arXiv subjects

Marco Ellero

Publications and source records attributed to Marco Ellero.

26 records · Page 2Linked to original sources

arXiv2023

On the Generalization of PINNs outside the training domain and the Hyperparameters influencing it

Physics-Informed Neural Networks (PINNs) are Neural Network architectures trained to emulate solutions of differential equations without the necessity of solution data. They are currently ubiquitous in the scientific literature due to their flexible and promising settings. However, very little of the available research provides practical studies that aim for a better quantitative understanding of such architecture and its functioning. In this paper, we perform an empirical analysis of the behavior of PINN predictions outside their training domain. The primary goal is to investigate the scenarios in which a PINN can provide consistent predictions outside the training area. Thereinafter, we assess whether the algorithmic setup of PINNs can influence their potential for generalization and showcase the respective effect on the prediction. The results obtained in this study returns insightful and at times counterintuitive perspectives which can be highly relevant for architectures which combines PINNs with domain decomposition and/or adaptive training strategies.

cs.LG↗

arXiv2022

Computational modelling of passive transport of functionalized nanoparticles

Functionalized nanoparticles (NPs) are complex objects present in a variety of systems ranging from synthetic grafted nanoparticles to viruses. The morphology and number of the decorating groups can vary widely between systems. Thus, the modelling of functionalized NPs typically considers simplified spherical objects as a first-order approximation. At the nanoscale label, complex hydrodynamic interactions are expected to emerge as the morphological features of the particles change, and they can be further amplified when the NPs are confined or near walls. Direct estimation of these variations can be inferred via diffusion coefficients of the NPs. However, the evaluation of the coefficients requires an improved representation of the NPs morphology to reproduce important features hidden by simplified spherical models. Here, we characterize the passive transport of free and confined functionalized nanoparticles using the Rigid Multi-Blob (RMB) method. The main advantage of RMB is its versatility to approximate the mobility of complex structures at the nanoscale with significant accuracy and reduced computational cost. In particular, we investigate the effect of functional groups distribution, size and morphology over nanoparticle translational and rotational diffusion. We identify that the presence of functional groups significantly affects the rotational diffusion of the nanoparticles, moreover, the morphology of the groups and number induce characteristic mobility reduction compared to non-functionalized nanoparticles. Confined NPs also evidenced important alterations in their diffusivity, with distinctive signatures in the off-diagonal contributions of the rotational diffusion. These results can be exploited in various applications, including biomedical, polymer nanocomposite fabrication, drug delivery, and imaging

cond-mat.mes-hall↗

arXiv2022

Generalized Lagrangian Heterogenous Multiscale Modeling of Complex Fluids

We introduce a full-Lagrangian heterogeneous multiscale method (LHMM) to model complex fluids with microscopic features that can extend over large spatio-temporal scales, such as polymeric solutions and multiphasic systems. The proposed approach discretizes the fluctuating Navier-Stokes equations in a particle-based setting using Smoothed Dissipative Particle Dynamics (SDPD). This multiscale method uses microscopic information derived on-the-fly to provide the stress tensor of the momentum balance in a macroscale problem, therefore bypassing the need for approximate constitutive relations for the stress. We exploit the intrinsic multiscale features of SDPD to account for thermal fluctuations as the characteristic size of the discretizing particles decrease. We validate the LHMM using different flow configurations (reverse Poiseuille flow, flow passing a cylinder array, and flow around a square cavity) and fluid (Newtonian and non-Newtonian). We showed the framework's flexibility to model complex fluids at the microscale using multiphase and polymeric systems. We showed that stresses are adequately captured and passed from micro to macro scales, leading to richer fluid response at the continuum. In general, the proposed methodology provides a natural link between variations at a macroscale, whereas accounting for memory effects of microscales.

physics.flu-dyn↗

arXiv2019

Investigation of dissipative particle dynamics with colored noise

We investigate the behavior of dissipative particle dynamics (DPD) with time-correlated random noise. A new stochastic force for DPD is proposed which consists of a random force whose noise has an algebraic correlation proportional to 1/t and is generated by the so called Kangaroo process. We stress the benefits of a time correlated noise in stochastic systems. We show that the system exhibits significantly different properties from classical DPD, driven by Wiener noise. While the probability distribution function of the velocity is Gaussian, the acceleration develops a bi-modal character. Although the fluctuation dissipation theorem may not strictly hold, we demonstrate that the system reaches equilibrium states with fluctuation-dissipation balance. We believe that our explorative research on the DPD model may stimulate the application of modified DPD to unconventional problems beyond molecular modeling.

cond-mat.stat-mech↗

arXiv2007

Lattice Boltzmann inverse kinetic approach for the incompressible Navier-Stokes equations

In spite of the large number of papers appeared in the past which are devoted to the lattice Boltzmann (LB) methods, basic aspects of the theory still remain unchallenged. An unsolved theoretical issue is related to the construction of a discrete kinetic theory which yields \textit{exactly} the fluid equations, i.e., is non-asymptotic (here denoted as \textit{LB inverse kinetic theory}). The purpose of this paper is theoretical and aims at developing an inverse kinetic approach of this type. In principle infinite solutions exist to this problem but the freedom can be exploited in order to meet important requirements. In particular, the discrete kinetic theory can be defined so that it yields exactly the fluid equation also for arbitrary non-equilibrium (but suitably smooth) kinetic distribution functions and arbitrarily close to the boundary of the fluid domain. Unlike previous entropic LB methods the theorem can be obtained without functional constraints on the class of the initial distribution functions. Possible realizations of the theory and asymptotic approximations are provided which permit to determine the fluid equations \textit{with prescribed accuracy.} As a result, asymptotic accuracy estimates of customary LB approaches and comparisons with the Chorin artificial compressibility method are discussed.

physics.flu-dyn↗

arXiv2006

An exact pressure evolution equation for the incompressible Navier-Stokes equations

In this paper the issue of the determination of the fluid pressure in incompressible fluids is addressed, with particular reference to the search of algorithms which permit to advance in time the fluid pressure without actually solving numerically the Poisson equation. Based on an inverse kinetic approach recently proposed for the incompressible Navier-Stokes equations we intend to prove that an exact evolution equation can be obtained which advances in time self-consistently the fluid pressure. The new equation is susceptible of numerical implementation in Lagrangian CFD simulation codes.

physics.flu-dyn↗

arXiv2006

On the uniqueness of continuous inverse kinetic theory for incompressible fluids

Fundamental aspects of inverse kinetic theories for incompressible Navier-Stokes equations concern the possibility of defining uniquely the kinetic equation underlying such models and furthermore, the construction of a kinetic theory implying also the energy equation. The latter condition is consistent with the requirement that fluid fields result classical solutions of the fluid equations. These issues appear of potential relevance both from the mathematical viewpoint and for the physical interpretation of the theory. In this paper we intend to prove that the non-uniqueness feature can be resolved by imposing suitable assumptions. These include, in particular, the requirement that the kinetic equation be equivalent, in a suitable sense, to a Fokker-Planck kinetic equation. Its Fokker-Planck coefficients are proven to be uniquely determined by means of appropriate prescriptions. In addition, as a further result, it is proven that the inverse kinetic equation satisfies both an entropy principle and the energy equation for the fluid fields.

physics.flu-dyn↗

arXiv2006

Inverse kinetic theory for quantum hydrodynamic equations

We propose a solution for the inverse kinetic theory for quantum hydrodynamic equations associated to the non-relativistic Schrödinger equation. It is shown that an inverse kinetic equation of the form of the Vlasov equation can be non-uniquely determined under suitable mathematical prescriptions.

quant-ph↗