This article discusses the modeling of liquid flow inside nanotube membranes. Applying known simplifications to the classical fluid model leads to the so-called Hagen–Poiseuille equation, which ...predicts no flow for diameters up to 1 nm, and very modest flows in nanochannels up to 100 nm. The main feature of classical fluid dynamics that negates the possibility of high flow is the assumption that fluid molecules closest to the channel wall stick to it, the no-slip boundary condition. In the past 10 years, a wealth of experimental evidence has, on the contrary, demonstrated significant water flow in nanotubes with diameters equal to or smaller than 1 nm, opening the possibility of nanotube membranes capable of high flows and fine separation. These high flows have also been observed in molecular dynamics simulations, particularly for water flowing through carbon nanotubes, showing the presence of strong water slip near the walls of the nanotubes. The term “flow enhancement” has been introduced to refer to the ratio of predicted (or measured) flows and the no-slip Hagen–Poiseuille equation. Both experimental and modeling results point to a strong effect on flow enhancement of the interaction between the fluid and the tube’s wall, particularly the wall surface chemistry and structure.
We address a new numerical method based on machine learning and in particular based on the concept of the so-called Extreme Learning Machines, to approximate the solution of linear elliptic partial ...differential equations with collocation. We show that a feedforward neural network with a single hidden layer and sigmoidal transfer functions and fixed, random, internal weights and biases can be used to compute accurately enough a collocated solution for such problems. We discuss how one can set the range of values for both the weights between the input and hidden layer and the biases of the hidden layer in order to obtain a good underlying approximating subspace, and we explore the required number of collocation points. We demonstrate the efficiency of the proposed method with several one-dimensional diffusion–advection–reaction benchmark problems that exhibit steep behaviors, such as boundary layers. We point out that there is no need of iterative training of the network, as the proposed numerical approach results to a linear problem that can be easily solved using least-squares and regularization. Numerical results show that the proposed machine learning method achieves a good numerical accuracy, outperforming central Finite Differences, thus bypassing the time-consuming training phase of other machine learning approaches.
•Collocation with Extreme Machine Learning networks for elliptic pdes is considered.•The proposed approach does not require the training of the network.•The underlying space is constructed by fixing the internal weights and biases.•The proposed method is tested on benchmark problems, also with steep gradients.•The proposed method is efficient and significantly reduces the computational costs.
Experimental and simulation measurements of water flow through carbon nanotubes have shown orders of magnitude higher flow rates than what was predicted using continuum fluid mechanics models. ...Different explanations have been offered, from slippage of water on the hydrophobic surface of the nanotubes to size confinement effects. In this work a model capable of explaining these observations, linking the enhanced flow rates observed to the solid–liquid molecular interactions at the nanotube wall is proposed. The model is capable of separating the effects on flow enhancement of the tube characteristic dimensions and the solid–liquid molecular interactions, accurately predicting the effect of each component for nanotubes of different sizes, wall surface chemistry and structure. Comparison with the experimental data available shows good agreement.
We address a new numerical method based on a class of machine learning methods, the so-called Extreme Learning Machines (ELM) with both sigmoidal and radial-basis functions, for the computation of ...steady-state solutions and the construction of (one-dimensional) bifurcation diagrams of nonlinear partial differential equations (PDEs). For our illustrations, we considered two benchmark problems, namely (a) the one-dimensional viscous Burgers with both homogeneous (Dirichlet) and non-homogeneous boundary conditions, and, (b) the one- and two-dimensional Liouville–Bratu–Gelfand PDEs with homogeneous Dirichlet boundary conditions. For the one-dimensional Burgers and Bratu PDEs, exact analytical solutions are available and used for comparison purposes against the numerical derived solutions. Furthermore, the numerical efficiency (in terms of numerical accuracy, size of the grid and execution times) of the proposed numerical machine-learning method is compared against central finite differences (FD) and Galerkin weighted-residuals finite-element (FEM) methods. We show that the proposed numerical machine learning method outperforms in terms of numerical accuracy both FD and FEM methods for medium to large sized grids, while provides equivalent results with the FEM for low to medium sized grids; both methods (ELM and FEM) outperform the FD scheme. Furthermore, the computational times required with the proposed machine learning scheme were comparable and in particular slightly smaller than the ones required with FEM.
Neural Networks (NN) are a powerful tool in approximation theory because of the existence of Universal Approximation (UA) results. In the last decades, a significant attention has been given to ...Extreme Learning Machines (ELMs), typically employed for the training of single layer NNs, and for which a UA result can also be proven. In a generic NN, the design of the optimal approximator can be recast as a non-convex optimization problem that turns out to be particularly demanding from the computational viewpoint. However, under the adoption of ELM, the optimization task reduces to a – possibly rectangular – linear problem. In this work, we detail how to design a sequence of ELM networks trained via a target dataset. Different convergence procedures are proposed and tested for some reference datasets constructed to be equivalent to approximation problems.
•We study the concept of convergence of NN trained via ELM for interpolation.•The concepts of increasing approximation capabilities -new neurons/data- are unified.•The convergence rate is tested on standard test problems of interpolation theory.•The matrix formulation of the training processes in all different cases is detailed.
Potential Celiac Patients (PCD) bear the Celiac Disease (CD) genetic predisposition, a significant production of antihuman transglutaminase antibodies, but no morphological changes in the small bowel ...mucosa. A minority of patients (17%) showed clinical symptoms and need a gluten free diet at time of diagnosis, while the majority progress over several years (up to a decade) without any clinical problem neither a progression of the small intestine mucosal damage even when they continued to assume gluten in their diet. Recently we developed a traditional multivariate approach to predict the natural history, on the base of the information at enrolment (time 0) by a discriminant analysis model. Still, the traditional multivariate model requires stringent assumptions that may not be answered in the clinical setting. Starting from a follow-up dataset available for PCD, we propose the application of Machine Learning (ML) methodologies to extend the analysis on available clinical data and to detect most influent features predicting the outcome. These features, collected at time of diagnosis, should be capable to classify patients who will develop duodenal atrophy from those who will remain potential. Four ML methods were adopted to select features predictive of the outcome; the feature selection procedure was indeed capable to reduce the number of overall features from 85 to 19. ML methodologies (Random Forests, Extremely Randomized Trees, and Boosted Trees, Logistic Regression) were adopted, obtaining high values of accuracy: all report an accuracy above 75%. The specificity score was always more than 75% also, with two of the considered methods over 98%, while the best performance of sensitivity was 60%. The best model, optimized Boosted Trees, was able to classify PCD starting from the selected 19 features with an accuracy of 0.80, sensitivity of 0.58 and specificity of 0.84. Finally, with this work, we are able to categorize PCD patients that can more likely develop overt CD using ML. ML techniques appear to be an innovative approach to predict the outcome of PCD, since they provide a step forward in the direction of precision medicine aimed to customize healthcare, medical therapies, decisions, and practices tailoring the clinical management of PCD children.
In the context of integrated projects aimed at enhancing historical centres, one of the most important aspects is the re-use of unused public buildings. The effectiveness of the decision-making ...process that leads to the identification of preferable, feasible and sustainable solutions can be improved with the support of evaluation tools, of a monetary or qualitative type. This paper illustrates an experimental model of "Project of economic feasibility for the exploitation of unused public buildings" called SOSTEC; this model can be used when the public decision maker intends to verify whether the economic conditions exist for the use of forms of private public partnership to create and/or manage a work. The contribution, after the general illustration of the model, focuses on the ways in which the economic-estimative aspects of the feasibility of the enhancement projects are dealt with and resolved through the use of a monetary technique, the Cash Flow Analysis. La programmazione integrata per la valorizzazione dei centri storici minori. Il Modello SOSTEC per la verifica della fattibilità economica per la valorizzazione degli immobili pubblici inutilizzati Nell’ambito dei progetti integrati finalizzati alla valorizzazione dei centri storici, uno degli aspetti di particolare rilevanza è costituito dal riuso degli immobili pubblici inutilizzati. L’efficacia del processo decisionale che porta all’individuazione delle soluzioni preferibili, fattibili e sostenibili può essere migliorata con il supporto di strumenti valutativi, di tipo monetario o di tipo qualitativo. Il presente contributo illustra un modello sperimentale di “Progetto di fattibilità economica per la valorizzazione degli immobili pubblici inutilizzati” denominato SOSTEC, utilizzabile quando il decisore pubblico intenda verificare se sussistono le condizioni economiche per il ricorso a forme di partenariato pubblico privato per la realizzazione e/o gestione di un’opera. Il contributo, dopo l’illustrazione generale del modello, si sofferma sulle modalità con le quali sono affrontati e risolti gli aspetti economico-estimativi della fattibilità dei progetti di valorizzazione attraverso l’utilizzo di una tecnica di tipo monetario, la Cash Flow Analysis.
New Metropolitan Perspectives Bevilacqua, Carmelina; Calabrò, Francesco; Della Spina, Lucia
2020, 2020-07-24, Letnik:
177
eBook
?This open access book presents the outcomes of the symposium "NEW METROPOLITAN PERSPECTIVES," held at Mediterranea University, Reggio Calabria, Italy on May 26-28, 2020. Addressing the challenge of ...Knowledge Dynamics and Innovation-driven Policies Towards Urban and Regional Transition, the book presents a multi-disciplinary debate on the new frontiers of strategic and spatial planning, economic programs and decision support tools in connection with urban-rural area networks and metropolitan centers. The respective papers focus on six major tracks: Innovation dynamics, smart cities and ICT; Urban regeneration, community-led practices and PPP; Local development, inland and urban areas in territorial cohesion strategies; Mobility, accessibility and infrastructures; Heritage, landscape and identity;and Risk management,environment and energy. The book also includes a Special Section on Rhegion United Nations 2020-2030. Given its scope, the book will benefit all researchers, practitioners and policymakers interested in issues concerning metropolitan and marginal areas.
In this work, four different methods based on Physics-Informed Neural Networks (PINNs) for solving Differential Equations (DE) are compared: Classic-PINN that makes use of Deep Neural Networks (DNNs) ...to approximate the DE solution;Deep-TFC improves the efficiency of classic-PINN by employing the constrained expression from the Theory of Functional Connections (TFC) so to analytically satisfy the DE constraints;PIELM that improves the accuracy of classic-PINN by employing a single-layer NN trained via Extreme Learning Machine (ELM) algorithm;X-TFC, which makes use of both constrained expression and ELM. The last has been recently introduced to solve challenging problems affected by discontinuity, learning solutions in cases where the other three methods fail. The four methods are compared by solving the boundary value problem arising from the 1D Steady-State Advection–Diffusion Equation for different values of the diffusion coefficient. The solutions of the DEs exhibit steep gradients as the value of the diffusion coefficient decreases, increasing the challenge of the problem.
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