arXiv subjects

Michele Girfoglio

Publications and source records attributed to Michele Girfoglio.

At least 19 recordsLinked to original sources

arXiv2026

An isotropic recovery-based error estimator algorithm for mesh adaptation in a finite volume environment with application to atmospheric flows

We develop an Isotropic Recovery-based Error Estimator (IREE) to drive mesh adaptation within a finite volume framework. Recovery-based error estimators are widely used in practice thanks to their simplicity, relying solely on the available discrete solution and a suitable post-processing step. While recovery-based estimators are well established in the finite element framework, their application to finite volume methods, despite the widespread use of the latter in industrial and commercial codes, remains largely unexplored and motivates the present study. We assess the performance of the proposed IREE-driven mesh adaptation procedure through well-known benchmarks for dry atmospheric flows modeling and compare it against a widely-used plain mesh adaptation algorithm. Both qualitative and quantitative results show that the IREE algorithm is more effective at suppressing numerical instabilities compared with the plain approach and, for most of the simulation time, provides a superior accuracy, though at a moderately higher computational cost. In addition, both the adaptive approaches offer substantial computational savings (between 35% and 94%) relative to simulations based on fixed uniformly fine meshes. These findings demonstrate that IREE-based mesh adaptation is a promising and effective strategy for atmospheric flow simulations and has the potential to substantially reduce the computational effort of generating reanalysis-quality data.

math.NA↗

arXiv2026

A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems

Forecasting the evolution of complex dynamical systems remains a fundamentally challenging task, primarily due to pronounced nonlinear interactions, high-dimensional state spaces, and the concomitant requirement for rigorous and reliable uncertainty quantification. Contemporary reduced-order modelling (ROM) frameworks frequently exhibit inherent trade-offs among predictive accuracy, numerical stability, and interpretability, and thus often fail to achieve an optimal balance among these competing objectives. To address these limitations, we propose a framework for forecasting complex dynamical systems via a kernel autonomous ordinary differential equation approach based on Gaussian Processes and Quadratic Order Model Reduction. Our base method, the Gaussian Process Ordinary Differential Equations model, allows accurate short-term forecasting with uncertainty quantification, and it provably converges to the real autonomous equation in the smooth case. We integrate it with quadratic order reduced-order modelling and sphere projection for learning the latent dynamics efficiently while preserving stability. Numerical experiments demonstrate that our full model outperforms ROM forecasting methods such as Extended Dynamic Mode Decomposition, Bagging Optimised Dynamic Mode Decomposition and Linear and Nonlinear Disambiguation Optimisation in terms of accuracy or computational costs. These results demonstrate the potential of the framework as a robust and stable tool for forecasting complex dynamical systems with rigorous uncertainty quantification.

math.NA↗

arXiv2026

Enhancing the accuracy of under-resolved numerical simulations of atmospheric flows with super resolution

Super-resolution (SR) techniques based on deep learning have recently emerged as a promising approach to enhance the spatial resolution of computational fluid dynamics simulations while containing computational cost. In this paper, we investigate several SR architectures to improve coarse-grid simulations of mesoscale atmospheric flows, with training data generated from simulations of the weakly compressible Euler equations. We compare a baseline convolutional neural network (CNN), an attention-enhanced CNN, a multi-scale CNN designed to capture flow structures across different spatial scales, and a diffusion-based SR model. The methods are evaluated on two standard atmospheric benchmarks: the rising thermal bubble and the density current. Results show that the baseline CNN can accurately reconstruct simpler flow features, while more complex flows require multi-scale architectures. Overall, SR based on the multi-scale CNN provides the best balance of accuracy, robustness, and computational efficiency, outperforming even a state-of-the-art diffusion-based approach. We also analyze the sensitivity of the models to the size of the training dataset, highlighting limitations and trade-offs of the proposed SR strategies.

physics.flu-dyn↗

arXiv2025

On an adjoint-based numerical approach for time-dependent optimal control problems of biomedical interest

This work develops a rigorous numerical framework for solving time-dependent Optimal Control Problems (OCPs) governed by partial differential equations, with a particular focus on biomedical applications. The approach deals with adjoint-based Lagrangian methodology, which enables efficient gradient computation and systematic derivation of optimality conditions for both distributed and concentrated control formulations. The proposed framework is first verified using a time-dependent advection-diffusion problem endowed with a manufactured solution to assess accuracy and convergence properties. Subsequently, two representative applications involving drug delivery are investigated: (i) a light-triggered drug delivery system for targeted cancer therapy and (ii) a catheter-based drug delivery system in a patient-specific coronary artery. Numerical experiments not only demonstrate the accuracy of the approach, but also its flexibility and robustness in handling complex geometries, heterogeneous parameters, and realistic boundary conditions, highlighting its potential for the optimal design and control of complex biomedical systems.

math.OC↗

arXiv2025

A Review of Equation-Based and Data-Driven Reduced Order Models featuring a Hybrid cardiovascular application

Cardiovascular diseases are a leading cause of death in the world, driving the development of patient-specific and benchmark models for blood flow analysis. This chapter provides a theoretical overview of the main categories of Reduced Order Models (ROMs), focusing on both projection-based and data-driven approaches within a classical setup. We then present a hybrid ROM tailored for simulating blood flow in a patient-specific aortic geometry. The proposed methodology integrates projection-based techniques with neural network-enhanced data-driven components, incorporating a lifting function strategy to enforce physiologically realistic outflow pressure conditions. This hybrid methodology enables a substantial reduction in computational cost while mantaining high fidelity in reconstructing both velocity and pressure fields. We compare the full- and reduced-order solutions in details and critically assess the advantages and limitations of ROMs in patient-specific cardiovascular modeling.

math.NA↗

arXiv2025

A Deep-Learning Enhanced Gappy Proper Orthogonal Decomposition Method for Conjugate Heat Transfer Problem

The current study aims to develop a non-intrusive Reduced Order Model (ROM) to reconstruct the full temperature field for a large-scale industrial application based on both numerical and experimental datasets. The proposed approach is validated against a domestic refrigerator. At the full order level, air circulation and heat transfer in fluid and between fluid and surrounding solids in the fridge were numerically studied using the Conjugated Heat Transfer (CHT) method to explore both the natural and forced convection-based fridge model followed by a parametric study-based on the ambient temperature, fridge fan velocity, and evaporator temperature. The main novelty of the current work is the introduction of a stable Artificial Neural Network (ANN) enhanced Gappy Proper Orthogonal Decomposition (GPOD) method which shows better performance than the conventional GPOD approach in such large-scale industrial applications. The full-order model is validated with the experimental results and the prediction accuracy of the surrogate model associated with different reduced-order approaches is compared with the benchmark numerical results or high-fidelity results. In our current work, we show that a prediction error of one degree centigrade and computational speed-up of 5000 is achieved even at a very sparse training dataset using the proposed deep-learning enhanced GPOD approach.

physics.flu-dyn↗

arXiv2025

Projection-based Reduced Order Modelling for Unsteady Parametrized Optimal Control Problems in 3D Cardiovascular Flows

This paper presents a projection-based reduced order modelling (ROM) framework for unsteady parametrized optimal control problems (OCP$_{(μ)}$s) arising from cardiovascular (CV) applications. In real-life scenarios, accurately defining outflow boundary conditions in patient-specific models poses significant challenges due to complex vascular morphologies, physiological conditions, and high computational demands. These challenges make it difficult to compute realistic and reliable CV hemodynamics by incorporating clinical data such as 4D magnetic resonance imaging. To address these challenges, we focus on controlling the outflow boundary conditions to optimize CV flow dynamics and minimize the discrepancy between target and computed flow velocity profiles. The fluid flow is governed by unsteady Navier--Stokes equations with physical parametric dependence, i.e. the Reynolds number. Numerical solutions of OCP$_{(μ)}$s require substantial computational resources, highlighting the need for robust and efficient ROMs to perform real-time and many-query simulations. Here, we aim at investigating the performance of a projection-based reduction technique that relies on the offline-online paradigm, enabling significant computational cost savings. The Galerkin finite element method is used to compute the high-fidelity solutions in the offline phase. We implemented a nested-proper orthogonal decomposition (nested-POD) for fast simulation of OCP$_{(μ)}$s that encompasses two stages: temporal compression for reducing dimensionality in time, followed by parametric-space compression on the precomputed POD modes. We tested the efficacy of the methodology on vascular models, namely an idealized bifurcation geometry and a patient-specific coronary artery bypass graft, incorporating stress control at the outflow boundary, observing consistent speed-up with respect to high-fidelity strategies.

math.NA↗

arXiv2025

Randomized Proper Orthogonal Decomposition for data-driven reduced order modeling of a two-layer quasi-geostrophic ocean model

The two-layer quasi-geostrophic equations (2QGE) serve as a simplified model for simulating wind-driven, stratified ocean flows. However, their numerical simulation remains computationally expensive due to the need for high-resolution meshes to capture a wide range of turbulent scales. This becomes especially problematic when several simulations need to be run because of, e.g., uncertainty in the parameter settings. To address this challenge, we propose a data-driven reduced order model (ROM) for the 2QGE that leverages randomized proper orthogonal decomposition (rPOD) and long short-term memory (LSTM) networks. To efficiently generate the snapshot data required for model construction, we apply a nonlinear filtering stabilization technique that allows for the use of larger mesh sizes compared to a direct numerical simulations (DNS). Thanks to the use of rPOD to extract the dominant modes from the snapshot matrices, we achieve up to 700 times speedup over the use of deterministic POD. LSTM networks are trained with the modal coefficients associated with the snapshots to enable the prediction of the time- and parameter-dependent modal coefficients during the online phase, which is hundreds of thousands of time faster than a DNS. We assess the accuracy and efficiency of our rPOD-LSTM ROM through an extension of a well-known benchmark called double-gyre wind forcing test. The dimension of the parameter space in this test is increased from two to four.

math.NA↗

arXiv2025

Data-driven Optimization for the Evolve-Filter-Relax regularization of convection-dominated flows

Numerical stabilization techniques are often employed in under-resolved simulations of convection-dominated flows to improve accuracy and mitigate spurious oscillations. Specifically, the evolve--filter--relax (EFR) algorithm is a framework which consists in evolving the solution, applying a filtering step to remove high-frequency noise, and relaxing through a convex combination of filtered and original solutions. The stability and accuracy of the EFR solution strongly depend on two parameters, the filter radius $δ$ and the relaxation parameter $χ$. Standard choices for these parameters are usually fixed in time, and related to the full order model setting, i.e., the grid size for $δ$ and the time step for $χ$. The key novelties with respect to the standard EFR approach are: (i) time-dependent parameters $δ(t)$ and $χ(t)$, and (ii) data-driven adaptive optimization of the parameters in time, considering a fully-resolved simulation as reference. In particular, we propose three different classes of optimized-EFR (Opt-EFR) strategies, aiming to optimize one or both parameters. The new Opt-EFR strategies are tested in the under-resolved simulation of a turbulent flow past a cylinder at $Re=1000$. The Opt-EFR proved to be more accurate than standard approaches by up to 99$\%$, while maintaining a similar computational time. In particular, the key new finding of our analysis is that such accuracy can be obtained only if the optimized objective function includes: (i) a global metric (as the kinetic energy), and (ii) spatial gradients' information.

math.NA↗

arXiv2025

Combining Extended Convolutional Autoencoders and Reservoir Computing for Accurate Reduced-Order Predictions of Atmospheric Flows

Forecasting atmospheric flows with traditional discretization methods, also called full order methods (e.g., finite element methods or finite volume methods), is computationally expensive. We propose to reduce the computational cost with a Reduced Order Model (ROM) that combines Extended Convolutional Autoencoders (E-CAE) and Reservoir Computing (RC). Thanks to an extended network depth, the E-CAE encodes the high-resolution data coming from the full order method into a compact latent representation and can decode it back into high-resolution with 75% lower reconstruction error than standard CAEs. The compressed data are fed to an RC network, which predicts their evolution. The advantage of RC networks is a reduced computational cost in the training phase compared to conventional predictive models. We assess our data-driven ROM through well-known 2D and 3D benchmarks for atmospheric flows. We show that our ROM accurately reconstructs and predicts the future system dynamics with errors below 6% in 2D and 8% in 3D, while significantly reducing the computational cost of a full-order simulation. Compared to other ROMs available in the literature, such as Dynamic Mode Decomposition and Proper Orthogonal Decomposition with Interpolation, our ROM is as efficient but more accurate. Thus, it is a promising alternative to high-dimensional atmospheric simulations.

math.NA↗

arXiv2025

On the choice of proper outlet boundary conditions for numerical simulation of cardiovascular flows

It is well known that in the computational fluid dynamics simulations related to the cardiovascular system the enforcement of outflow boundary conditions is a crucial point. In fact, they highly affect the computed flow and a wrong setup could lead to unphysical results. In this chapter we discuss the main features of two different ways for the estimation of proper outlet boundary conditions in the context of hemodynamics simulations: on one side, a lumped parameter model of the downstream circulation and, on the other one, a technique based on optimal control.

physics.flu-dyn↗

arXiv2025

A hybrid Reduced Order Model to enforce outflow pressure boundary conditions in computational haemodynamics

This paper deals with the development of a Reduced-Order Model (ROM) to investigate haemodynamics in cardiovascular applications. It employs the use of Proper Orthogonal Decomposition (POD) for the computation of the basis functions and the Galerkin projection for the computation of the reduced coefficients. The main novelty of this work lies in the extension of the lifting function method, which typically is adopted for treating nonhomogeneous inlet velocity boundary conditions, to the handling of nonhomogeneous outlet boundary conditions for the pressure, representing a very delicate point in the numerical simulations of the cardiovascular system. Moreover, we incorporate a properly trained neural network in the ROM framework to approximate the mapping from the time parameter to the outflow pressure, which in the most general case is not available in closed form. We define our approach as "hybrid", because it merges physics-based elements with data-driven ones. At full order level, a Finite Volume method is employed for the discretization of the unsteady Navier-Stokes equations while a two-element Windkessel model is adopted to enforce a valuable estimation of the outflow pressure. Numerical results, firstly related to a 2D idealized blood vessel and then to a 3D patient-specific aortic arch, demonstrate that our ROM is able to accurately approximate the FOM with a significant reduction in the computational cost.

math.NA↗

arXiv2024

Optimal Transport-Based Displacement Interpolation with Data Augmentation for Reduced Order Modeling of Nonlinear Dynamical Systems

We present a novel reduced-order Model (ROM) that leverages optimal transport (OT) theory and displacement interpolation to enhance the representation of nonlinear dynamics in complex systems. While traditional ROM techniques face challenges in this scenario, especially when data (i.e., observational snapshots) is limited, our method addresses these issues by introducing a data augmentation strategy based on OT principles. The proposed framework generates interpolated solutions tracing geodesic paths in the space of probability distributions, enriching the training dataset for the ROM. A key feature of our approach is its ability to provide a continuous representation of the solution's dynamics by exploiting a virtual-to-real time mapping. This enables the reconstruction of solutions at finer temporal scales than those provided by the original data. To further improve prediction accuracy, we employ Gaussian Process Regression to learn the residual and correct the representation between the interpolated snapshots and the physical solution. We demonstrate the effectiveness of our methodology with atmospheric mesoscale benchmarks characterized by highly nonlinear, advection-dominated dynamics. Our results show improved accuracy and efficiency in predicting complex system behaviors, indicating the potential of this approach for a wide range of applications in computational physics and engineering.

math.NA↗

arXiv2024

On the accuracy and efficiency of reduced order models: towards real-world applications

This chapter provides an extended overview about Reduced Order Models (ROMs), with a focus on their features in terms of efficiency and accuracy. In particular, the aim is to browse the more common ROM frameworks, considering both intrusive and data-driven approaches. We present the validation of such techniques against several test cases. The first one is an academic benchmark, the thermal block problem, where a Poisson equation is considered. Here a classic intrusive ROM framework based on a Galerkin projection scheme is employed. The second and third test cases come from real-world applications, the one related to the investigation of the blood flow patterns in a patient specific coronary arteries configuration where the Navier Stokes equations are addressed and the other one concerning the granulation process within pharmaceutical industry where a fluid-particle system is considered. Here we employ two data-driven ROM approaches showing a very relevant trade-off between accuracy and efficiency. In the last part of the contribution, two novel technological platforms, ARGOS and ATLAS, are presented. They are designed to provide a user-friendly access to data-driven models for real-time predictions for complex biomedical and industrial problems.

math.NA↗

arXiv2024

Data-driven reduced order modeling of a two-layer quasi-geostrophic ocean model

The two-layer quasi-geostrophic equations (2QGE) is a simplified model that describes the dynamics of a stratified, wind-driven ocean in terms of potential vorticity and stream function. Its numerical simulation is plagued by a high computational cost due to the size of the typical computational domain and the need for high resolution to capture the full spectrum of turbulent scales. In this paper, we present a data-driven reduced order model (ROM) for the 2QGE that drastically reduces the computational time to predict ocean dynamics, especially when there are variable physical parameters. The main building blocks of our ROM are: i) proper orthogonal decomposition (POD) and ii) long short-term memory (LSTM) recurrent neural networks. Snapshots data are collected from a high-resolution simulation for part of the time interval of interest and for given parameter values in the case of variable parameters. POD is applied to each field variable to extract the dominant modes and a LSTM model is trained on the modal coefficients associated with the snapshots for each variable. Then, the trained LSTM models predict the modal coefficients for the remaining part of the time interval of interest and for a new parameter value. To illustrate the predictive performance of our POD-LSTM ROM and the corresponding time savings, we consider an extension of the so-called double-gyre wind forcing test. We show that the POD-LSTM ROM is accurate in predicting both time-averaged fields and time-dependent quantities (modal coefficients, enstrophy, and kinetic energy), even when retaining only 10-20\% of the singular value energy of the system. The computational speed up for the prediction is about up to 1E+07 compared to a finite volume based full order method.

math.NA↗

arXiv2024

A brief review of Reduced Order Models using intrusive and non-intrusive techniques

Reduced Order Models (ROMs) have gained a great attention by the scientific community in the last years thanks to their capabilities of significantly reducing the computational cost of the numerical simulations, which is a crucial objective in applications like real time control and shape optimization. This contribution aims to provide a brief overview about such a topic. We discuss both an intrusive framework based on a Galerkin projection technique and non-intrusive approaches, including Physics Informed Neural Networks (PINN), purely Data-Driven Neural Networks (DDNN), Radial Basis Functions (RBF), Dynamic Mode Decomposition (DMD) and Gaussian Process Regression (GPR). We also briefly mention geometrical parametrization and dimensionality reduction methods like Active Subspaces (AS). Then we present some results related to academic test cases as well as a preliminary investigation related to an industrial application.

math.NA↗

arXiv2024

Computational study of numerical flux schemes for mesoscale atmospheric flows in a Finite Volume framework

We develop, and implement in a Finite Volume environment, a density-based approach for the Euler equations written in conservative form using density, momentum, and total energy as variables. Under simplifying assumptions, these equations are used to describe non-hydrostatic atmospheric flow. The well-balancing of the approach is ensured by a local hydrostatic reconstruction updated in runtime during the simulation to keep the numerical error under control. To approximate the solution of the Riemann problem, we consider four methods: Roe-Pike, HLLC, AUSM+-up and HLLC-AUSM. We assess our density-based approach and compare the accuracy of these four approximated Riemann solvers using two two classical benchmarks, namely the smooth rising thermal bubble and the density current.

math.NA↗

arXiv2024

Stabilized POD Reduced Order Models for convection-dominated incompressible flows

We present a comparative computational study of two stabilized Reduced Order Models (ROMs) for the simulation of convection-dominated incompressible flow (Reynolds number of the order of a few thousands). Representative solutions in the parameter space, which includes either time only or time and Reynolds number, are computed with a Finite Volume method and used to generate a reduced basis via Proper Orthogonal Decomposition (POD). Galerkin projection of the Navier-Stokes equations onto the reduced space is used to compute the ROM solution. To ensure computational efficiency, the number of POD modes is truncated and ROM solution accuracy is recovered through two stabilization methods: i) adding a global constant artificial viscosity to the reduced dimensional model, and ii) adding a different value of artificial viscosity for the different POD modes. We test the stabilized ROMs for fluid flow in an idealized medical device consisting of a conical convergent, a narrow throat, and a sudden expansion. Both stabilization methods significantly improve the ROM solution accuracy over a standard (non-stabilized) POD-Galerkin model.

physics.flu-dyn↗