1,721,013 research outputs found
Asymptotic-Preserving Neural Networks for inverse and forward problems in multiscale epidemic dynamics
No full textThe aim of this talk is to present some recent results in the mathematical modeling of epidemic phenomena through the use of kinetic equations and their numerical solution using physics-informed machine learning techniques.
To account for aspects of spatial heterogeneity, the spatial spread of an infectious disease can be described by means of a class of multiscale systems of partial differential equations, in which a part of the population acting on an urban scale is characterized by parabolic diffusive behavior and the rest, acting on an extra-urban scale, follows a hyperbolic transport mechanism. However, the model parameters required to simulate the predictive dynamics of the propagation of the virus of interest entail a delicate calibration phase, often made even more challenging by the scarcity and uncertainty of data from official sources. Moreover, the initial and boundary conditions of the problem are always difficult to determine.
In this context, Asymptotic-Preserving Neural Networks (APNNs) for hyperbolic transport models of epidemic spread were designed to solve the inverse problem (of estimating model parameters) and the forward problem (of predicting epidemic evolution) even in the face of sparse and incomplete observed data, and without losing the ability to describe the multiscale dynamics of the phenomenon, thanks to an appropriate AP formulation of the physics-informed neural network loss function.
A series of numerical tests performed considering different epidemic scenarios confirms the validity of the proposed approach, highlighting the importance of the AP property of the neural network for the study of multiscale systems, especially when partially observed
Solving multiscale problems with neural networks: the importance of asymptotic-preservation
No full textData-driven approaches have begun to gain popularity throughout science, leading to
a fundamental change in the scientific method as a result of the rapid advancement of
Machine Learning techniques and the enormous increase in the availability of scientific data. However, the use of conventional Deep Neural Networks (DNNs) or even conventional Physics-Informed Neural Networks (PINNs) to analyse the dynamics of complex multiscale systems can lead to incorrect inferences and predictions. This is due to the presence of small scales leading to simplified or reduced models in the system that must be satisfied during the learning process. In this talk, these problems will be addressed in light of recent results obtained in the development of Asymptotic-Preserving Neural Networks (APNNs) for hyperbolic models with diffusive scaling. A series of numerical tests will demonstrate how APNNs significantly outperform traditional DNNs and PINNs at various model scales, particularly when examining cases where only sparse information is available
Multiscale kinetic transport models for the spread of epidemics with uncertain data
No full textMost epidemiological models are rooted in the pioneering work proposed by Kermack and McKendrick and are based on systems of deterministic ODEs, which describe the temporal evolution of the spread of an infectious disease assuming population and territorial homogeneity. Generally, the concept of the average behavior of a population is sufficient to have a first reliable description of an epidemic development, but the inclusion of the spatial component becomes crucial when it is necessary to consider spatially heterogeneous interventions, as in the case of the COVID-19 pandemic. Moreover, any realistic data-driven model must take into account the large uncertainty in the values reported by official sources such as the amount of infectious individuals. In this work, drawing inspiration from kinetic theory, recent advances on the development of stochastic multiscale kinetic transport models for the spread of epidemics under uncertain data are presented. The propagation of the infectious disease is described by the spatial movement and interactions of individuals divided into commuters moving in the territory on a wide scale and non-commuters acting only on urban scales. The resulting models are solved numerically through a suitable stochastic Asymptotic-Preserving IMEX Runge-Kutta Finite Volume Collocation Method, which ensures a consistent treatment of the system of equations, without loss of accuracy when entering in the stiff, diffusive regime. Application studies concerning the spread of the COVID-19 pandemic in Italy assess the validity of the proposed methodology
Asymptotic-Preserving Neural Networks for hyperbolic systems with diffusive scaling
Get PDFWith the rapid advance of Machine Learning techniques and the deep increase
of availability of scientific data, data-driven approaches have started to
become progressively popular across science, causing a fundamental shift in the
scientific method after proving to be powerful tools with a direct impact in
many areas of society. Nevertheless, when attempting to analyze dynamics of
complex multiscale systems, the usage of standard Deep Neural Networks (DNNs)
and even standard Physics-Informed Neural Networks (PINNs) may lead to
incorrect inferences and predictions, due to the presence of small scales
leading to reduced or simplified models in the system that have to be applied
consistently during the learning process. In this Chapter, we will address
these issues in light of recent results obtained in the development of
Asymptotic-Preserving Neural Networks (APNNs) for hyperbolic models with
diffusive scaling. Several numerical tests show how APNNs provide considerably
better results with respect to the different scales of the problem when
compared with standard DNNs and PINNs, especially when analyzing scenarios in
which only little and scattered information is available.Comment: arXiv admin note: text overlap with arXiv:2206.1262
Hyperbolic compartmental models for epidemic spread on networks with uncertain data: Application to the emergence of COVID-19 in Italy
No full textThe importance of spatial networks in the spread of an epidemic is an essential aspect in modeling the dynamics of an infectious disease. Additionally, any realistic data-driven model must take into account the large uncertainty in the values reported by official sources such as the amount of infectious individuals. In this paper, we address the above aspects through a hyperbolic compartmental model on networks, in which nodes identify locations of interest such as cities or regions, and arcs represent the ensemble of main mobility paths. The model describes the spatial movement and interactions of a population partitioned, from an epidemiological point of view, on the basis of an extended compartmental structure and divided into commuters, moving on a suburban scale, and non-commuters, acting on an urban scale. Through a diffusive rescaling, the model allows us to recover classical diffusion equations related to commuting dynamics. The numerical solution of the resulting multiscale hyperbolic system with uncertainty is then tackled using a stochastic collocation approach in combination with a finite volume Implicit-Explicit (IMEX) method. The ability of the model to correctly describe the spatial heterogeneity underlying the spread of an epidemic in a realistic city network is confirmed with a study of the outbreak of COVID-19 in Italy and its spread in the Lombardy Region
1D augmented fluid-structure interaction systems with viscoelasticity: from water pipelines to blood vessels
No full textNowadays, mathematical models and numerical simulations are widely used in the whole fluid dynamics research field. They represent a powerful resource to better understand phenomena and processes and to significantly reduce the costs that would otherwise be necessary for carrying out laboratory experiments (sometimes even allowing to obtain useful data that could not be collected by measurements).
Currently there are many important industries of hydraulic systems which, for the correct analysis of the behavior of the designed systems, require the preventive use of an accurate mathematical model, able to describe the trend of the properties of the fluid in the pipelines. On the other hand, the availability of robust and efficient mathematical instruments, together with the engineering know-how in the fluid mechanics sector, represents an invaluable tool for a consistent support even in hemodynamics studies, providing practical approaches for the quantification of variables involved in the cardiovascular fluid dynamics.
The correct characterization of the interactions occurring between the fluid and the wall that circumscribes the motion of the fluid itself, is a fundamental aspect in all the contexts involving deformable ducts, which requires the utmost attention at every stage of both the development of the computational scheme and the interpretation of the results and at their application to cases of practical interest.
In this PhD Thesis, innovative mathematical models able to predict the behavior of the fluid-structure interaction mechanism that underlies the dynamics of flows in different compliant ducts is presented. Starting from the purely civil engineering sector, with the study of plastic water pipelines, the final application of the proposed tool is linked to the medical research field, to reproduce the mechanics of blood flow in both arteries and veins. With this aim, various linear viscoelastic models, from the simplest to the more sophisticated, have been applied and extended to obtain augmented fluid-structure interaction systems in which the constitutive equation of the material is directly inserted into the system as partial differential equation. These systems are solved recurring to second-order Finite Volume Methods that take into account the recent evolution in the computational literature of hyperbolic balance laws systems. The models have been extensively validated through different types of test cases, highlighting the advantages of using the augmented formulation of the system of equations. Numerical results have been compared with quasi-exact solutions of idealized time-dependent tests for situations close to reality or with reference values obtained with numerical schemes generally adopted in the specific research field investigated. Furthermore, comparisons with experimental data have been considered both for the water pipelines scenario and the blood flow modeling, recurring to ad hoc in-vivo measurements for the latter. Accuracy and efficiency analyses have been performed in different contexts, as well as a sensitivity analysis with regards to the final part of the project, related to a more applicative study on arterial hypertension.Oggigiorno, modelli matematici e simulazioni numeriche sono ampiamente utilizzati nell’intero campo della ricerca fluidodinamica. Essi rappresentano una potente risorsa per comprendere meglio i fenomeni e i processi e per ridurre significativamente i costi che sarebbero altrimenti necessari per la realizzazione di esperimenti di laboratorio (a volte anche per ottenere utili dati che non potrebbero essere raccolti mediante misurazioni).
Attualmente esistono molte importanti industrie di sistemi idraulici che, per la corretta analisi del comportamento dei sistemi progettati, richiedono l’uso preventivo di un accurato modello matematico, in grado di descrivere l’andamento delle proprietà del fluido nelle tubazioni. D’altra parte, la disponibilità di strumenti matematici robusti ed efficienti, insieme al know-how ingegneristico nel settore della fluidodinamica, rappresenta uno strumento inestimabile per un supporto costante anche negli studi emodinamici,
fornendo approcci pratici per la quantificazione delle variabili coinvolte nella fluidodinamica cardiovascolare.
La corretta caratterizzazione delle interazioni tra il fluido e la parete che ne circoscrive il moto, è un aspetto fondamentale in tutti i contesti di condotte deformabili, che richiede la massima attenzione in ogni fase dello sviluppo dello schema di calcolo e della interpretazione dei risultati e nella loro applicazione a casi di interesse pratico.
In questa Tesi di Dottorato vengono presentati innovativi modelli matematici in grado di prevedere il comportamento del meccanismo di interazione fluido-struttura che sta alla base della dinamica dei flussi in diverse condotte deformabili. Partendo dal settore dell’ingegneria puramente civile, con lo studio di condotte idrauliche in plastica, l’applicazione finale dello strumento proposto è legata al campo della ricerca medica, per riprodurre la meccanica del flusso sanguigno sia nelle arterie che nelle vene. A tal fine, sono stati applicati ed estesi diversi modelli viscoelastici lineari, dai più semplici ai più sofisticati, per ottenere sistemi aumentati di interazione fluido-struttura in cui l’equazione costitutiva del materiale è direttamente inserita nel sistema come equazione alle derivate parziali. Questi sistemi sono risolti ricorrendo a Metodi ai Volumi Finiti al secondo ordine che tengono conto della recente evoluzione della letteratura computazionale dei sistemi iperbolici di leggi di bilancio. I modelli sono stati ampiamente validati attraverso diversi tipi di casi test, evidenziando i vantaggi dell’utilizzo del sistema di equazioni in forma aumentata. I risultati numerici sono stati confrontati con soluzioni quasi esatte di problemi ideali dipendenti dal tempo per situazioni vicine alla realtà o con valori di riferimento ottenuti con schemi numerici adottati solitamente nello specifico campo di ricerca indagato. Inoltre, sono stati presi in considerazione confronti con dati sperimentali sia per lo scenario delle condotte idriche che per la modellazione del flusso sanguigno, ricorrendo a misurazioni in-vivo ad hoc per quest’ultimo. Sono state effettuate analisi di accuratezza ed efficienza in diversi contesti, nonché un’analisi di sensitività per quanto riguarda la parte finale del progetto, relativa ad uno studio più applicativo sull’ipertensione arteriosa
Computational blood flow modeling: A multiscale constitutive framework
No full textThis study presents and discusses a multiscale constitutive framework for 1D blood flow modeling. By analyzing the proposed model’s asymptotic limits, it is demonstrated that different blood propagation phenomena can be described by selecting scaling parameters appropriately, which are connected to various
characterizations of the fluid-structure interaction mechanism that exists between vessel walls and blood flow. The resulting multiscale hyperbolic model is solved using a third-order asymptotic-preserving Implicit-Explicit Runge-Kutta Finite Volume method
Augmented fluid-structure interaction systems for viscoelastic pipelines and blood vessels
Get PDF[EN] In this work, innovative 1D hyperbolic models able to predict the behavior of the
fluid-structure interaction mechanism that underlies the dynamics of flows in different compliant
ducts are presented. Starting from the study of plastic water pipelines, the proposed tool is then
applied to the biomathematical field to reproduce the mechanics of blood flow in both arteries
and veins. With this aim, various different viscoelastic models have been applied and extended
to obtain augmented fluid-structure interaction systems in which the constitutive equation of
the material is directly embedded into the system as partial differential equation. These systems
are solved recurring to Finite Volume Methods that take into account the recent evolution in the
computational literature of hyperbolic balance laws systems. To avoid the loss of accuracy in
the stiff regimes of the proposed systems, asymptotic-preserving Implicit-Explicit Runge-Kutta
schemes are considered for the time discretization, which are able to maintain the consistency
and the accuracy in the diffusive limit, without restrictions due to the scaling parameters.Bertaglia, G. (2022). Augmented fluid-structure interaction systems for viscoelastic pipelines and blood vessels. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 431-438. https://doi.org/10.4995/YIC2021.2021.13450OCS43143
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