Nonlinear Autoregressive Network Research Articles

Predicting chemotherapy-induced thrombotoxicity by NARX neural networks and transfer learning

BackgroundThrombocytopenia is a common side effect of cytotoxic chemotherapies, which is often dose-limiting. Predicting an individual’s risk is of high clinical importance, as otherwise, a small subgroup of patients limits dosages for the overall population for safety reasons.MethodsWe aim to predict individual platelet dynamics using non-linear auto-regressive networks with exogenous inputs (NARX). We consider different architectures of the NARX networks, namely feed-forward networks (FNN) and gated recurrent units (GRU). To cope with the relative sparsity of individual patient data, we employ transfer learning (TL) approaches based on a semi-mechanistic model of hematotoxicity. We use a large data set of patients with high-grade non-Hodgkin’s lymphoma to learn the respective models on an individual scale and to compare prediction performances with that of the semi-mechanistic model.ResultsOf the examined network models, the NARX with GRU architecture performs best. In comparison to the semi-mechanistic model, the network model can result in a substantial improvement of prediction accuracy for patients with irregular dynamics, given well-spaced measurements. TL improves individual prediction performances.ConclusionNARX networks can be utilized to predict an individual’s thrombotoxic response to cytotoxic chemotherapy treatment. For reasonable model learning, we recommend at least three well-spaced measurements per cycle: at baseline, during the nadir phase and during the recovery phase. We aim at generalizing our approach to other treatment scenarios and blood lineages in the future.

Forecasting wastewater flows and pollutant loads: A comparison of data-driven models within the urban water system framework

The ability to forecast key features of wastewater treatment plant (WWTP) influent, is emerging as an important tool to enable advanced WWTP operational strategies. Various data driven models have been reported in the scientific literature for WWTP influent forecast however, there has been no quantitative comparison of them against each other. The present study is the first to undertake this comparison utilising a high-frequency reference dataset generated from the Urban Water System model. Specifically, the performance of autoregressive models was compared against time-delay networks, nonlinear autoregressive networks and long short-term memory networks. Time-delay networks were generally found to outperform the other tested methods, although the reliability of the generated forecasts decreases as the prediction horizon exceeds one hour. While longer prediction horizons would be desirable, there is a trade-off between model accuracy and overall optimisation of plant operation. This study also highlights the challenge of dealing with both concentration and flow variations suggesting the need for future research to analyse the separate impacts of flow and concentration variations on model performance.

Model-based prediction of water levels for the Great Lakes: a comparative analysis

This comprehensive study addresses the correlation between water levels and meteorological features, including air temperature, evaporation, and precipitation, to accurately predict water levels in lakes within the Great Lakes basin. Various models, namely multiple linear regression (MLR), nonlinear autoregressive network with exogenous inputs (NARX), Facebook Prophet (FB-Prophet), and long short-term memory (LSTM), are employed to enhance predictions of lake water levels. Results indicate that all models, except for FB-Prophet, perform well, particularly for Lakes Erie, Huron-Michigan, and Superior. However, MLR and LSTM show reduced performance for Lakes Ontario and St. Clair. NARX emerges as the top performer across all lakes, with Lakes Erie and Superior exhibiting the lowest error metrics—root mean square error (RMSE: 0.048 and 0.034), mean absolute error (MAE: 0.036 and 0.026), mean absolute percent error (MAPE: 0.021% and 0.014%), and alongside the highest R-squared value (R2: 0.977 and 0.968), respectively. Similarly, for Lake Huron-Michigan, NARX demonstrates exceptional predictive precision with an RMSE (0.029), MAE (0.022), MAPE (0.013%), and an outstanding R2 value of 0.995. Despite slightly higher error metrics, NARX consistently performs well for Lake Ontario. However, Lake St. Clair presents challenges for predictive performance across all models, with NARX maintaining relatively strong metrics with an RMSE (0.076), MAE (0.050), MAPE (0.029%), and R2 (0.953), reaffirming its position as the leading model for water level prediction in the Great Lakes basin. The findings of this study suggest that the NARX model accurately predicts water levels, providing insights for managing water resources in the Great Lakes region.

Applying High‐Speed Video Images to Inverse Channel Base Current Based on NARX Neural Network

AbstractThe high‐speed video (HSV) images were taken as the input data of the nonlinear autoregressive network (NARX) to reconstruct the return‐stroke channel base current (CBC). The integrated luminosity (IL) of discharge channel is firstly obtained by summing the pixel values in HSV images, and the correlation between the IL and CBC is analyzed as well. Then, a NARX model is trained by taking the IL and CBC as the input and output data, respectively. With the input of the IL of another discharge channel, the trained NARX model is applied to inverse the corresponding CBC. The inversed result suggests that the proposed method can be used to infer the CBC that was not yet measured.

Prediction of daily river water temperatures using an optimized model based on NARX networks

Water temperature is an important physical indicator of rivers because it impacts many other physical and biogeochemical processes and controls the metabolism of aquatic species in rivers. Having a good knowledge of river thermal dynamics is of great importance. In this study, an advanced machine learning based model that is fast, accurate and easy to use, namely the nonlinear autoregressive network with exogenous inputs (NARX) neural network, was coupled with Bayesian Optimization (BO) algorithm for optimizing the number of NARX hidden nodes and lagged input/target values and the Bayesian Regularization (BR) backpropagation algorithm for the NARX training, to forecast daily river water temperatures (RWT). Long-term observed data from 18 rivers of the Vistula River Basin, one of the largest rivers in Europe, were used for model testing, and model performance was compared with the air2stream model. The results showed that the NARX-based model performs significantly better than the air2stream model in the calibration and validation stages, and can better capture the seasonal pattern and peak values of RWT. Input combinations impact the performance of the NARX-based model in RWT modeling, and air temperature and the day of the year (DOY) are the major inputs, while streamflow and rainfall play a minor role on modeling RWT at the Vistula River Basin. Considering that future times series of air temperatures are easily accessible from climate models and DOY is easy to be considered in the model, the NARX-based model can serve as a promising tool to investigate the impact of climate change on river thermal dynamics.

Measurement of State of Charge of Lithium-Nickel Manganese Cobalt Battery using Artificial Neural Network and NARX Algorithm

The battery's SoC is a crucial variable since it reflects its performance. An accurate estimation of SoC protects the battery, prevents overcharging or discharge, and extends its life time. Since most of the traditional methods use complex equations, ANN has been implemented to reduce the complications and provide better accuracy. In this research, Li-NMC with capacity rating of 2000mAh is used for the estimation of SoC. In this paper, Feedforward Neural Network (FNN) algorithm and Nonlinear Auto-Regressive network with exogenous inputs (NARX) have been used for designing a neural network model. Here, the performance matrixes of both neural network models have been compared and analyzed with the same dataset.

An optimized NARX-based model for predicting thermal dynamics and heatwaves in rivers

The thermal dynamics within river ecosystems represent critical areas of study due to their profound impact on overall aquatic health. With the rising prevalence of heatwaves in rivers, a consequence of climate change, it is imperative to deepen our understanding through comprehensive research efforts. Despite this urgency, there remains a noticeable dearth in studies aimed at refining modeling techniques to precisely characterize the duration and intensity of these events. In response to this gap, the present study endeavors to augment the NARX-based model (Nonlinear Autoregressive network with Exogenous Inputs) to enhance predictive capabilities regarding thermal dynamics and river heatwaves. The optimized NARX-based model included the Bayesian Optimization (BO) algorithm, which allows fine-tuning the number of NARX hidden nodes and lagged input/target values, and the Bayesian Regularization (BR) backpropagation algorithm to improve the NARX calibration process. A long-term dataset spanning from 1991 to 2021, encompassing 18 rivers across the expansive Vistula River Basin, one of Europe's largest river systems, was employed for this study. The performance of the BO-NARX-BR model was compared with that of the widely utilized air2stream model for modeling river water temperature (RWT). The results unequivocally demonstrated the superior performance of the NARX-based model across the calibration and validation periods, and four heatwave years. In the context of river heatwaves, the study revealed an escalating frequency and intensity within the Vistula River Basin. Furthermore, the NARX-based model exhibited superior proficiency in characterizing river heatwaves compared to the air2stream model. This study, as the inaugural examination of river heatwaves in Poland and one of the few globally, furnishes crucial reference points for subsequent research endeavors on this phenomenon.

Real-time mapping of crop canopy temperature using a wireless network of infrared thermometers on a central pivot

Efficient irrigation is essential for sustainable food production and regional water security. Temperature measurements provide information about crop water status, which allows the estimation of water needs and precise irrigation scheduling. This paper proposes a technology for agricultural irrigation management that combines cost-effective implementation with the ability to map crop canopy temperatures using a wireless network of infrared thermometers on a center pivot. The technology integrates Wireless Sensor Networks (WSN) with scalability options, IoT capabilities, and web data availability, enabling precise plant water stress quantification based on canopy temperature and soil water content. It facilitates real-time irrigation prescriptions while the center pivot is in motion, with canopy temperature sensors providing accurate readings of +/- 0.5 °C without additional calibration. Nonlinear Autoregressive Network with Exogenous Inputs (NARX) and Long Short-Term Memory (LSTM) neural network models were trained to predict irrigation prescriptions, achieving Root Mean Squared Error (RMSE < 4.18 mm) and correlation coefficient (r^2 > 0.82). This technology will allow the definition of real-time and site-specific prescriptions for variable-rate irrigation systems using infrared temperature sensors. Future work includes exploring LoRaWAN technologies, implementing a Differential Global Positioning System (DGPS), improving spatial resolution with data fusion algorithms, refining irrigation prescription models, reducing sensor costs and developing models considering soil and crop effects.

Data-driven approach for the detection of faults in district heating networks

At present, District Heating Networks (DHNs) are required to operate more and more reliably and efficiently in order to further save primary energy and reduce environmental impact. Thus, monitoring and diagnostic approaches are necessary to identify the typical faults that affect this type of systems (e.g., anomalous heat and pressure losses), with the final goal of optimizing DHN operation and management. To this aim, this paper presents a data-driven diagnostic methodology that exploits NARX (nonlinear autoregressive network with exogenous inputs) neural networks to simulate DHN healthy operation and a threshold-based criterion for fault detection and identification. The novel diagnostic methodology is tested for evaluating the health state of the DHN of the campus of the University of Parma (Italy), based on the availability of time series of measurable variables (mass flow rate, pressure, and temperature) for both the power plant and the end-users. Both single and multiple faults of anomalous heat losses and anomalous pressure losses, with different magnitudes and location, were artificially implanted in DHN pipes. The main novel contribution of this paper with respect to state-of-the-art literature relies on the development of a real-time simulation approach aimed to predict DHN future operation and detect abnormal deviations from normal operation. The methodology proves to correctly detect and identify all simulated faults related to heat and pressure losses, by also correctly estimating their magnitude even in the most challenging scenarios.

A New Approach to Current Transformer Saturation Compensation for Transmission Line Differential Protection

A non-linear autoregressive network with external inputs (NARX) model to reconstruct the current transformer (CT) secondary waveform distortion in the presence of protected transmission lines is presented. The qualitative analysis carried out on the autonomous model reveals the accurate performance of the current differential relay, because of the ability of the NARX to make accurate predictions and signal reconstruction even when faced with noisy or incomplete datasets. The suggested method uses samples of the line-protected remote current signal to produce a desired waveform. The unsaturated section is artificially expanded because it can estimate up to one sample after saturation with a respectable level of accuracy. The proposed method is evaluated by MATLAB and PSCAD software. The effectiveness of the suggested method for different fault types under varied situations has been proved. The simulation outcome confirms the method’s high accuracy concerning the unusual system conditions in the presence of CT saturation.

Synchronized and Co-Located Ionospheric and Atmospheric Anomalies Associated with the 2023 Mw 7.8 Turkey Earthquake

Earth observations from remotely sensed data have a substantial impact on natural hazard surveillance, specifically for earthquakes. The rapid emergence of diverse earthquake precursors has led to the exploration of different methodologies and datasets from various satellites to understand and address the complex nature of earthquake precursors. This study presents a novel technique to detect the ionospheric and atmospheric precursors using machine learning (ML). We examine the multiple precursors of different spatiotemporal nature from satellites in the ionosphere and atmosphere related to the Turkey earthquake on 6 February 2023 (Mw 7.8), in the form of total electron content (TEC), land surface temperature (LST), sea surface temperature (SST), air pressure (AP), relative humidity (RH), outgoing longwave radiation (OLR), and air temperature (AT). As a confutation analysis, we also statistically observe datasets of atmospheric parameters for the years 2021 and 2022 in the same epicentral region and time period as the 2023 Turkey earthquake. Moreover, the aim of this study is to find a synchronized and co-located window of possible earthquake anomalies by providing more evidence with standard deviation (STDEV) and nonlinear autoregressive network with exogenous inputs (NARX) models. It is noteworthy that both the statistical and ML methods demonstrate abnormal fluctuations as precursors within 6 to 7 days before the impending earthquake over the epicenter. Furthermore, the geomagnetic anomalies in the ionosphere are detected on the ninth day after the earthquake (Kp &gt; 4; Dst &lt; −70 nT; ap &gt; 50 nT). This study indicates the relevance of using multiple earthquake precursors in a synchronized window from ML methods to support the lithosphere–atmosphere–ionosphere coupling (LAIC) phenomenon.

Performance of TANN, NARX, and GMDHT Models for Urban Water Demand Forecasting: A Case Study in a Residential Complex in Qom, Iran

To keep the balance between demand and supply, methods based on the average per capita consumption were usually applied to predict water demand. More complicated models such as linear regression and time series models were developed for this purpose. However, after the introduction of artificial neural networks (ANNs), different applications of this method were used in the field of water supply management, especially for urban water demand prediction. In this study, multiple types of ANNs were studied to understand their suitability for a residential complex water demand prediction in the city of Qom, Iran. The results indicated that time series ANN (TANN), nonlinear autoregressive network with exogenous inputs (NARX), group method of data handling time series (GMDHT), and their wavelet counterparts (i.e., w-TANN and w-NARX) exhibited varying degrees of performance. Among the aforementioned models, w-NARX performed the best (based on the average overall error) with the test set root mean squared error (MSE) of 49.5 (m3 /h) and R of 0.93, followed by the GMDHT model with the test set MSE of 104 (m3 /h) and R of 0.97 and w-TANN with the test set MSE of 68.8 (m3 /h) and R of 0.91. In addition, the feedback connection in NARX compared to TANN demonstrated overall performance improvement.

Insight into Secondary Inorganic Aerosol (SIA) production enhanced by domestic ozone using a machine learning technique

Taiwan has prioritized management and air pollution control of ozone in the past decade. Atmospheric ozone reacts with gaseous precursors to produce secondary inorganic aerosols (SIAs), which worsen air quality to a great extent. The present study applied a bivariate polar plot, K-means clustering, and a nonlinear autoregressive network with exogenous input neural network (NARX-NN) to identify the sources of O3 and the formation mechanism of SIAs in an urban area, aiming to facilitate the development of exposure risk assessment methods and an O3 pollution early warning system for human health protection. Results show that the present NARX-NN model could be used to capture 72 h ahead of water-soluble inorganic salts (WIS) and O3 concentrations accurately with R2 of 0.71 for NO3-, 0.72 for SO42-, 0.80 for NH4+, and 0.79 for O3 concentrations. Based on the statistical and K-means clustering analysis, the domestic high O3 hours in a year (O3 concentrations>60 ppb) account for up to 76% and 99% of the total high O3 hours in northern and southern Taiwan, respectively. Under volatile organic compounds (VOCs)-limited regime, an increase in O3 concentrations by 57.4% was found to enhance heterogeneous oxidation reaction to produce SIAs by 48.0% of NO3- and 56.6% of SO42- under prevailing northeast monsoon during winter and spring seasons. It is evident that strict control measures are still necessary for local ozone sources to maintain air quality. The source tracing framework developed in the present study is applicable for policymakers to develop early warning systems and maintain air quality during the decision-making process.

Defining the optimal conditions using FFNNs and NARX neural networks for modelling the extraction of Sc from aqueous solution by Cryptand-2.2.1 and Cryptand-2.1.1

The main aim of this study is to figure out how well cryptand-2.2.1 (C 2.2.1) and cryptand-2.1.1 (C 2.1.1) macrocyclic compounds (MCs) work as novel extractants for scandium (Sc) by using an artificial neural network (ANN) models in MATLAB software. Moreover, C2.2.1 and C2.1.1 have never been evaluated to recover Sc. The independent variables impacting the extraction process (concentration of MC, concentration of Sc, pH, and time), and a nonlinear autoregressive network with exogenous input (NARX) and feed-forward neural network (FFNN) models were used to estimate their optimum values. The greatest obstacle in the selective recovery process of the REEs is the similarity in their physicochemical properties, specifically their ionic radius. The recovery of Sc from the aqueous solution was experimentally evaluated, then the non-linear relationship between those parameters was predictively modeled using (NARX) and (FFNN). To confirm the extraction and stripping efficiency, an atomic absorption spectrophotometer (AAS) was employed. The results of the extraction investigations show that, for the best conditions of 0.008 mol/L MC concentration, 10 min of contact time, pH 2 of the aqueous solution, and 75 mg/L Sc initial concentration, respectively, the C 2.1.1 and C 2.2.1 extractants may reach 99 % of Sc extraction efficiency. Sc was recovered from a multi-element solution of scandium (Sc), yttrium (Y), and lanthanum (La) under these circumstances. Whereas, at a concentration of 0.3 mol/L of hydrochloric acid, the extraction of Sc was 99 %, as opposed to Y 10 % and La 7 %. The Levenberg-Marquardt training algorithm had the best training performance with an mean-squared-error, MSE, of 5.232x10−6 and 6.1387x10−5 for C 2.2.1 and C 2.1.1 respectively. The optimized FFNN architecture of 4-10-1 was constructed for modeling recovery of Sc. The extraction process was well modeled by the FFNN with an R2 of 0.999 for the two MC, indicating that the observed Sc recovery efficiency consistent with the predicted one.

Atmospheric precursors from multiple satellites associated with the 2020 Mw 6.5 Idaho (USA) earthquake

Remote sensing has became a powerful tool for identifying lithosphere and atmosphere anomalies associated with the impending Earthquakes (EQs) in the vicinity of seismic breeding zone. In this paper, Land Surface Temperature (LST) of both the daytime and nighttime from the Moderate Resolution Imaging Spectroradiometer (MODIS) along with Air Temperature (AT), Relative Humidity (RH), Air Pressure (AP) and Outgoing Longwave Radiations (OLR) are studied for the 2020 Idaho (USA) EQ of Mw 6.5. We found the EQ induced surface and atmospheric parameters anomalies just one day prior to EQ main shock using statistical analysis. Moreover, we observed a sharp increment in LST and AT followed by the drop in both AP and RH, which are responsible for cooling the hot gases emitted from epicenter during preparation period. Also, we observed a large increase in OLR on the same day confirming these anomalous variations to be related with the main shock. Furthermore, these abrupt variations are also confirmed using neural networks (nonlinear autoregressive network with exogenous inputs (NARX), multilayer perceptron (MLP) and continuous wavelet transformation (CWT). These multi-parameter and multi-technique analyses can contribute to assist in the main shock forecasting in future with an enhanced cluster of satellite observations.

A novel optimized model based on NARX networks for predicting thermal anomalies in Polish lakes during heatwaves, with special reference to the 2018 heatwave

In 2018, Europe experienced one of the most severe heatwaves ever recorded. This extreme event's impact on lake surface water temperature (LSWT) in Polish lakes has largely remained unknown. In this study, the impact of the 2018 European heatwave on LSWT in 24 Polish lakes was investigated based on a long-term observed dataset (1987–2020). To capture the LSWT dynamics during the heatwave period and reproduce lake heatwaves, a novel BO-NARX-BR model was developed and evaluated. This model combines the capabilities of the Nonlinear Autoregressive network with Exogenous Inputs (NARX) neural network, the Bayesian Optimization (BO) algorithm for optimizing the number of NARX hidden nodes and lagged input/target values, and the Bayesian Regularization (BR) backpropagation algorithm for the NARX training. The results showed that from April to October 2018, the mean and maximum LSWTs were 2.35 and 3.38 °C warmer than the base-period average (1987–2010) due to the impact of the extreme heatwave. The NARX-based model outperformed another widely used model called air2water in calibration and validation periods. The results also revealed that the BO-NARX-BR model produced significantly better results in capturing lake heatwaves, with computed duration and intensity of lake heatwaves close to the in-situ data. Additionally, LSWT anomaly significantly impacted the duration and intensity of heatwaves that occurred in lakes. Extreme climatic events are gaining increasing importance for the functioning of various elements of the hydrosphere. Such a situation encourages the search for more accurate methods and tools for their prediction. The model applied in the paper corresponds with these assumptions, and its good performance allows for its adaptation to lakes in other regions.

Physics Informed Machine Learning Approach for Performance Degradation Monitoring of Gas Turbine

The heavy-duty gas turbine is playing an increasingly significant role on power generation due to its lower-emission, higher flexibility and thermo-efficiency. Main subsystems of the gas turbine like compressor, combustor and turbine degrade over the operating time under the harsh environmental conditions, which largely impacts the efficiency and productivity of the system. Therefore, it is critical to develop effective approaches to monitor performance degradation of a heavy-duty gas turbine for system predictive maintenance thus improving the efficiency and productivity of the machine. This paper presents a new physics informed machine learning methodology to predict the degradation of gas turbine by seamlessly integrating thermodynamic heat balancing mechanism, component characteristics, multi-source data and artificial neural network model. The mechanism-based thermodynamic model is established for multiple subsystems considering the balance of flow, mass and energy, and then integrated to a system level for performance simulation of the gas turbine under different conditions. The system model is able to effectively simulate values for those parameters that are not measurable (e.g. GT exhaust flow) or inaccurately measured (e.g. fuel flow). Machine learning based data cleaning approach is employed to preprocess the multivariate raw data of the gas turbine. The difference between design performance data and corrected value obtained from the physics-informed model under ISO conditions is utilized to assess the performance degradation. A Long Short-Term Memory (LSTM) model is established from the fusion of the actual and simulation data to predict the performance degradation of the gas turbine. A comparison study with the classical Nonlinear Autoregressive Network with External Input (NARX) neural network is conducted to demonstrate the advantage of the proposed method. Key Word: Gas Turbine, Thermodynamic Balance, Performance Degradation Predict, Machine Learning, LSTM

River flow modeling for flood prediction using machine learning techniques in Godavari river, India

Floods are highly impactful natural calamities, inflicting significant damage to infrastructure and causing numerous fatalities. These devastating events occur when rivers exceed their capacity or breach their banks due to intense precipitation.Forecasting river flow in the minimum Godavari river basin of eastern India allowed researchers to examine the potential of four data-driven techniques, including the artificial neural network (ANN), support vector machine (SVM), nonlinear autoregressive network with exogenous input (NARX) and Gaussian process regression (GPR), and compare the outcomes to those of the proposed neuro-tree method. By combining values of the antecedent river flow from two gauging stations, various models were built utilizing the methodologies, and the results were compared to see which models had the best match. The performances of the generated models were examined using mean square error, coefficient of correlation (R), and Nash-Sutcliffe coefficient, three widely used statistical performance assessment metrics (NS).An extensive analysis of the overall performance indicators revealed that the proposed neuro-tree algorithm models were more effective in flood prediction than the other four techniques employed in this study.

Individual modelling of haematotoxicity with NARX neural networks: A knowledge transfer approach

Cytotoxic cancer therapy often results in dose-limiting haematotoxic side effects. Predicting an individual's risk is a major objective in precision medicine of cancer treatment. In this regard, patient heterogeneity presents a significant challenge. In this paper, we explore the use of hypothesis-free machine learning models based on recurrent nonlinear auto-regressive networks with exogenous inputs (NARX) as an approach to achieve this goal. Also, we propose a knowledge transfer approach to ameliorate the issue of sparse individual data, which typically hampers learning of individual networks. We demonstrate the feasibility of our approach based on a virtual patient population generated using a semi-mechanistic model of haematopoiesis and imposing different cytotoxic therapy scenarios on it. Employing different techniques of model optimisation, we derive robust and parsimonious individual networks with good generalisation performances. Moreover, we analyse in detail possible factors influencing the generalisation performance. Results suggest that our transfer learning approach using NARX networks can provide robust predictions of individual patient's response to treatment. As a practical perspective, we apply our approach to individual time series data of two patients with non-Hodgkin's lymphoma.

An artificial neural network based method for company valuation

Purpose - Company value is a crucial issue for everyone operating in financial markets. Both firm managers and investors should calculate the value of a firm, and there are many methods available to do so. Calculating valuation methods is challenging due to the multiple parameters and stages that are involved. Due to these reasons, it's possible for managers, owners, investors, and other stakeholders to estimate a company's value inaccurately or with difficulty. The main objective of this essay is to demonstrate how to evaluate a company's value using the NARX model as an alternative to other models. Methodology – It is estimated that the firm value using an artificial neural network nonlinear external input autoregressive network model for 50 companies operating in the consumer products and industrial products and services sectors in the Euro Stoxx 50 index. The dataset covers the period from 2000 to 2021, and 20 financial ratios were included as input to the model, with FCFF as the output. Findings- The NARX model with a 20-6-6-1 or 20-10-10-1 network structure provided the best value for both R and MSE at two-time delays. However, the 20-12-12-1 network structure of the NARX model with a time delay of three has a lower error rate after training and the best R value. The model's prediction success rate is 90.82% using the 20-12-12-1 network structure with a time delay of three. Conclusion- As a result, this model can be used by investors and business managers to value a company. By using this method, businesses may gain access to more precise and unbiased appraisals that can guide resource allocation and strategic decision-making. By including macroeconomic factors that have an impact on the sector and employing a longer time frame, the study could be improved. Keywords: Company value, company valuation, cash flow to firm, artificial neural networks, nonlinear external input autoregressive network JEL Codes: C45, C80, G12