arXiv subjects

Giovanni Stabile

Publications and source records attributed to Giovanni Stabile.

At least 19 recordsLinked to original sources

arXiv2026

A Hybrid Discretize-then-Project Reduced Order Model for Turbulent Flows on Collocated Grids with Data-Driven Closure

This study presents a hybrid reduced-order modeling (ROM) framework for turbulent incompressible flows on collocated finite volume grids. The methodology employs the "discretize-then-project" consistent flux strategy, which ensures mass conservation and pressure-velocity coupling without requiring auxiliary stabilization like boundary control or pressure stabilization techniques. However, because standard Galerkin projection fails to yield physically consistent results for the turbulent viscosity field, a hybrid strategy is adopted: velocity and pressure are resolved via intrusive projection, while the turbulent viscosity is reconstructed using a non-intrusive data-driven closure. We evaluate three neural network architectures, Multilayer Perceptron (MLP), Transformers, and Long Short-Term Memory (LSTM), to model the temporal evolution of the viscosity coefficients. Validated against a 3D Large Eddy Simulation of a lid-driven cavity, the LSTM-based closure demonstrates superior performance in capturing transient dynamics, achieving relative errors of 0.7\% for velocity and 4\% for turbulent viscosity. The resulting framework effectively combines the mathematical rigor of the consistent flux formulation with the adaptability of deep learning for turbulence modeling.

math.NA↗

arXiv2026

An efficient hyper reduced-order model for segregated solvers for geometrical parametrization problems

We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first assembled using finite volume or finite element discretizations and then projected onto low-dimensional spaces using a small set of spatial sampling points, selected through hyper-reduction techniques such as DEIM. This approach removes the dependence of the online computational cost on the full mesh size. The method is assessed on three benchmark problems: a linear transport equation, a nonlinear Burgers equation, and the incompressible Navier--Stokes equations. The results show that the hyper-reduced models closely match full-order solutions while achieving substantial reductions in computational time. Since only a sparse subset of mesh cells is evaluated during the online phase, the method is naturally parallelizable and scalable to very large meshes. These findings demonstrate that hyper-reduction can be effectively combined with segregated solvers and geometric parametrization to enable fast and accurate CFD simulations.

math.NA↗

arXiv2026

Data-driven reduced order model for residence time distribution analysis of an industrial-scale continuous casting tundish

The continuous casting tundish plays a critical role as a metallurgical reactor in the continuous casting process, with its flow characteristics serving as a key parameter in the production of high-quality steel. These characteristics are typically assessed through residence time distribution (RTD) curves. This study examines the flow behaviour in a single-strand continuous casting tundish through a combination of numerical simulations and experimental validation. Steady-state full order model (FOM) simulations are performed under both isothermal and non-isothermal conditions to evaluate the influence of thermal buoyancy on the velocity field, which is found to be negligible. The resulting flow fields are used to initialize transient tracer transport simulations for determining the RTD and flow volume partitioning. Subsequently, a data-driven reduced order model (ROM) is developed to predict the RTD response. Comparison of RTD curves obtained from experiments, FOM, and ROM shows excellent agreement, with the ROM accurately capturing the key flow characteristics at a fraction of the computational cost. These results highlight the potential of ROM techniques for efficient real-time analysis, design, and optimization of tundish operations in metallurgical processes.

physics.flu-dyn↗

arXiv2025

ROM for Viscous, Incompressible Flow in Polygons -- exponential $n$-width bounds and convergence rate

We demonstrate exponential convergence of Reduced Order Model (ROM) approximations for mixed boundary value problems of the stationary, incompressible Navier-Stokes equations in plane, polygonal domains $\Omega$. Admissible boundary conditions comprise mixed BCs, no-slip, slip and open boundary conditions, subject to corner-weighted analytic boundary data and volume forcing. The small data hypothesis is assumed to ensure existence of a unique weak solution in the sense of Leray-Hopf. Recent results on corner-weighted, analytic regularity of velocity and pressure fields in $\Omega$, imply exponential convergence rates of so-called mixed $hp$-Finite Element Methods in $H^1(\Omega)^2\times L^2(\Omega)$ on sequences of geometric partitions of $\Omega$, with corner-refinement. Based on these exponential convergence rate bounds, we infer exponential bounds for the Kolmogorov $n$-widths of solution sets for analytic forcing and boundary data. This implies corresponding exponential convergence rates of POD Galerkin methods that are based on truth solutions which are obtained offline from low-order, divergence stable mixed Finite Element discretizations. Numerical experiments confirm the exponential rates and the theoretical results.

math.NA↗

arXiv2025

Reservoir computing based predictive reduced order model for steel grade intermixing in an industrial continuous casting tundish

Continuous casting is a widely adopted process in the steel industry, where maintaining high steel quality is paramount. Efficient prediction of grade intermixing during ladle changeover operations is critical for maintaining steel quality and minimizing material losses in the continuous casting process. Among various factors influencing grade intermixing, operating parameters play a significant role, in addition to tundish geometry and flow control devices. In this study, three-dimensional, transient, two-phase turbulent flow simulations are conducted to investigate the ladle changeover operation. During this process, the molten steel level in the tundish typically varies over time, significantly affecting the grade intermixing phenomena. The influence of ladle change time on intermixing time has been presented. However, high-fidelity full-order simulations of such complex transient phenomena are computationally expensive and are impractical for real-time monitoring or design-space exploration in industrial-scale applications. To address this issue, a reduced order modelling approach based on proper orthogonal decomposition (POD) and reservoir computing (RC) is employed to efficiently predict intermixing time. The proposed reduced order model (ROM) demonstrates excellent predictive accuracy using limited training data while requiring significantly less computational resources and training time. The results demonstrate the potential of the proposed methodology as a fast, reliable tool for real-time process monitoring and optimization in industrial continuous casting operations.

physics.flu-dyn↗

arXiv2025

Coupling Physics Informed Neural Networks with External Solvers

The current work aims to incorporate physics-based loss in Physics Informed Neural Network (PINN) directly using the numerical residual obtained from the governing equation in any dicretized forward solver. PINN's major difficulties in coupling with external forward solvers arise from the inability to access the discretized form (Finite difference, finite volume, finite element, etc.) of the governing equation directly through the network and to include them in its computational graph. This poses a significant challenge to conventional automatic-differentiation-based derivative computation of physics-based loss terms concerning the neural network hyperparameters if gradient-based optimization techniques are adopted. Therefore, we propose modifying the physics-based loss term to account for the residual arising from the external solver and to compute the derivative required for the optimization machinery. The proposed methodologies are demonstrated on benchmark full-order and reduced-order systems.

math.NA↗

arXiv2025

Projection-based model order reduction for residence time distribution analysis of an industrial-scale continuous casting tundish

The flow behavior in the continuous casting tundish plays a critical role in steel quality and is typically characterized via residence time distribution (RTD) curves. This study investigates the fluid flow behaviour in a single-strand tundish using numerical and experimental approaches. Full-order model (FOM) steady-state simulations were conducted under both isothermal and non-isothermal conditions to assess the influence of thermal buoyancy on the flow characteristics. The results show that buoyancy effects under non-isothermal conditions have a negligible impact on the overall velocity field. The converged flow fields serve as initial conditions for transient tracer transport simulations, enabling evaluation of RTD curves and volume partitioning. A Galerkin projection-based reduced-order model (ROM) is developed to efficiently derive RTD curves. Comparison of RTD curves from experiments, FOM simulations, and ROM predictions demonstrates strong agreement, with both computational approaches closely matching experimental data. A parameter-time dependent ROM is subsequently developed using Galerkin projection and operator interpolation. This enables efficient evaluation of RTD curves across varying parameter values with significantly reduced computational cost compared to full-order simulations. The ROM framework is well-suited for real-time analysis, design processes, optimization, and digital twin applications in metallurgical processes.

physics.flu-dyn↗

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

Building an Accelerated OpenFOAM Proof-of-Concept Application using Modern C++

The modern trend in High-Performance Computing (HPC) involves the use of accelerators such as Graphics Processing Units (GPUs) alongside Central Processing Units (CPUs) to speed up numerical operations in various applications. Leading manufacturers such as NVIDIA, Intel, and AMD are constantly advancing these architectures, augmenting them with features such as mixed precision, enhanced memory hierarchies, and specialised accelerator silicon blocks (e.g., Tensor Cores on GPU or AMX/SME engines on CPU) to enhance compute performance. At the same time, significant efforts in software development are aimed at optimizing the use of these innovations, seeking to improve usability and accessibility. This work contributes to the state-of-the-art of OpenFOAM development by presenting a working Proof-Of-Concept application built using modern ISO C++ parallel constructs. This approach, combined with an appropriate compiler runtime stack, like the one provided by the NVIDIA HPC SDK, makes it possible to accelerate well-defined kernels, allowing multi-core execution and GPU offloading using a single codebase. The study demonstrates that it is possible to increase the performance of the OpenFOAM laplacianFoam application by offloading the computations on NVIDIA GPUs using the C++ parallel construct.

cs.MS↗

arXiv2025

A new data-driven energy-stable Evolve-Filter-Relax model for turbulent flow simulation

We present a novel approach to define the filter and relax steps in the evolve-filter-relax (EFR) framework for simulating turbulent flows. The EFR main advantages are its ease of implementation and computational efficiency. However, as it only contains two parameters (one for the filter step and one for the relax step) its flexibility is rather limited. In this work, we propose a data-driven approach in which the optimal filter is found based on DNS data in the frequency domain. The optimization step is computationally efficient and only involves one-dimensional least-squares problems for each wavenumber. Across both decaying turbulence and Kolmogorov flow, our learned filter decisively outperforms the standard differential filter and the Smagorinsky model, yielding significantly improved accuracy in energy spectra and in the temporal evolution of both energy and enstrophy. In addition, the relax parameter is determined by requiring energy and/or enstrophy conservation, which enforces stability of the method and reduces the appearance of numerical wiggles, especially when the filter is built in scarce data regimes. Applying the learned filter is also more computationally efficient compared to traditional differential filters, as it circumvents solving a linear system.

math.NA↗

arXiv2025

Exact operator inference with minimal data

This work introduces a novel method to generate snapshot data for operator inference that guarantees the exact reconstruction of intrusive projection-based reduced-order models (ROMs). To ensure exact reconstruction, the operator inference least squares matrix must have full rank, without regularization. Existing works have achieved this full rank using heuristic strategies to generate snapshot data and a-posteriori checks on full rank, but without a guarantee of success. Our novel snapshot data generation method provides this guarantee thanks to two key ingredients: first we identify ROM states that induce full rank, then we generate snapshots corresponding to exactly these states by simulating multiple trajectories for only a single time step. This way, the number of required snapshots is minimal and orders of magnitude lower than typically reported with existing methods. The method avoids non-Markovian terms and does not require re-projection. Since the number of snapshots is minimal, the least squares problem simplifies to a linear system that is numerically more stable. In addition, because the inferred operators are exact, properties of the intrusive ROM operators such as symmetry or skew-symmetry are preserved. Numerical results for differential equations involving 2nd, 3rd and 8th order polynomials demonstrate that the novel snapshot data generation method leads to exact reconstruction of the intrusive reduced order models.

math.NA↗

arXiv2025

Data-driven Closure Strategies for Parametrized Reduced Order Models via Deep Operator Networks

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in standard reduced-order approaches are not taken into account. In particular, in this work we focus on a Proper Orthogonal Decomposition (POD)-based formulation and our goal is to build a closure or correction model, aimed to re-introduce the contribution of the discarded modes. The approach has been investigated in previous works, and the goal of this manuscript is to extend the model to a parametric setting making use of machine learning procedures, and, in particular, of deep operator networks. More in detail, we model the closure terms through a deep operator network taking as input the reduced variables and the parameters of the problem. We tested the methods on three test cases with different behaviors: the periodic turbulent flow past a circular cylinder, the unsteady turbulent flow in a channel-driven cavity, and the geometrically-parametrized backstep flow. The performance of the machine learning-enhanced ROM is deeply studied in different modal regimes, and considerably improved the pressure and velocity accuracy with respect to the standard POD-Galerkin approach.

math.NA↗

arXiv2025

Model Reduction for Transport-Dominated Problems via Cross-Correlation Based Snapshot Registration

Traditional linear approximation methods, such as proper orthogonal decomposition and the reduced basis method, are ill-suited for transport-dominated problems due to the slow decay of the Kolmogorov $n$-width, leading to inefficient and inaccurate reduced-order models. In this work, we propose a model reduction approach for transport-dominated problems by employing cross-correlation based snapshot registration to accelerate the Kolmogorov $n$-width decay, thereby enabling the construction of efficient and accurate reduced-order models using linear approximation methods. We propose a complete framework comprising offline-online stages for the development of reduced order models using the cross-correlation based snapshots registration. The effectiveness of the proposed approach is demonstrated using two test cases: 1D travelling waves and the higher-order methods benchmark test case, 2D isentropic convective vortex.

math.NA↗

arXiv2024

Stochastic Parameter Prediction in Cardiovascular Problems

Patient-specific modeling of cardiovascular flows with high-fidelity is challenging due to its dependence on accurately estimated velocity boundary profiles, which are essential for precise simulations and directly influence wall shear stress calculations - key in predicting cardiovascular diseases like atherosclerosis. This data, often derived from in vivo modalities like 4D flow MRI, suffers from low resolution and noise. To address this, we employ a stochastic data assimilation technique that integrates computational fluid dynamics with an advanced Ensemble-based Kalman filter, enhancing model accuracy while accounting for uncertainties. Our approach sequentially collects velocity data over time within the vascular model, enabling real-time refinement of unknown boundary estimations. The mathematical model uses the incompressible Navier-Stokes equation to simulate aortic blood flow. We consider unknown boundaries as constant, time-dependent, and space-time dependent in two- and three-dimensional models. In our 2-dimensional model, relative errors were as low as 0.996\% for constant boundaries and up to 2.63\% and 2.61\% for time-dependent and space-time dependent boundaries, respectively, over an observation span of two-time steps. For the 3-dimensional patient-specific model, the relative error was 7.37\% for space-time dependent boundaries. By refining the velocity boundary profile, our method improves wall shear stress predictions, enhancing the accuracy and reliability of models specific to individual cardiovascular patients. These advancements could contribute to better diagnosis and treatment of cardiovascular diseases.

math.NA↗

arXiv2024

Non-intrusive model reduction of advection-dominated hyperbolic problems using neural network shift augmented manifold transformation

Advection-dominated problems are predominantly noticed in nature, engineering systems, and various industrial processes. Traditional linear compression methods, such as proper orthogonal decomposition (POD) and reduced basis (RB) methods are ill-suited for these problems, due to slow Kolmogorov $n$-width decay. This results in inefficient and inaccurate reduced order models (ROMs). There are few non-linear approaches to accelerate the Kolmogorov $n$-width decay. In this work, we use a neural network shift augmented transformation technique that employs automatic shift detection. This approach leverages a deep-learning framework to derive a parameter-dependent mapping between the original manifold $\mathcal{M}$ and the transformed manifold $\tilde{\mathcal{M}}$. We apply a linear compression method to obtain a low-dimensional linear approximation subspace of the transformed manifold $\tilde{\mathcal{M}}$. Furthermore, we construct non-intrusive reduced order models on the resulting transformed linear approximation subspace and employ automatic shift detection for predictions in the online stage. We propose a complete framework, the neural network shift-augmented proper orthogonal decomposition-based reduced order model (NNsPOD-ROM) algorithm, comprising both offline and online stages for model reduction of advection-dominated problems. We test our proposed methodology on numerous experiments to evaluate its performance on the 1D linear advection equation, a higher order method benchmark case - the 2D isentropic convective vortex, and 2D two-phase flow.

math.NA↗

arXiv2024

A hybrid reduced-order model for segregated fluid-structure interaction solvers in an ALE approach at high Reynolds number

This study introduces a first step for constructing a hybrid reduced-order models (ROMs) for segregated fluid-structure interaction in an Arbitrary Lagrangian-Eulerian (ALE) approach at a high Reynolds number using the Finite Volume Method (FVM). The ROM is driven by proper orthogonal decomposition (POD) with hybrid techniques that combines the classical Galerkin projection and two data-driven methods (radial basis networks , and neural networks/ long short term memory). Results demonstrate the ROM ability to accurately capture the physics of fluid-structure interaction phenomena. This approach is validated through a case study focusing on flow-induced vibration (FIV) of a pitch-plunge airfoil at a high Reynolds number 10000000.

physics.flu-dyn↗

arXiv2024

Parametric Intrusive Reduced Order Models enhanced with Machine Learning Correction Terms

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in standard ROMs are not taken into account. In particular, in this work we consider two types of contributions: the turbulence modeling, added through a reduced-order approximation of the eddy viscosity field, and the correction model, aimed to re-introduce the contribution of the discarded modes. Both approaches have been investigated in previous works and the goal of this paper is to extend the model to a parametric setting making use of ad-hoc machine learning procedures. More in detail, we investigate different neural networks' architectures, from simple dense feed-forward to Long-Short Term Memory neural networks, in order to find the most suitable model for the re-introduced contributions. We tested the methods on two test cases with different behaviors: the periodic turbulent flow past a circular cylinder and the unsteady turbulent flow in a channel-driven cavity. In both cases, the parameter considered is the Reynolds number and the machine learning-enhanced ROM considerably improved the pressure and velocity accuracy with respect to the standard ROM.

math.NA↗

arXiv2024

A segregated reduced order model of a pressure-based solver for turbulent compressible flows

This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing closely accurate solutions with respect to the high fidelity flow fields. Full-order solutions are often obtained through the use of segregated solvers (solution variables are solved one after another), employing slightly modified conservation laws so that they can be decoupled and then solved one at a time. Classical reduction architectures, on the contrary, rely on the Galerkin projection of a complete Navier-Stokes system to be projected all at once, causing a mild discrepancy with the high order solutions. This article relies on segregated reduced-order algorithms for the resolution of turbulent and compressible flows in the context of physical and geometrical parameters. At the full-order level turbulence is modeled using an eddy viscosity approach. Since there is a variety of different turbulence models for the approximation of this supplementary viscosity, one of the aims of this work is to provide a reduced-order model which is independent on this selection. This goal is reached by the application of hybrid methods where Navier-Stokes equations are projected in a standard way while the viscosity field is approximated by the use of data-driven interpolation methods or by the evaluation of a properly trained neural network. By exploiting the aforementioned expedients it is possible to predict accurate solutions with respect to the full-order problems characterized by high Reynolds numbers and elevated Mach numbers.

physics.flu-dyn↗