Extrapolation Capability Research Articles

Application of multilayer perceptron with data augmentation in nuclear physics

Neural networks have become popular in many fields of science since they serve as promising, reliable and powerful tools. In this work, we study the effect of data augmentation on the predictive power of neural network models for nuclear physics data. We present two different data augmentation techniques, and we conduct a detailed analysis in terms of different depths, optimizers, activation functions and random seed values to show the success and robustness of the model. Using the experimental uncertainties for data augmentation for the first time, the size of the training data set is artificially boosted and the changes in the root-mean-square error between the model predictions on the test set and the experimental data are investigated. Our results show that the data augmentation decreases the prediction errors, stabilizes the model and prevents overfitting. The extrapolation capabilities of the MLP models are also tested for newly measured nuclei in AME2020 mass table, and it is shown that the predictions are significantly improved by using data augmentation.

Physics-Based Neural Network Models for Prediction of Cam-Follower Dynamics Beyond Nominal Operations

Cam-follower mechanisms are key in various mechatronic applications to convert rotary to linear reciprocating motions. The dynamic behavior of these systems relies on the design parameters such as the cam shape and follower mass. It appears that for some combinations of system parameters, continuous contact between the cam and follower cannot be assured, leading to harmful periodic impacts. This research presents a data-driven approach to predict the influence of parameter settings on the system dynamics by learning from a limited data set of nominal operating conditions. More specifically, we present a hybrid model architecture encompassing an ordinary differential equation, consisting of a close interconnection of neural and physics-based network layers. Due to an increased generalization established by the physical laws, these physics-based neural network models exhibit enhanced extrapolation capabilities compared to their black-box counterparts. Consequently, the presented models can accurately simulate the system behavior for parameter settings far beyond the nominal values included in the training data. This way, starting from a limited set of nominal time-series data, we could accurately estimate the set of critical system parameters that lead to hazardous jump phenomena in cam-follower systems.

An encoder-decoder network for direct image reconstruction on sinograms of a long axial field of view PET.

Deep learning is an emerging reconstruction method for positron emission tomography (PET), which can tackle complex PET corrections in an integrated procedure. This paper optimizes the direct PET reconstruction from sinogram on a long axial field of view (LAFOV) PET. This paper proposes a novel deep learning architecture to reduce the biases during direct reconstruction from sinograms to images. This architecture is based on an encoder-decoder network, where the perceptual loss is used with pre-trained convolutional layers. It is trained and tested on data of 80 patients acquired from recent Siemens Biograph Vision Quadra long axial FOV (LAFOV) PET/CT. The patients are randomly split into a training dataset of 60 patients, a validation dataset of 10 patients, and a test dataset of 10 patients. The 3D sinograms are converted into 2D sinogram slices and used as input to the network. In addition, the vendor reconstructed images are considered as ground truths. Finally, the proposed method is compared with DeepPET, a benchmark deep learning method for PET reconstruction. Compared with DeepPET, the proposed network significantly reduces the root-mean-squared error (NRMSE) from 0.63 to 0.6 (p < 0.01) and increases the structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR) from 0.93 to 0.95 (p < 0.01) and from 82.02 to 82.36 (p < 0.01), respectively. The reconstruction time is approximately 10s per patient, which is shortened by 23 times compared with the conventional method. The errors of mean standardized uptake values (SUVmean) for lesions between ground truth and the predicted result are reduced from 33.5 to 18.7% (p = 0.03). In addition, the error of max SUV is reduced from 32.7 to 21.8% (p = 0.02). The results demonstrate the feasibility of using deep learning to reconstruct images with acceptable image quality and short reconstruction time. It is shown that the proposed method can improve the quality of deep learning-based reconstructed images without additional CT images for attenuation and scattering corrections. This study demonstrated the feasibility of deep learning to rapidly reconstruct images without additional CT images for complex corrections from actual clinical measurements on LAFOV PET. Despite improving the current development, AI-based reconstruction does not work appropriately for untrained scenarios due to limited extrapolation capability and cannot completely replace conventional reconstruction currently.

Hybrid Models Based on Machine Learning and an Increasing Degree of Process Knowledge: Application to Cell Culture Processes

In this work, we aim to introduce the concept of the degree of hybridization for cell culture process modeling. We propose that a family of hybrid models can be created with varying fractions of process knowledge explicitly encoded in the model, defined as the degree of hybridization, with the two extremes being fully data-driven (0%) and fully mechanistic (100%) models. Subsequently, the aim is to compare the different models based on different metrics: model accuracy, the experimental effort for model development, extrapolation capability, the capability of generating new process understanding, and ease of utilization in practice, and to demonstrate that this could provide an additional degree of freedom for model selection. We could quantitatively demonstrate that for the cell culture process, either extreme has limitations. The major drawback of the data-driven model is the poor performance at low data availability as well as poor extrapolation capability, inability to provide process understanding, and subsequently inefficient practical application. On the other hand, the mechanistic model has poor accuracy due to the addition of excessive knowledge that then biases the models. Moving from data-driven to mechanistic models, the performance of the models improves progressively, as long as the knowledge added is not too biased. We show that the choice of the hybrid models to be used is based on the goal of model development. For instance, hybrid models including mass balances on each species show better performance in transferring models across different modes of operation. On the other hand, models with a higher degree of hybridization allow for more process interpretation possibilities. For modeling accuracy, amount of training data, extrapolation, and practical applications, the Hybrid Rate (HR) model is found to have the optimal degree of hybridization. This is likely due to the compromise between adding process knowledge and increasing the model parameters achieved by the HR model. The HR model features the incorporation of mass balance and channels the data-driven modeling to cell-specific rates, and thus these two pieces of information appear to be the most crucial ones. Finally, we believe that the concept will be instrumental in progressively developing and testing hypotheses about complex processes such as cell cultures.

Similarity learning for wells based on logging data

One of the crucial steps of geological object exploration is interwell correlation. The correlation matches similar parts of different wells helping to construct geological models and assess hydrocarbon reserves. Today, a detailed interwell correlation relies on manual analysis of well-logging data: a process prone to significant time consumption and subjectivity. Alternative automation attempts include rule-based, classic machine learning, and more recent deep learning methods. However, most approaches are still of limited usage and inherit cons of manual correlation.We propose a method based on a deep learning model to solve the geological profile similarity estimation. Our similarity model takes well-logging data as input, constructs well representations and uses them to provide the similarity of wells. The developed algorithm enables extracting patterns and essential characteristics of geological profiles within the wells. We follow an unsupervised paradigm that allows us to utilize large pools of logging data available in the industry and does not rely on subjective labelling.For model testing, we used two open datasets originating in New Zealand and Norway. Our data-based similarity model has decent quality. For example, the accuracy of our model is 0.926 compared to 0.787 for a widespread gradient boosting baseline. The selected representation learning approach also provides high extrapolation capabilities to work for formations other than those used during training and start to work for limited amounts of available data, the experiments show.

Assessing statistical downscaling in Argentina: Daily maximum and minimum temperatures

AbstractEmpirical statistical downscaling (ESD) under the perfect prognosis approach was carried out to simulate daily maximum (Tx) and minimum temperatures (Tn) in 101 meteorological stations over the different climatic regions of Argentina. To this end, three ESD families were evaluated: analogs (AN), generalized linear models (GLM) and artificial neural networks (ANN) considering a variety of predictor sets with multiple configurations driven by three different reanalyses (ERA, JRA, NCEP). ESD models were cross‐validated using folds of nonconsecutive years (1979–2014) and then evaluated in a warmer set of years (independent warm period, 2015–2018) to assess their extrapolation capability. Depending on the aspect analysed, AN, GLM or ANN models were more/less skilful, but no method fulfilled all the features of both predicand variables. In this sense, the predictor set and model configuration were key factors. For each ESD method, the different predictor structures (point‐wise, spatial‐wise and combinations of them) introduced the main differences, regardless of the predictand variable, region and reanalysis choice. However, some specific results could be highlighted. ERA (NCEP)‐driven ESD models were the most (least) skilful in representing Tx and Tn. In the case of Tn, models' skills considerably increased when humidity information was included in the predictor set. Our results showed that downscaling models were able to capture the general characteristics of Tx and Tn in all regions, with better performance in the latter variable. However, regions with complex topography (Argentinian Patagonia and the subtropical Andes) pose a further challenge for capturing the local variability of daily extreme temperatures. The performance of the ESD models in the atypical warm conditions was similar to the one during the cross‐validated period, showing some extrapolation skill. The results of this work set a reference for future ESD developments and comparisons in Argentina.

Integration of machine learning and first principles models

AbstractModel building and parameter estimation are traditional concepts widely used in chemical, biological, metallurgical, and manufacturing industries. Early modeling methodologies focused on mathematically capturing the process knowledge and domain expertise of the modeler. The models thus developed are termed first principles models (or white‐box models). Over time, computational power became cheaper, and massive amounts of data became available for modeling. This led to the development of cutting edge machine learning models (black‐box models) and artificial intelligence (AI) techniques. Hybrid models (gray‐box models) are a combination of first principles and machine learning models. The development of hybrid models has captured the attention of researchers as this combines the best of both modeling paradigms. Recent attention to this field stems from the interest in explainable AI (XAI), a critical requirement as AI systems become more pervasive. This work aims at identifying and categorizing various hybrid models available in the literature that integrate machine‐learning models with different forms of domain knowledge. Benefits such as enhanced predictive power, extrapolation capabilities, and other advantages of combining the two approaches are summarized. The goal of this article is to consolidate the published corpus in the area of hybrid modeling and develop a comprehensive framework to understand the various techniques presented. This framework can further be used as the foundation to explore rational associations between several models.

Hybrid modelling of water resource recovery facilities: status and opportunities.

Mathematical modelling is an indispensable tool to support water resource recovery facility (WRRF) operators and engineers with the ambition of creating a truly circular economy and assuring a sustainable future. Despite the successful application of mechanistic models in the water sector, they show some important limitations and do not fully profit from the increasing digitalisation of systems and processes. Recent advances in data-driven methods have provided options for harnessing the power of Industry 4.0, but they are often limited by the lack of interpretability and extrapolation capabilities. Hybrid modelling (HM) combines these two modelling paradigms and aims to leverage both the rapidly increasing volumes of data collected, as well as the continued pursuit of greater process understanding. Despite the potential of HM in a sector that is undergoing a significant digital and cultural transformation, the application of hybrid models remains vague. This article presents an overview of HM methodologies applied to WRRFs and aims to stimulate the wider adoption and development of HM. We also highlight challenges and research needs for HM design and architecture, good modelling practice, data assurance, and software compatibility. HM is a paradigm for WRRF modelling to transition towards a more resource-efficient, resilient, and sustainable future.

A critical view on the suitability of machine learning techniques to downscale climate change projections: Illustration for temperature with a toy experiment

AbstractMachine learning is a growing field of research with many applications. It provides a series of techniques able to solve complex nonlinear problems, and that has promoted their application for statistical downscaling. Intercomparison exercises with other classical methods have so far shown promising results. Nevertheless, many evaluation studies of statistical downscaling methods neglect the analysis of their extrapolation capability. In this study, we aim to make a wakeup call to the community about the potential risks of using machine learning for statistical downscaling of climate change projections. We present a set of three toy experiments, applying three commonly used machine learning algorithms, two different implementations of artificial neural networks and a support vector machine, to downscale daily maximum temperature, and comparing them with the classical multiple linear regression. We have tested the four methods in and out of their calibration range, and have found how the three machine learning techniques can perform poorly under extrapolation. Additionally, we have analysed the impact of this extrapolation issue depending on the degree of overlapping between the training and testing datasets, and we have found very different sensitivities for each method and specific implementation.

Shape-Constrained Symbolic Regression-Improving Extrapolation with Prior Knowledge.

We investigate the addition of constraints on the function image and its derivatives for the incorporation of prior knowledge in symbolic regression. The approach is called shape-constrained symbolic regression and allows us to enforce, for example, monotonicity of the function over selected inputs. The aim is to find models which conform to expected behavior and which have improved extrapolation capabilities. We demonstrate the feasibility of the idea and propose and compare two evolutionary algorithms for shape-constrained symbolic regression: (i) an extension of tree-based genetic programming which discards infeasible solutions in the selection step, and (ii) a two-population evolutionary algorithm that separates the feasible from the infeasible solutions. In both algorithms we use interval arithmetic to approximate bounds for models and their partial derivatives. The algorithms are tested on a set of 19 synthetic and four real-world regression problems. Both algorithms are able to identify models which conform to shape constraints which is not the case for the unmodified symbolic regression algorithms. However, the predictive accuracy of models with constraints is worse on the training set and the test set. Shape-constrained polynomial regression produces the best results for the test set but also significantly larger models.

A new method to improve the generalization ability of neural networks: A case study of nuclear mass training

As one of the fundamental input quantities in nuclear physics, an accurate calculation of the nucleus mass is necessary. Currently, neural network methods improve the accuracy of mass models. However, the reliability for extrapolation cannot be predicted. In this paper, a training method of neural network method is proposed. A fitting method similar to the macroscopic microscopic mass model is used. After fitting the liquid drop model the neural network method is used for training, and then afterwards the parameters are refitted and the neural network model is retrained, and so on several times. Taking the Weizsäcker-Skyrme (WS) model as an example, for known nuclei, it can improve the calculation results by about 20% over the original results. The extrapolation results for unknown neutron-deficient nuclei are also significantly improved. We believe that this method can calculate the masses of partially unknown nuclei more accurately. Further, it may be possible to improve the extrapolation capability of the neural network method using this approach. It is hoped that the present work can be useful for nuclear physics experiments and applications of neural network methods.

Functional-Hybrid modeling through automated adaptive symbolic regression for interpretable mathematical expressions

Mathematical models used for the representation of (bio)-chemical processes can be grouped into two broad paradigms: white-box or mechanistic models, completely based on knowledgeor black-box data-driven models based on patterns observed in data. However, in the past two-decade, hybrid modeling that explores the synergy between the two paradigms has emerged as a pragmatic compromise. The data-driven part of these has been largely based on conventional machine learning algorithms (e.g., artificial neural network, support vector regression), which prevents interpretability of the finally learnt model by the domain experts. In this work, we present a novel hybrid modeling framework, the Functional-Hybrid model, that uses the ranked domain-specific functional beliefs together with symbolic regression to develop dynamic models. We demonstrate the successful implementation of the Functional-Hybrid model and its interpretability, focusing on applying chemical reaction kinetic principles to classical chemical reactions, biochemistry, ecology, physiology, and a bioreactor. Furthermore, we demonstrate that during interpolation, the Functional-Hybrid model performs similarly to a Hybrid-ANN hybrid model implementing a conventional ANN. However, it provides the advantage of being –to some extent– interpretable, unlike the conventional Hybrid-ANN model. Additionally, it is shown that the Functional-Hybrid model outperforms the Hybrid-ANN model for a very low number of experiments, making it more suitable when data is scarce. Finally, the Functional-Hybrid models show superior extrapolation capabilities compared to the Hybrid-ANN model. This improved performance can be attributed to the structure imposed by the functional transformations introduced in the Functional-Hybrid model.

Comparative Study of Performance-Oriented Feedforward Compensation Strategies for Precision Mechatronic Motion Systems

To meet the progressively stringent demands for trajectory tracking performance in precision/ultra-precision industry, multiple advanced feedforward compensation strategies have been reported in recent years. However, there is no fair and comprehensive performance comparison of advantages and drawbacks of various methods under different industrial working conditions. In this paper, a comparative study of several performance-oriented feedforward strategies represented by standard iterative learning control (ILC), cascaded ILC (CILC), gated recurrent units based feedforward compensation (GRU-FFC), and real-time iterative compensation (RIC) has been systematically conducted by theoretical clarification and experimental verification. Various trajectory tracking tasks are accomplished on a precision mechatronic motion stage, and the tracking performances to be examined include (i) tracking accuracy; (ii) extrapolation capability for non-repetitive trajectories; (iii) disturbance rejection ability. Experimental results are sufficiently summarized with the combination of underlying control mechanism analysis, which can provide a comprehensive and reliable selection guidance of feedforward compensation strategies in different practical industrial scenarios.

Multi-Task Learning for Low-Frequency Extrapolation and Elastic Model Building From Seismic Data

Low-frequency signal content in seismic data as well as a realistic initial model are key ingredients for robust and efficient full-waveform inversions. However, acquiring low-frequency data is challenging in practice for active seismic surveys. Data-driven solutions show promise to extrapolate low-frequency data given a high-frequency counterpart. While being established for synthetic acoustic examples, the application of bandwidth extrapolation to field datasets remains non-trivial. Rather than aiming to reach superior accuracy in bandwidth extrapolation, we propose to jointly reconstruct low-frequency data and a smooth background subsurface model within a multi-task deep learning framework. We automatically balance data, model and trace-wise correlation loss terms in the objective functional and show that this approach improves the extrapolation capability of the network. We also design a pipeline for generating synthetic data suitable for field data applications. Finally, we apply the same trained network to synthetic and real marine streamer datasets and run an elastic full-waveform inversion from the extrapolated dataset.

Nonlinearity encoding to improve extrapolation capabilities for unobserved physical states.

The fundamental goal of machine learning (ML) in physical science is to predict the physical properties of unobserved states. However, an accurate prediction for input data outside of training distributions is a challenging problem in ML due to the nonlinearities in input and target dynamics. For an accurate extrapolation of ML algorithms, we propose a new data-driven method that encodes the nonlinearities of physical systems into input representations. Based on the proposed encoder, a given physical system is described as linear-like functions that are easy to extrapolate. By applying the proposed encoder, the extrapolation errors were significantly reduced by 48.39% and 40.04% in n-body problem and materials property prediction, respectively.

Reliable nonlinear dynamic gray-box modeling by regularized training data estimation and sensitivity analysis

Dynamic process models are a key requirement for advanced process control and the application of process optimization techniques. The derivation of these models is time consuming and error-prone in cases where a lack of physico-chemical understanding is present. Machine learning (ML) methods can be employed in these cases to extract models or model elements from data. To reduce the amount of necessary data and to increase the extrapolation capabilities, gray-box models can be used that combine mechanistic equations with ML models. For embedded ML-models, the selection of a suitable model structure is challenging. Therefore, we propose a methodology to approach this problem in several steps by firstly estimating what values the ML-models should predict to accurately describe the experimental data. Subsequently, the ML-submodels can be trained using any ML-toolbox. Finally, a full parameter estimation is performed using a dynamic simulation in the cost function. We investigate different algorithmic options and show promising results for a case study of the fermentation of a sporulating bacterium.

Real-Time Emission Prediction with Detailed Chemistry under Transient Conditions for Hardware-in-the-Loop Simulations

The increasing requirements to further reduce pollutant emissions, particularly with regard to the upcoming Euro 7 (EU7) legislation, cause further technical and economic challenges for the development of internal combustion engines. All the emission reduction technologies lead to an increasing complexity not only of the hardware, but also of the control functions to be deployed in engine control units (ECUs). Virtualization has become a necessity in the development process in order to be able to handle the increasing complexity. The virtual development and calibration of ECUs using hardware-in-the-loop (HiL) systems with accurate engine models is an effective method to achieve cost and quality targets. In particular, the selection of the best-practice engine model to fulfil accuracy and time targets is essential to success. In this context, this paper presents a physically- and chemically-based stochastic reactor model (SRM) with tabulated chemistry for the prediction of engine raw emissions for real-time (RT) applications. First, an efficient approach for a time-optimal parametrization of the models in steady-state conditions is developed. The co-simulation of both engine model domains is then established via a functional mock-up interface (FMI) and deployed to a simulation platform. Finally, the proposed RT platform demonstrates its prediction and extrapolation capabilities in transient driving scenarios. A comparative evaluation with engine test dynamometer and vehicle measurement data from worldwide harmonized light vehicles test cycle (WLTC) and real driving emissions (RDE) tests depicts the accuracy of the platform in terms of fuel consumption (within 4% deviation in the WLTC cycle) as well as NOx and soot emissions (both within 20%).

Generic Framework for Downscaling Statistical Quantities at Fine Time-Scales and Its Perspectives towards Cost-Effective Enrichment of Water Demand Records

The challenging task of generating a synthetic time series at finer temporal scales than the observed data, embeds the reconstruction of a number of essential statistical quantities at the desirable (i.e., lower) scale of interest. This paper introduces a parsimonious and general framework for the downscaling of statistical quantities based solely on available information at coarser time scales. The methodology is based on three key elements: (a) the analysis of statistics’ behaviour across multiple temporal scales; (b) the use of parametric functions to model this behaviour; and (c) the exploitation of extrapolation capabilities of the functions to downscale the associated statistical quantities at finer scales. Herein, we demonstrate the methodology using residential water demand records and focus on the downscaling of the following key quantities: variance, L-variation, L-skewness and probability of zero value (no demand; intermittency), which are typically used to parameterise a stochastic simulation model. Specifically, we downscale the above statistics down to a 1 min scale, assuming two scenarios of initial data resolution, i.e., 5 and 10 min. The evaluation of the methodology on several cases indicates that the four statistics can be well reconstructed. Going one step further, we place the downscaling methodology in a more integrated modelling framework for a cost-effective enhancement of fine-resolution records with synthetic ones, embracing the current limited availability of fine-resolution water demand measurements.

Abstract P006: Novel machine-learning tools improve cost-effective development of personalised immunotherapies: Lowering false positive rates in the search for actionable (personalised and largely shared) immunogenic neoantigens

Abstract Personalised immunotherapy approaches rely on the ability of tumour-derived neoantigens to elicit a T-cell immune reaction able to recognise and kill the tumour cells expressing them. Clinical attempts to leverage the power of neoantigens have however yielded mixed results. This can mostly be attributed to the difficulty of finding truly immunogenic peptides from the set of novel peptides generated by mutations in a given cancer patient. In silico approaches can help alleviate this heavy cost by reducing the neoantigen search space, prioritising epitopes based on various parameters such as epitope expression or MHC binding likelihood. Here we present a suite of tools aimed at further assisting clinicians in selecting the most actionable peptides from a set of potential candidates. We developed neoMS, a neural network algorithm able to predict epitope presentation at the cell surface with unparalleled performance. The model achieves up to 0.61 precision at recall 0.4 on its test set, vastly outperforming the current industry standards. In addition, due to his sequence-based comparison method, neoMS exhibits extrapolation capabilities, achieving non-zero predictive power when evaluated on ground truth ligandome data derived from an HLA allele completely absent from the training set. In some cancer indications we showed, moreover, that the neoMS-predicted rate of neoantigen presentation can be used in combination with tumour mutational burden as a high-specificity predictor of response to immune checkpoint inhibitor treatment. Furthermore, the neoIM algorithm is able to discriminate, in an HLA-agnostic fashion, which of the presented peptides will elicit a T-cell immune reaction. This first-in-class algorithm is a random forest classifier specifically trained to classify short peptides of length 9-11 amino acids as immunogenic or non-immunogenic. neoIM vastly outperforms the currently available methods and can predict peptide immunogenicity with high accuracy (AUC=0.88). Interestingly, neoIM confirmed ELISPOT data obtained by Dillon et al. (2017) showing a response in 4 out of 11 breast cancer patients to a vaccine consisting of 9 MHC class-I restricted breast cancer-associated peptides. The 2 antigens that resulted in a CD8+ T-cell specific response were predicted by neoIM as the highest scoring showing its potential in finding the truly immunogenic neoantigens. Taken together, these tools decrease false positive rates significantly as they enable improved identification of immunogenic peptides and the predictions correlate with intensity of immune response and clinical benefits. As such, these tools represent a cost-efficient preliminary step in the search for actionable, immunogenic neoantigens. Citation Format: Cedric Bogaert, Lena Pfitzer, Nil Adell Mill, Bruno Fant. Novel machine-learning tools improve cost-effective development of personalised immunotherapies: Lowering false positive rates in the search for actionable (personalised and largely shared) immunogenic neoantigens [abstract]. In: Proceedings of the AACR-NCI-EORTC Virtual International Conference on Molecular Targets and Cancer Therapeutics; 2021 Oct 7-10. Philadelphia (PA): AACR; Mol Cancer Ther 2021;20(12 Suppl):Abstract nr P006.

Temperature drift compensation of a FOG based on an HKSVM optimized by an improved hybrid BAS-GSA algorithm.

In this paper, the optimal hybrid kernel support vector machine is employed to propose a compensation strategy intended for the temperature drift of a fiber optical gyroscope (FOG). First, the mode of the hybrid kernel with an interpolation and extrapolation capability is constructed, which consists of the radial basis function and the polynomial kernel function. Second, the combination model of the beetle antennae search algorithm and gravitational search algorithm that has both local and global search capability is proposed to optimize the structure-related parameters of a hybrid kernel support vector machine (HKSVM). Finally, the proposed approach is trained and tested using the experimental data of temperature drift at two different rates of temperature change (10°C/min and 5°C/min). In addition, the proposed method is validated against those conventional compensation algorithms. According to the research results, the compensation error (mean squared error) of the proposed approach is reduced by 92% compared to the traditional support vector machine based on the radial basis function.