descent as a theoretical framework to overcome this limitation, which is implemented through an alternative loss function for gradient descent we refer to as Hebbian descent loss. This loss is effectively the generalized log-likelihood loss and corresponds to an alternative weight update rule for the output layer wherein the derivative of the activation function is disregarded. We show how this update avoids vanishing error signals during backpropagation in saturated regions of the activation functions, which is particularly helpful in training shallow neural networks and deep neural networks where saturating activation functions are only used in the output layer. In combination with centering, Hebbian descent leads to better continual learning capabilities. It provides a unifying perspective on Hebbian learning, gradient descent, and generalized linear models, for all of which we discuss the advantages and disadvantages. Given activation functions with strictly positive derivative (as often the case in practice), Hebbian descent inherits the convergence properties of regular gradient descent. While established pairings of loss and output layer activation function (e.g., mean squared error with linear or cross-entropy with sigmoid/softmax) are subsumed by Hebbian descent, we provide general insights for designing arbitrary loss activation function combinations that benefit from Hebbian descent. For shallow networks, we show that Hebbian descent outperforms Hebbian learning, has a performance similar to regular gradient descent, and has a much better performance than all other tested update rules in continual learning. In combination with centering, Hebbian descent implements a forgetting mechanism that prevents catastrophic interference notably better than the other tested update rules. When training deep neural networks, our experimental results suggest that Hebbian descent has better or similar performance as gradient descent.

On the accuracy of interpolation based on single-layer artificial neural networks with a focus on defeating the Runge phenomenon

Artificial Neural Networks (ANNs) are a tool in approximation theory widely used to solve interpolation problems. In fact, ANNs can be assimilated to functions since they take an input and return an output. The structure of the specifically adopted network determines the underlying approximation space, while the form of the function is selected by fixing the parameters of the network. In the present paper, we consider one-hidden layer ANNs with a feedforward architecture, also referred to as shallow or two-layer networks, so that the structure is determined by the number and types of neurons. The determination of the parameters that define the function, called training, is done via the resolution of the approximation problem, so by imposing the interpolation through a set of specific nodes. We present the case where the parameters are trained using a procedure that is referred to as Extreme Learning Machine (ELM) that leads to a linear interpolation problem. In such hypotheses, the existence of an ANN interpolating function is guaranteed. Given that the ANN is interpolating, the error incurred occurs outside the sampling interpolation nodes provided by the user. In this study, various choices of nodes are analyzed: equispaced, Chebychev, and randomly selected ones. Then, the focus is on regular target functions, for which it is known that interpolation can lead to spurious oscillations, a phenomenon that in the ANN literature is referred to as overfitting. We obtain good accuracy of the ANN interpolating function in all tested cases using these different types of interpolating nodes and different types of neurons. The following study is conducted starting from the well-known bell-shaped Runge example, which makes it clear that the construction of a global interpolating polynomial is accurate only if trained on suitably chosen nodes, ad example the Chebychev ones. In order to evaluate the behavior when the number of interpolation nodes increases, we increase the number of neurons in our network and compare it with the interpolating polynomial. We test using Runge’s function and other well-known examples with different regularities. As expected, the accuracy of the approximation with a global polynomial increases only if the Chebychev nodes are considered. Instead, the error for the ANN interpolating function always decays, and in most cases we observe that the convergence follows what is observed in the polynomial case on Chebychev nodes, despite the set of nodes used for training. Then we can conclude that the use of such an ANN defeats the Runge phenomenon. Our results show the power of ANNs to achieve excellent approximations when interpolating regular functions also starting from uniform and random nodes, particularly for Runge’s function.

The Effect of Varying Artificial Neural Network and Adaptive Neuro-Fuzzy Inference System Parameters on Wind Energy Prediction: A Comparative Study

Owing to the development of technology, the majority of nations throughout the world now rely on fossil fuels and nuclear power plants to meet their energy needs. However, as academic research on this subject has shown, it has become clear that alternative energy uses are necessary due to the gradual depletion of these fuels and their significant negative effects on the environment. In order to ensure energy diversity and end the energy shortage, the development of renewable energy sources is crucial. The prediction of wind power is crucial for effectively utilizing the potential of wind energy. In this study, an adaptive neuro-fuzzy inference system (ANFIS) and an artificial neural network (ANN) have been developed for the prediction of wind power. In this study, data sets were created by taking the daily average wind speeds of the selected wind turbine, the daily average power values it produces, and the daily average wind speed values in the Velimese region. By creating single-hidden layer and multi-hidden layer ANN models, the network was trained multiple times with different activation functions and different numbers of neurons, and wind power prediction was performed. In the ANFIS model, the number of membership functions is kept constant, and wind power prediction is performed using different membership functions. With these ANFIS and ANN models developed with different parameter combinations, it is aimed to determine the most efficient model by performing daily average wind power prediction. Parameter combinations were tested to determine the appropriate models, and as a result, the ANN and ANFIS models were compared with each other.

An ANN-Based Output-Error-Driven Incremental Model Predictive Control for Buck Converter Against Parameter Variations

DC/DC buck converters have been widely applied in the power processing of distributed energy resources (DERs) penetrated DC microgrid. Model predictive control (MPC) provides optimal control for the buck converter, but it often requires multiple sensors or complex observers to realize zero-steady-state-error control against parameter variations. An output-error-driven incremental MPC (OEDIMPC) for buck converter is proposed in this paper. Different from the traditional concept of calculating the optimal duty cycle, the proposed MPC calculates the optimal rate of change of the duty cycle by using a reduced-state output-error-driven prediction model. As a result, the OEDIMPC achieves zero-steady-state-error control against parameter variations, including load value, input voltage, output inductor, and output capacitor, with significantly improved dynamic performance and minimal sensor and observer requirements Besides, small- and large-signal analyzes are used to study the stability boundary of the OEDIMPC under parameter variations, and a shallow layer artificial neural network (ANN) is utilized to realize the OEDIMPC on the hardware. The proposed technique has been evaluated experimentally on a buck converter with resistor load and constant power load (CPL), confirming its effectiveness.

The scope of artificial intelligence in retinopathy of prematurity (ROP) management.

Artificial Intelligence (AI) is a revolutionary technology that has the potential to develop into a widely implemented system that could reduce the dependence on qualified professionals/experts for screening the large at-risk population, especially in the Indian scenario. Deep learning involves learning without being explicitly told what to focus on and utilizes several layers of artificial neural networks (ANNs) to create a robust algorithm that is capable of high-complexity tasks. Convolutional neural networks (CNNs) are a subset of ANNs that are particularly useful for image processing as well as cognitive tasks. Training of these algorithms involves inputting raw human-labeled data, which are then processed through the algorithm's multiple layers and allow CNN to develop their own learning of image features. AI systems must be validated using different population datasets since the performance of the AI system would vary according to the population. Indian datasets have been used in AI-based risk model that could predict whether an infant would develop treatment-requiring retinopathy of prematurity (ROP). AI also served as an epidemiological tool by objectively showing that a higher ROP severity was in Neonatal intensive care units (NICUs) that did not have the resources to monitor and titrate oxygen. There are rising concerns about the medicolegal aspect of AI implementation as well as discussion on the possibilities of catastrophic life-threatening diseases like retinoblastoma and lipemia retinalis being missed by AI. Computer-based systems have the advantage over humans in not being susceptible to biases or fatigue. This is especially relevant in a country like India with an increased rate of ROP and a preexisting strained doctor-to-preterm child ratio. Many AI algorithms can perform in a way comparable to or exceeding human experts, and this opens possibilities for future large-scale prospective studies.

The significance of radiative heat and mass transfer through a vertical sheet with chemical reaction: Designing by artificial approach Levenberg-Marquardt

The present study examines the impact of incorporating soft computing algorithms during neural network training on the evaluation and prediction performance of artificial neural networks. The research centers on a magneto hydrodynamic flow model (RHMT-VSCR) that depicts the movement of rotating fluid along a vertical sheet in a permeable medium. Furthermore, the model considers the impact of heat source-sink interactions, thermal radiation, and reactive species in conjunction with the effects of Hall current on the enhancement of energy and solute profiles. Because the induced magnetic field has a negligible magnetic Reynolds number, it is disregarded. A set of governing nonlinear PDEs is converted to a system of ODEs by applying an appropriate postulate of similarity variables in order to analyze the system. The multilayer perceptron network utilizes a supervised Levenberg–Marquardt Backpropagation algorithm (LMLA-BPNN) to ascertain the ideal quantity of neurons to be included in the hidden layer of artificial neural networks intended for modeling purposes. The bvp4c numerical approach is utilized to establish a continuous neural network mapping, which produces datasets that are utilized for the purposes of authentication, training, and testing. The range i.e., 10−2−10−8 of absolute error of the reference and target data demonstrates the optimal accuracy performance of LMLA-BPNN networks. After acquiring knowledge of neural network mapping, it is applied to approximate solutions for a wide range of scenarios through the manipulation of physical constraints, including suction/injection quantities, magnetic parameter, and porosity parameter, which influence the characteristics of flow, energy, and concentration.To assess the precision of the proposed method, statistical graphs based on regression, mean squared error analysis graphs, and error histogram graphs are employed. The results of the research demonstrate that the Levenberg-Marquardt Backpropagation neural network mappings' derivation, convergence, authentication, and stability were effectively validated.

Updated Predictive Models for Permanent Seismic Displacement of Slopes for Greece and Their Effect on Probabilistic Landslide Hazard Assessment

Earthquake-triggered landslides have been widely recognized as a catastrophic hazard in mountainous regions. They may lead to direct consequences, such as property losses and casualties, as well as indirect consequences, such as disruption of the operation of lifeline infrastructures and delays in emergency response actions after earthquakes. Regional landslide hazard assessment is a useful tool to identify areas that are vulnerable to earthquake-induced slope instabilities and design prioritization schemes towards more detailed site-specific slope stability analyses. A widely used method to assess the seismic performance of slopes is by calculating the permanent downslope sliding displacement that is expected during ground shaking. Nathan M. Newmark was the first to propose a method to estimate the permanent displacement of a rigid body sliding on an inclined plane in 1965. The expected permanent displacement for a slope using the sliding block method is implemented by either selecting a suite of representative earthquake ground motions and computing the mean and standard deviation of the displacement or by using analytical equations that correlate the permanent displacement with ground motion intensity measures, the slope’s yield acceleration and seismological characteristics. Increased interest has been observed in the development of such empirical models using strong motion databases over the last decades. It has been almost a decade since the development of the latest empirical model for the prediction of permanent ground displacement for Greece. Since then, a significant amount of strong motion data have been collected. In the present study, several nonlinear regression-based empirical models are developed for the prediction of the permanent seismic displacements of slopes, including various ground motion intensity measures. Moreover, single-hidden layer Artificial Neural Network (ANN) models are developed to demonstrate their capability of simplifying the construction of empirical models. Finally, implementation of the produced modes based on Probabilistic Landslide Hazard Assessment is undertaken, and their effect on the resulting hazard curves is demonstrated and discussed.

What does artificial intelligence mean in rheumatology?

Intelligence is the ability of humans to learn from experiences to ascribe conscious weights and unconscious biases to modulate their outputs from given inputs. Transferring this ability to computers is artificial intelligence (AI). The ability of computers to understand data in an intelligent manner is machine learning. When such learning is with images and videos, which involves deeper layers of artificial neural networks, it is described as deep learning. Large language models are the latest development in AI which incorporate self-learning into deep learning through transformers. AI in Rheumatology has immense potential to revolutionize healthcare and research. Machine learning could aid clinical diagnosis and decision-making, and deep learning could extend this to analyze images of radiology or positron emission tomography scans or histopathology images to aid a clinician's diagnosis. Analysis of routinely obtained patient data or continuously collected information from wearables could predict disease flares. Analysis of high-volume genomics, transcriptomics, proteomics, or metabolomics data from patients could help identify novel markers of disease prognosis. AI might identify newer therapeutic targets based on in-silico modelling of omics data. AI could help automate medical administrative work such as inputting information into electronic health records or transcribing clinic notes. AI could help automate patient education and counselling. Beyond the clinic, AI has the potential to aid medical education. The ever-expanding capabilities of AI models bring along with them considerable ethical challenges, particularly related to risks of misuse. Nevertheless, the widespread use of AI in Rheumatology is inevitable and a progress with great potential.

Image classification system for COVID-19 patient X-Ray results using median filter with deep learning method

An image is a representation of an object that is rewritten on a medium with specific values (intensity) and has x and y coordinates. X-ray images are one type of medical image that can be used to detect and study a disease. However, X-ray images can sometimes appear blurry, making interpretation a bit challenging. Furthermore, there is variation in X-ray attenuation between normal tissue and tissue affected by a disease. By using the median filter and implementing deep learning as a method for classifying images based on feature extraction and weights in artificial neural networks. The stages carried out include preprocessing, with training and testing, feature extraction using layers of artificial neural networks that have undergone the filtering process. Then, a custom classifier layer is created to train the classification of COVID and normal classes using data from bottleneck.npy. The results of training and testing yielded an average accuracy of 95%, while the F1 Score evaluation result was 0.9."

Predicting the flowability of UHPC and identifying its significant influencing factors using an accurate ANN model

In this research, a one-hidden layer artificial neural network paradigm (ANN) was created to forecast the slump flow of ultra-high-performance concrete (UHPC). To achieve this goal, 3,200 ANNs were evaluated to estimate the fresh UHPC’s slump flow utilizing 793 observations. The performance metrics measured on training and test data subsets were in the same order of magnitude, thereby pointing out the proper work of the k-fold validation procedure. The results of the connection weight approach analysis (CWA) indicated that water dosage had the highest positive importance in slump flow, preceding the superplasticizer volume ratio. Other factors that positively influenced slump flow were the water-to-powder ratio, the dosage of high-alkali glass powder, the water-to-binder ratio, and limestone concentration. The most negative influences on rheology were the high-alumina FC3R and metakaolin. The ANN accurately predicted the slump flow of UHPC, while the results of the CWA analysis were well-correlated with previous research.

Deep learning in bioinformatics.

Deep learning is a powerful machine learning technique that can learn from large amounts of data using multiple layers of artificial neural networks. This paper reviews some applications of deep learning in bioinformatics, a field that deals with analyzing and interpreting biological data. We first introduce the basic concepts of deep learning and then survey the recent advances and challenges of applying deep learning to various bioinformatics problems, such as genome sequencing, gene expression analysis, protein structure prediction, drug discovery, and disease diagnosis. We also discuss future directions and opportunities for deep learning in bioinformatics. We aim to provide an overview of deep learning so that bioinformaticians applying deep learning models can consider all critical technical and ethical aspects. Thus, our target audience is biomedical informatics researchers who use deep learning models for inference. This review will inspire more bioinformatics researchers to adopt deep-learning methods for their research questions while considering fairness, potential biases, explainability, and accountability.

Neuronal diversity can improve machine learning for physics and beyond

Diversity conveys advantages in nature, yet homogeneous neurons typically comprise the layers of artificial neural networks. Here we construct neural networks from neurons that learn their own activation functions, quickly diversify, and subsequently outperform their homogeneous counterparts on image classification and nonlinear regression tasks. Sub-networks instantiate the neurons, which meta-learn especially efficient sets of nonlinear responses. Examples include conventional neural networks classifying digits and forecasting a van der Pol oscillator and physics-informed Hamiltonian neural networks learning Hénon–Heiles stellar orbits and the swing of a video recorded pendulum clock. Such learned diversity provides examples of dynamical systems selecting diversity over uniformity and elucidates the role of diversity in natural and artificial systems.

Safe and Trustful AI for Closed-Loop Control Systems

In modern times, closed-loop control systems (CLCSs) play a prominent role in a wide application range, from production machinery via automated vehicles to robots. CLCSs actively manipulate the actual values of a process to match predetermined setpoints, typically in real time and with remarkable precision. However, the development, modeling, tuning, and optimization of CLCSs barely exploit the potential of artificial intelligence (AI). This paper explores novel opportunities and research directions in CLCS engineering, presenting potential designs and methodologies incorporating AI. Combining these opportunities and directions makes it evident that employing AI in developing and implementing CLCSs is indeed feasible. Integrating AI into CLCS development or AI directly within CLCSs can lead to a significant improvement in stakeholder confidence. Integrating AI in CLCSs raises the question: How can AI in CLCSs be trusted so that its promising capabilities can be used safely? One does not trust AI in CLCSs due to its unknowable nature caused by its extensive set of parameters that defy complete testing. Consequently, developers working on AI-based CLCSs must be able to rate the impact of the trainable parameters on the system accurately. By following this path, this paper highlights two key aspects as essential research directions towards safe AI-based CLCSs: (I) the identification and elimination of unproductive layers in artificial neural networks (ANNs) for reducing the number of trainable parameters without influencing the overall outcome, and (II) the utilization of the solution space of an ANN to define the safety-critical scenarios of an AI-based CLCS.

BIDL: a brain-inspired deep learning framework for spatiotemporal processing.

Brain-inspired deep spiking neural network (DSNN) which emulates the function of the biological brain provides an effective approach for event-stream spatiotemporal perception (STP), especially for dynamic vision sensor (DVS) signals. However, there is a lack of generalized learning frameworks that can handle various spatiotemporal modalities beyond event-stream, such as video clips and 3D imaging data. To provide a unified design flow for generalized spatiotemporal processing (STP) and to investigate the capability of lightweight STP processing via brain-inspired neural dynamics, this study introduces a training platform called brain-inspired deep learning (BIDL). This framework constructs deep neural networks, which leverage neural dynamics for processing temporal information and ensures high-accuracy spatial processing via artificial neural network layers. We conducted experiments involving various types of data, including video information processing, DVS information processing, 3D medical imaging classification, and natural language processing. These experiments demonstrate the efficiency of the proposed method. Moreover, as a research framework for researchers in the fields of neuroscience and machine learning, BIDL facilitates the exploration of different neural models and enables global-local co-learning. For easily fitting to neuromorphic chips and GPUs, the framework incorporates several optimizations, including iteration representation, state-aware computational graph, and built-in neural functions. This study presents a user-friendly and efficient DSNN builder for lightweight STP applications and has the potential to drive future advancements in bio-inspired research.

Unsupervised anomaly detection in pressurized water reactor digital twins using autoencoder neural networks

Deep learning (DL), that is becoming quite popular for prediction and analysis of complex patterns in large amounts of data is used to investigate the safety behaviour of the nuclear plant items. This is achieved by using multiple layers of artificial neural networks to process and transform input data, allowing for the creation of highly accurate predictive models. Particularly to the aim the unsupervised machine learning approach and the digital twin concept in form of pressurized water reactor 2-loop simulator are used. This innovative methodology is based on neural network algorithm that makes capable to predict failures of plant structure, system, and components earlier than the activation of safety and emergency systems. Moreover, to match the objective of the study several scenarios of loss of cooling accident (LOCA) of different break size were simulated. To make the acquisition platform realistic, Gaussian noise was added to the input signals. The neural network has been fed by synthetic dataset provide by PCTRAN simulator and the efficiency in event identification was studied. Further, due to the very limited studies on the unsupervised anomaly detection by means of autoencoder neural networks applied for plant monitoring and surveillance, the methodology has been validated with experimental data from resonant test rig designed for fatigue testing of tubular components. The obtained results demonstrate the reliability and the efficiency of the methodology in detecting anomalous events prior the activation of safety system. Particularly, if the difference between the expected readings and the collected data goes beyond the predetermined threshold, then the anomalous event is identified, e.g., the model detected anomalies up to 38 min before the reactor scram intervention.

Comparative Study to Identify the Heart Disease Using Machine Learning Algorithms

Abstract: Heart disease is a major health concern globally, and it is a leading cause of death, especially in developing countries in Africa and Asia. Early detection of heart disease can play a crucial role in preventing its occurrence and reducing its impact. This is where the use of deep neural networks (CNNs) and the Django framework can be highly beneficial. The CNN algorithm is a machine learning technique that uses multiple layers of artificial neural networks to analyze complex data and identify patterns. In the case of heart disease prediction, the CNN algorithm can be trained on a dataset such as the UCI dataset, which contains a large amount of data related to heart disease risk factors and patient characteristics. The dataset can be split into training and testing data to enable the algorithm to learn and validate its accuracy.

A predictive analytics model for designing deep underground foundations using artificial neural networks

Artificial neural networks (ANNs) are commonly used to solve nonlinear problems. ANNs are composed of parallel interconnected layers that include processing elements called neurons. These neurons use mathematical functions to process the data, mimicking the human brain. In this study, we use ANNs for designing deep underground supports. We develop a predictive model for the ultimate axial capacity of deep foundations called drilled shafts, commonly used as support for highways, bridges and high-rise buildings. Different single hidden layer ANN architectures are utilized to predict the ultimate axial capacity of drilled shafts. The data used in this study are load tests collected from the extended version of the Nevada Deep Foundation Load Test Database. This study focuses on certain difficulties in foundation engineering problems, such as the variability in the soil or construction method which, conventional methods might not fully address. This can sometimes lead to overestimation or underestimation of the capacity. Consequently, a project can be unsafe or expensive. Therefore, the objective of this study is to improve prediction accuracy which is important and can save design and construction costs and time. A total of 45 load tests were divided into 85% for training, and 15% for validation. The developed ANN model achieved good generalization and prediction accuracy with a Root Mean-Squared Error of 2807.08 Kilopounds force (kips), a Mean Absolute Error of 2380.6 kips, and an R-squared (R2) of 87% on unseen data. The results can be adapted in future studies and the industry as a first-order estimate for the architecture of an ANN predictive model and the ultimate nominal axial capacity of drilled shafts.