Universal Approximation Using Radial-Basis-Function Networks

System Transformation-Based Neural Control for Full-State-Constrained Pure-Feedback Systems via Disturbance Observer

In this article, a novel disturbance observer-based adaptive neural control (ANC) scheme is proposed for full-state-constrained pure-feedback nonlinear systems using a new system transformation method. A nonlinear transformation function in a uniformed design framework is constructed to convert the original states with constrained bounds into the ones without any constraints. By combining an auxiliary first-order filter, an augmented nonlinear system without any state constraint is derived to circumvent the difficulty of the controller design caused by the nonaffine input signal. Based on the augmented nonlinear system, a nonlinear disturbance observer (NDO) is designed to enhance the disturbance rejection ability. Subsequently, the NDO-based ANC scheme is presented by combining the second-order filters with backstepping. The proposed scheme confines all states within the predefined bounds, eliminates the condition on both the known sign and bounds of control gains, improves the robustness of the closed-loop system, and alleviates the computational burden. Two simulation examples are performed to show the validity of the presented scheme.

1-Norm random vector functional link networks for classification problems

This paper presents a novel random vector functional link (RVFL) formulation called the 1-norm RVFL (1N RVFL) networks, for solving the binary classification problems. The solution to the optimization problem of 1N RVFL is obtained by solving its exterior dual penalty problem using a Newton technique. The 1-norm makes the model robust and delivers sparse outputs, which is the fundamental advantage of this model. The sparse output indicates that most of the elements in the output matrix are zero; hence, the decision function can be achieved by incorporating lesser hidden nodes compared to the conventional RVFL model. 1N RVFL produces a classifier that is based on a smaller number of input features. To put it another way, this method will suppress the neurons in the hidden layer. Statistical analyses have been carried out on several real-world benchmark datasets. The proposed 1N RVFL with two activation functions viz., ReLU and sine are used in this work. The classification accuracies of 1N RVFL are compared with the extreme learning machine (ELM), kernel ridge regression (KRR), RVFL, kernel RVFL (K-RVFL) and generalized Lagrangian twin RVFL (GLTRVFL) networks. The experimental results with comparable or better accuracy indicate the effectiveness and usability of 1N RVFL for solving binary classification problems.

A Two-Phase Evolutionary Method to Train RBF Networks

This article proposes a two-phase hybrid method to train RBF neural networks for classification and regression problems. During the first phase, a range for the critical parameters of the RBF network is estimated and in the second phase a genetic algorithm is incorporated to locate the best RBF neural network for the underlying problem. The method is compared against other training methods of RBF neural networks on a wide series of classification and regression problems from the relevant literature and the results are reported.

Neural Network Non-Singular Terminal Sliding Mode Control for Target Tracking of Underactuated Underwater Robots with Prescribed Performance

This paper proposes a neural network-based nonsingular terminal sliding mode controller with prescribed performances for the target tracking problem of underactuated underwater robots. Firstly, the mathematical formulation of the target tracking problem is presented with an underactuated underwater robot model and the corresponding control objectives. Then, the target tracking errors from the line-of-sight guidance law are transformed using the prescribed performance technique to achieve good dynamic performance and steady-state performance that meet the pre-set conditions. Meanwhile, considering the model’s uncertainties and the external disturbances to the underwater robots, a target tracking controller is proposed based on the radial basis function (RBF) neural network and the non-singular terminal sliding mode control. Lyapunov stability analysis and homogeneity theory prove the tracking errors can converge on a small region that contains the origin with prescribed performance in finite time. In the simulation comparison, the controller proposed in this paper had better dynamic performance, steady-state performance and chattering supression. In particular, the steady-state error of the tracking error was lower, and the convergence time of the tracking error in the vertical distance was reduced by 19.1%.

Accurate parameterization of the kinetic energy functional

The absence of a reliable formulation of the kinetic energy density functional has hindered the development of orbital free density functional theory. Using the data-aided learning paradigm, we propose a simple prescription to accurately model the kinetic energy density of any system. Our method relies on a dictionary of functional forms for local and nonlocal contributions, which have been proposed in the literature, and the appropriate coefficients are calculated via a linear regression framework. To model the nonlocal contributions, we explore two new nonlocal functionals-a functional that captures fluctuations in electronic density and a functional that incorporates gradient information. Since the analytical functional forms of the kernels present in these nonlocal terms are not known from theory, we propose a basis function expansion to model these seemingly difficult nonlocal quantities. This allows us to easily reconstruct kernels for any system using only a few structures. The proposed method is able to learn kinetic energy densities and total kinetic energies of molecular and periodic systems, such as H₂, LiH, LiF, and a one-dimensional chain of eight hydrogens using data from Kohn-Sham density functional theory calculations for only a few structures.

Realization of Spatial Sparseness by Deep ReLU Nets With Massive Data

The great success of deep learning poses urgent challenges for understanding its working mechanism and rationality. The depth, structure, and massive size of the data are recognized to be three key ingredients for deep learning. Most of the recent theoretical studies for deep learning focus on the necessity and advantages of depth and structures of neural networks. In this article, we aim at rigorous verification of the importance of massive data in embodying the outperformance of deep learning. In particular, we prove that the massiveness of data is necessary for realizing the spatial sparseness, and deep nets are crucial tools to make full use of massive data in such an application. All these findings present the reasons why deep learning achieves great success in the era of big data though deep nets and numerous network structures have been proposed at least 20 years ago.

Multi-objective optimization of thermophysical properties of multiwalled carbon nanotubes based nanofluids

The experimental determination of thermophysical properties of nanofluid (NF) is time-consuming and costly, leading to the use of soft computing methods such as response surface methodology (RSM) and artificial neural network (ANN) to estimate these properties. The present study involves modelling and optimization of thermal conductivity and viscosity of NF, which comprises multi-walled carbon nanotubes (MWCNTs) and thermal oil. The modelling is performed to predict the thermal conductivity and viscosity of NF by using Response Surface Methodology (RSM) and Artificial Neural Network (ANN). Both models were tested and validated, which showed promising results. In addition, a detailed optimization study was conducted to investigate the optimum thermal conductivity and viscosity by varying temperature and NF weight per cent. Four case studies were explored using different objective functions based on NF application in various industries. The first case study aimed to maximize thermal conductivity (0.15985 W/m ^oC) while minimizing viscosity (0.03501 Pa s) obtained at 57.86 °C and 0.85 NF wt%. The goal of the second case study was to minimize thermal conductivity (0.13949 W/m °C) and viscosity (0.02526 Pa s) obtained at 55.88 °C and 0.15 NF wt%. The third case study targeted maximizing thermal conductivity (0.15797 W/m °C) and viscosity (0.07611 Pa s), and the optimum temperature and NF wt% were 30.64 °C and 0.0.85,' respectively. The last case study explored the minimum thermal conductivity (0.13735) and maximum viscosity (0.05263 Pa s) obtained at 30.64 °C and 0.15 NF wt%.

Multiple Laplacian Regularized RBF Neural Network for Assessing Dry Weight of Patients With End-Stage Renal Disease

Dry weight (DW) is an important dialysis index for patients with end-stage renal disease. It can guide clinical hemodialysis. Brain natriuretic peptide, chest computed tomography image, ultrasound, and bioelectrical impedance analysis are key indicators (multisource information) for assessing DW. By these approaches, a trial-and-error method (traditional measurement method) is employed to assess DW. The assessment of clinician is time-consuming. In this study, we developed a method based on artificial intelligence technology to estimate patient DW. Based on the conventional radial basis function neural (RBFN) network, we propose a multiple Laplacian-regularized RBFN (MLapRBFN) model to predict DW of patient. Compared with other model and body composition monitor, our method achieves the lowest value (1.3226) of root mean square error. In Bland-Altman analysis of MLapRBFN, the number of out agreement interval is least (17 samples). MLapRBFN integrates multiple Laplace regularization terms, and employs an efficient iterative algorithm to solve the model. The ratio of out agreement interval is 3.57%, which is lower than 5%. Therefore, our method can be tentatively applied for clinical evaluation of DW in hemodialysis patients.

The Compact Support Neural Network

Neural networks are popular and useful in many fields, but they have the problem of giving high confidence responses for examples that are away from the training data. This makes the neural networks very confident in their prediction while making gross mistakes, thus limiting their reliability for safety-critical applications such as autonomous driving and space exploration, etc. This paper introduces a novel neuron generalization that has the standard dot-product-based neuron and the radial basis function (RBF) neuron as two extreme cases of a shape parameter. Using a rectified linear unit (ReLU) as the activation function results in a novel neuron that has compact support, which means its output is zero outside a bounded domain. To address the difficulties in training the proposed neural network, it introduces a novel training method that takes a pretrained standard neural network that is fine-tuned while gradually increasing the shape parameter to the desired value. The theoretical findings of the paper are bound on the gradient of the proposed neuron and proof that a neural network with such neurons has the universal approximation property. This means that the network can approximate any continuous and integrable function with an arbitrary degree of accuracy. The experimental findings on standard benchmark datasets show that the proposed approach has smaller test errors than the state-of-the-art competing methods and outperforms the competing methods in detecting out-of-distribution samples on two out of three datasets.

Associative anticipatory learning and control of the cerebellar cortex based on the spike-timing-dependent plasticity of the parallel fiber-Purkinje cell synapses

Time delays are inevitable in the neural processing of sensorimotor systems; small delays can cause severe damage to movement accuracy and stability. It is strongly suggested that the cerebellum compensates for delays in neural signal processing and performs predictive control. Neural computational theories have explored concepts of the internal models of control objects-believed to avoid delays by providing internal feedback information-although there has been no clear relevance to neural processing. The timing-dependent plasticity of parallel fiber-Purkinje cell synapses is well known. The long-term depression of the synapse is observed when parallel fiber activation precedes climbing fiber activation within -50-300 ms, and is the greatest within 50-200 ms. This paper presents a theory that this temporal difference of 50-200 ms is the basis for an associative anticipation of as many milliseconds. Associative learning can theoretically connect an input signal to a desired signal; therefore, a 50-200 ms earlier input signal can be connected to a desired output signal through temporary asymmetric plasticity. After learning is completed, an input signal generates a desired output signal that appears 50-200 ms later. For the associative learning of temporally continuous signals, this study integrates the universal function approximation capability of the cerebellar cortex model and temporally asymmetric synaptic plasticity to create the theory of associative anticipatory learning of the cerebellum. The effective motor control of this learning is demonstrated by adaptively stabilizing an inverted pendulum with a delay similar to that done by humans.

Tracking Control of Unknown and Constrained Nonlinear Systems via Neural Networks With Implicit Weight and Activation Learning

For systems with irregular (asymmetric and positively-negatively alternating) constraints being imposed/removed during system operation, there is no uniformly applicable control method. In this work, a control design framework is established for uncertain pure-feedback systems subject to the aforementioned constraints. By introducing a novel transformation function and with the help of auxiliary constraining boundaries, the original output-constrained system is augmented to unconstrained one. Unknown nonlinearity is approximated by neural networks (NNs) with not only neural weight updating but also activation online adjustment. The resultant control scheme is able to deal with constraints imposed or removed at some time moments during system operation without the need for altering control structure. When applied to high-speed trains, the developed control scheme ensures position tracking under speed constraints, simulation demands, and confirms the effectiveness of the proposed method.

Application of Extreme Learning Machine in the Survival Analysis of Chronic Heart Failure Patients With High Percentage of Censored Survival Time

Objective: To explore the application of the Cox model based on extreme learning machine in the survival analysis of patients with chronic heart failure.

Methods: The medical records of 5,279 inpatients diagnosed with chronic heart failure in two grade 3 and first-class hospitals in Taiyuan from 2014 to 2019 were collected; with death as the outcome and after the feature selection, the Lasso Cox, random survival forest (RSF), and the Cox model based on extreme learning machine (ELM Cox) were constructed for survival analysis and prediction; the prediction performance of the three models was explored based on simulated data with three censoring ratios of 25, 50, and 75%.

Results: Simulation results showed that the prediction performance of the three models decreased with increasing censoring proportion, and the ELM Cox model performed best overall; the ELM Cox model constructed with 21 highly influential survival predictors screened from actual chronic heart failure data showed the best performance with C-index and Integrated Brier Score (IBS) of 0.775(0.755, 0.802) and 0.166(0.150, 0.182), respectively.

Conclusion: The ELM Cox model showed good discrimination performance in the survival analysis of patients with chronic heart failure; it performs consistently for data with a high proportion of censored survival time; therefore, the model could help physicians identify patients at high risk of poor prognosis and target therapeutic measures to patients as early as possible.

Translation-Invariant Kernels for Multivariable Approximation

Suitability of shallow (one-hidden-layer) networks with translation-invariant kernel units for function approximation and classification tasks is investigated. It is shown that a critical property influencing the capabilities of kernel networks is how the Fourier transforms of kernels converge to zero. The Fourier transforms of kernels suitable for multivariable approximation can have negative values but must be almost everywhere nonzero. In contrast, the Fourier transforms of kernels suitable for maximal margin classification must be everywhere nonnegative but can have large sets where they are equal to zero (e.g., they can be compactly supported). The behavior of the Fourier transforms of multivariable kernels is analyzed using the Hankel transform. The general results are illustrated by examples of both univariable and multivariable kernels (such as Gaussian, Laplace, rectangle, sinc, and cut power kernels).

On Interpretability of Artificial Neural Networks: A Survey

Deep learning as represented by the artificial deep neural networks (DNNs) has achieved great success recently in many important areas that deal with text, images, videos, graphs, and so on. However, the black-box nature of DNNs has become one of the primary obstacles for their wide adoption in mission-critical applications such as medical diagnosis and therapy. Because of the huge potentials of deep learning, increasing the interpretability of deep neural networks has recently attracted much research attention. In this paper, we propose a simple but comprehensive taxonomy for interpretability, systematically review recent studies in improving interpretability of neural networks, describe applications of interpretability in medicine, and discuss possible future research directions of interpretability, such as in relation to fuzzy logic and brain science.

Approximation capabilities of neural networks on unbounded domains

There is limited study in the literature on the representability of neural networks on unbounded domains. For some application areas, results in this direction provide additional value in the design of learning systems. Motivated by an old option pricing problem, we are led to the study of this subject. For networks with a single hidden layer, we show that under suitable conditions they are capable of universal approximation in L^p(R×[0,1]ⁿ) but not in L^p(R²×[0,1]ⁿ). For deeper networks, we prove that the ReLU network with two hidden layers is a universal approximator in L^p(Rⁿ).

Graded heterogeneity of metabotropic signaling underlies a continuum of cell-intrinsic temporal responses in unipolar brush cells

Many neuron types consist of populations with continuously varying molecular properties. Here, we show a continuum of postsynaptic molecular properties in three types of neurons and assess the functional correlates in cerebellar unipolar brush cells (UBCs). While UBCs are generally thought to form discrete functional subtypes, with mossy fiber (MF) activation increasing firing in ON-UBCs and suppressing firing in OFF-UBCs, recent work also points to a heterogeneity of response profiles. Indeed, we find a continuum of response profiles that reflect the graded and inversely correlated expression of excitatory mGluR1 and inhibitory mGluR2/3 pathways. MFs coactivate mGluR2/3 and mGluR1 in many UBCs, leading to sequential inhibition-excitation because mGluR2/3-currents are faster. Additionally, we show that DAG-kinase controls mGluR1 response duration, and that graded DAG kinase levels correlate with systematic variation of response duration over two orders of magnitude. These results demonstrate that continuous variations in metabotropic signaling can generate a stable cell-autonomous basis for temporal integration and learning over multiple time scales.

Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations

We present a supervised learning method to learn the propagator map of a dynamical system from partial and noisy observations. In our computationally cheap and easy-to-implement framework, a neural network consisting of random feature maps is trained sequentially by incoming observations within a data assimilation procedure. By employing Takens's embedding theorem, the network is trained on delay coordinates. We show that the combination of random feature maps and data assimilation, called RAFDA, outperforms standard random feature maps for which the dynamics is learned using batch data.

Universal activation function for machine learning

This article proposes a universal activation function (UAF) that achieves near optimal performance in quantification, classification, and reinforcement learning (RL) problems. For any given problem, the gradient descent algorithms are able to evolve the UAF to a suitable activation function by tuning the UAF's parameters. For the CIFAR-10 classification using the VGG-8 neural network, the UAF converges to the Mish like activation function, which has near optimal performance [Formula: see text] when compared to other activation functions. In the graph convolutional neural network on the CORA dataset, the UAF evolves to the identity function and obtains [Formula: see text]. For the quantification of simulated 9-gas mixtures in 30 dB signal-to-noise ratio (SNR) environments, the UAF converges to the identity function, which has near optimal root mean square error of [Formula: see text]. In the ZINC molecular solubility quantification using graph neural networks, the UAF morphs to a LeakyReLU/Sigmoid hybrid and achieves RMSE=[Formula: see text]. For the BipedalWalker-v2 RL dataset, the UAF achieves the 250 reward in [Formula: see text] epochs with a brand new activation function, which gives the fastest convergence rate among the activation functions.

Fully Automatic Operation Algorithm of Urban Rail Train Based on RBFNN Position Output Constrained Robust Adaptive Control

High parking accuracy, comfort and stability, and fast response speed are important indicators to measure the control performance of a fully automatic operation system. In this paper, aiming at the problem of low accuracy of the fully automatic operation control of urban rail trains, a radial basis function neural network position output-constrained robust adaptive control algorithm based on train operation curve tracking is proposed. Firstly, on the basis of the mechanism of motion mechanics, the nonlinear dynamic model of train motion is established. Then, RBFNN is used to adaptively approximate and compensate for the additional resistance and unknown interference of the train model, and the basic resistance parameter adaptive mechanism is introduced to enhance the anti-interference ability and adaptability of the control system. Lastly, on the basis of the RBFNN position output-constrained robust adaptive control technology, the train can track the desired operation curve, thereby achieving the smooth operation between stations and accurate stopping. The simulation results show that the position output-constrained robust adaptive control algorithm based on RBFNN has good robustness and adaptability. In the case of system parameter uncertainty and external disturbance, the control system can ensure high-precision control and improve the ride comfort.

Globally Exponentially Stable Tracking Control of Self-Restructuring Nonlinear Systems

This article proposes a neural networks (NNs)-based tracking control approach for a class of uncertain high-order self-restructuring nonaffine dynamic systems. Unlike most existing NN-based works that normally ignore the precondition on the functionality and reliability of NN unit and thus can only ensure semiglobal stability, the proposed method explicitly addresses the issue of reliable in-loop operation of NN approximation-based control unit, resulting in a safeguarded NN-based control solution capable of ensuring globally stable tracking. Furthermore, the control method proposed guarantees exponentially globally stable tracking for systems with self-restructuring nonlinearities and uncertainties, distinguishing itself from those that only yield uniformly ultimately bounded (UUB) regulation/tracking results for nonlinear systems with fixed structures. All of these features are achieved by the proposed strategy consisting of two cooperative control units: 1) safeguard control and 2) NN-based control. The role of the safeguard control is to force the states (starting from any initial condition) to enter a stable region, so that the NN-based control can be activated trustworthily and safely. It is such cooperation of the two units that not only ensures the tracking error entering the stable region first within a prespecified finite time but also guarantees the tracking error converging to zero exponentially thereafter, resulting in global zero-error tracking. Both the theoretical analysis and numerical simulation authenticate the effectiveness of the proposed method.

Optimization of Urban Rail Automatic Train Operation System Based on RBF Neural Network Adaptive Terminal Sliding Mode Fault Tolerant Control

Aiming at the problem of the large tracking error of the desired curve for the automatic train operation (ATO) control strategy, an ATO control algorithm based on RBF neural network adaptive terminal sliding mode fault-tolerant control (ATSM-FTC-RBFNN) is proposed to realize the accurate tracking control of train operation curve. On the one hand, considering the state delay of trains in operation, a nonlinear dynamic model is established based on the mechanism of motion mechanics. Then, the terminal sliding mode control principle is used to design the ATO control algorithm, and the adaptive mechanism is introduced to enhance the adaptability of the system. On the other hand, RBFNN is used to adaptively approximate and compensate the additional resistance disturbance to the model so that ATO control with larger disturbance can be realized with smaller switching gain, and the tracking performance and anti-interference ability of the system can be enhanced. Finally, considering the actuator failure and the control input limitation, the fault-tolerant mechanism is introduced to further enhance the fault-tolerant performance of the system. The simulation results show that the control can compensate and process the nonlinear effects of control input saturation, delay, and actuator faults synchronously under the condition of uncertain parameters, external disturbances of the system model and can achieve a small error tracking the desired curve.

HemoNet: Predicting hemolytic activity of peptides with integrated feature learning

Quantifying the hemolytic activity of peptides is a crucial step in the discovery of novel therapeutic peptides. Computational methods are attractive in this domain due to their ability to guide wet-lab experimental discovery or screening of peptides based on their hemolytic activity. However, existing methods are unable to accurately model various important aspects of this predictive problem such as the role of N/C-terminal modifications, D- and L- amino acids, etc. In this work, we have developed a novel neural network-based approach called HemoNet for predicting the hemolytic activity of peptides. The proposed method captures the contextual importance of different amino acids in a given peptide sequence using a specialized feature embedding in conjunction with SMILES-based fingerprint representation of N/C-terminal modifications. We have analyzed the predictive performance of the proposed method using stratified cross-validation in comparison with previous methods, non-redundant cross-validation as well as validation on external peptides and clinical antimicrobial peptides. Our analysis shows the proposed approach achieves significantly better predictive performance (AUC-ROC of 88%) in comparison to previous approaches (HemoPI and HemoPred with AUC-ROC of 73%). HemoNet can be a useful tool in the search for novel therapeutic peptides. The python implementation of the proposed method is available at the URL: https://github.com/adibayaseen/HemoNet.

Neuroadaptive Fault-Tolerant Control Under Multiple Objective Constraints With Applications to Tire Production Systems

Many manufacturing systems not only involve nonlinearities and nonvanishing disturbances but also are subject to actuation failures and multiple yet possibly conflicting objectives, making the underlying control problem interesting and challenging. In this article, we present a neuroadaptive fault-tolerant control solution capable of addressing those factors concurrently. To cope with the multiple objective constraints, we propose a method to accommodate these multiple objectives in such a way that they are all confined in certain range, distinguishing itself from the traditional method that seeks for a common optimum (which might not even exist due to the complicated and conflicting objective requirement) for all the objective functions. By introducing a novel barrier function, we convert the system under multiple constraints into one without constraints, allowing for the nonconstrained control algorithms to be derived accordingly. The system uncertainties and the unknown actuation failures are dealt with by using the deep-rooted information-based method. Furthermore, by utilizing a transformed signal as the initial filter input, we integrate dynamic surface control (DSC) into backstepping design to eliminate the feasibility conditions completely and avoid off-line parameter optimization. It is shown that, with the proposed neuroadaptive control scheme, not only stable system operation is maintained but also each objective function is confined within the prespecified region, which could be asymmetric and time-varying. The effectiveness of the algorithm is validated via simulation on speed regulation of extruding machine in tire production lines.

Neuro-optimized numerical treatment of HIV infection model

In this paper, a neuro-optimized numerical method is presented for approximation of HIV virus progression model in the human body. The model is composed of coupled nonlinear system of differential equations (DEs) containing healthy and infected T-Cells and HIV free virus particles. The coupled system is transformed into feedforward artificial neural network (ANN) with Mexican hat wavelet function in the hidden layers. Two meta-heuristic algorithms based on chaotic particle swarm optimization (CPSO) and its hybrid version with local search technique are exploited to tune the parameters of ANN in an unsupervised manner of error function. A comprehensive testbed is established to observe the virus growth per day with performance metric containing fitness value, computational time complexity and convergence. The proposed solutions are compared with state of art Runge–Kutta method and Legendre Wavelet Collocation Method (LWCM). The core advantages of the proposed scheme are getting the solution on continuous grid, consistent convergence, simplicity in implementation and handling strong nonlinearity effectively.

Intrinsic Plasticity-Based Neuroadptive Control With Both Weights and Excitability Tuning

This brief presents an intrinsic plasticity (IP)-driven neural-network-based tracking control approach for a class of nonlinear uncertain systems. Inspired by the neural plasticity mechanism of individual neuron in nervous systems, a learning rule referred to as IP is employed for adjusting the radial basis functions (RBFs), resulting in a neural network (NN) with both weights and excitability tuning, based on which neuroadaptive tracking control algorithms for multiple-input-multiple-output (MIMO) uncertain systems are derived. Both theoretical analysis and numerical simulation confirm the effectiveness of the proposed method.

An empirical artifact correction for proton computed tomography

PURPOSE

To reduce image artifacts of proton computed tomography (pCT) from a preclinical scanner, for imaging of the relative stopping power (RSP) needed for particle therapy treatment planning using a simple empirical artifact correction method.

METHODS

We adapted and employed a correction method previously used for beam-hardening correction in x-ray CT which makes use of a single scan of a custom-built homogeneous phantom with known RSP. Exploiting the linearity of the filtered backprojection operation, a function was found which corrects water-equivalent path lengths (RSP line integrals) in experimental scans using a prototype pCT scanner. The correction function was applied to projection values of subsequent scans of a homogeneous water phantom, a sensitometric phantom with various inserts and an anthropomorphic head phantom. Data were acquired at two different incident proton energies to test the robustness of the method.

RESULTS

Inaccuracies in the detection process caused an offset and known ring artifacts in the water phantom which were considerably reduced using the proposed method. The mean absolute percentage error (MAPE) of mean RSP values of all inserts of the sensitometric phantom and the water phantom was reduced from 0.87% to 0.44% and from 0.86% to 0.48% for the two incident energies respectively. In the head phantom a clear reduction of artifacts was observed.

CONCLUSIONS

Image artifacts of experimental pCT scans with a prototype scanner could substantially be reduced both in homogeneous, heterogeneous and anthropomorphic phantoms. RSP accuracy was also improved.

Symplectic Gaussian process regression of maps in Hamiltonian systems

We present an approach to construct structure-preserving emulators for Hamiltonian flow maps and Poincaré maps based directly on orbit data. Intended applications are in moderate-dimensional systems, in particular, long-term tracing of fast charged particles in accelerators and magnetic plasma confinement configurations. The method is based on multi-output Gaussian process (GP) regression on scattered training data. To obtain long-term stability, the symplectic property is enforced via the choice of the matrix-valued covariance function. Based on earlier work on spline interpolation, we observe derivatives of the generating function of a canonical transformation. A product kernel produces an accurate implicit method, whereas a sum kernel results in a fast explicit method from this approach. Both are related to symplectic Euler methods in terms of numerical integration but fulfill a complementary purpose. The developed methods are first tested on the pendulum and the Hénon-Heiles system and results compared to spectral regression of the flow map with orthogonal polynomials. Chaotic behavior is studied on the standard map. Finally, the application to magnetic field line tracing in a perturbed tokamak configuration is demonstrated. As an additional feature, in the limit of small mapping times, the Hamiltonian function can be identified with a part of the generating function and thereby learned from observed time-series data of the system's evolution. For implicit GP methods, we demonstrate regression performance comparable to spectral bases and artificial neural networks for symplectic flow maps, applicability to Poincaré maps, and correct representation of chaotic diffusion as well as a substantial increase in performance for learning the Hamiltonian function compared to existing approaches.

A Survey on Distributed Fibre Optic Sensor Data Modelling Techniques and Machine Learning Algorithms for Multiphase Fluid Flow Estimation

Real-time monitoring of multiphase fluid flows with distributed fibre optic sensing has the potential to play a major role in industrial flow measurement applications. One such application is the optimization of hydrocarbon production to maximize short-term income, and prolong the operational lifetime of production wells and the reservoir. While the measurement technology itself is well understood and developed, a key remaining challenge is the establishment of robust data analysis tools that are capable of providing real-time conversion of enormous data quantities into actionable process indicators. This paper provides a comprehensive technical review of the data analysis techniques for distributed fibre optic technologies, with a particular focus on characterizing fluid flow in pipes. The review encompasses classical methods, such as the speed of sound estimation and Joule-Thomson coefficient, as well as their data-driven machine learning counterparts, such as Convolutional Neural Network (CNN), Support Vector Machine (SVM), and Ensemble Kalman Filter (EnKF) algorithms. The study aims to help end-users establish reliable, robust, and accurate solutions that can be deployed in a timely and effective way, and pave the wave for future developments in the field.