arXiv subjects

Anna Ivagnes

Publications and source records attributed to Anna Ivagnes.

13 recordsLinked to original sources

arXiv2026

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models

In the present work, we introduce a data-driven approach to enhance the accuracy of non-intrusive Reduced Order Models (ROMs). In particular, we focus on ROMs built using Proper Orthogonal Decomposition (POD) in an under-resolved and marginally-resolved regime, i.e. when the number of modes employed is not enough to capture the system dynamics. We propose a method to re-introduce the contribution of neglected modes through a quadratic correction term, given by the action of a quadratic operator on the POD coefficients. Differently from the state-of-the-art methodologies, where the operator is learned via least-squares optimisation, we propose to parametrise the operator by a Multi-Input Operators Network (MIONet). This way, we are able to build models with higher generalisation capabilities, where the operator itself is continuous in space -- thus agnostic of the domain discretisation -- and parameter-dependent. We test our model on two standard benchmarks in fluid dynamics and show that the correction term improves the accuracy of standard POD-based ROMs.

math.NA↗

arXiv2026

Efficient and Accurate Surrogate Modeling of Turbulent Flows via Space-Dependent Aggregation and Reduced Order Models

Reynolds-Averaged Navier-Stokes (RANS) models are widely used for turbulent flow simulations due to their computational efficiency, but their accuracy strongly depends on the selected turbulence closure and may vary across the flow domain. Space-dependent model aggregation has been shown to improve RANS predictions by combining multiple turbulence models, although at the cost of repeated high-fidelity simulations. The first novelty of this work is a unified framework that combines different turbulence models, space-dependent aggregation, and non-intrusive reduced order models to achieve both accuracy and efficiency. Two aggregation pipelines are proposed: a Mixed FOM-ROM (MFR) approach, where a reduced order model is trained on aggregated RANS solutions, and a Mixed-ROM (MR) approach, which directly aggregates multiple reduced order models built on top of different RANS full-order models. The second novelty is that the aggregation weights are learned via a neural-network that provides smooth, space-continuous weights and improves generalization with respect to standard weighting techniques. The resulting surrogate models are validated on the two-dimensional periodic hill benchmark and on the flow over a height-dependent bump, demonstrating improved accuracy over individual RANS and ROM predictions at near real-time computational cost.

math.NA↗

arXiv2026

Reinforcement Learning-Based Filters for Convection-Dominated Flows: Reference-Free and Reference-Guided Training

We propose a reinforcement learning (RL) framework for the dynamic selection of the filter parameter in Evolve-Filter (EF) regularization strategies for incompressible turbulent flows. Instead of prescribing the filter radius heuristically, the RL agent learns to adaptively control the filtering intensity in time, balancing numerical stability and physical accuracy. The methodology is assessed on two benchmark problems with fundamentally different dynamics: flow past a cylinder and decaying homogeneous turbulence. Both reference-guided and reference-free reward formulations are investigated. In the reference-guided setting, the agent is trained using direct numerical simulation (DNS) data over a limited time window and then evaluated in extrapolation. In the reference-free setting, the reward relies exclusively on physics-based quantities, without access to reference solutions, i.e., completely eliminating the computational costs related to DNS simulations. The results show that the proposed RL-EF strategies prevent numerical blow-up while avoiding the excessive dissipation typical of standard EF approaches based on a fixed Kolmogorov length scale. The learned policies accurately reproduce the relevant flow dynamics across scales, preserving the correct balance between large-scale structures and small-scale dissipation. Notably, the reference-free reward achieves performance comparable to the reference-guided approach, demonstrating that stable and spectrally consistent filtering strategies can be learned even without DNS data, drastically reducing the computational costs of the training phase. The proposed framework provides a robust and flexible alternative to manually tuned regularization parameters, enabling adaptive, physically consistent control of filtering in turbulent flow simulations.

math.NA↗

arXiv2026

StabOp: A Data-Driven Stabilization Operator for Reduced Order Modeling

Spatial filters have played a central role in large eddy simulation and, more recently, in reduced order model (ROM) stabilization for convection-dominated flows. Nevertheless, important open questions remain: in under-resolved regimes, which filter is most suitable for a given stabilization or closure model? Moreover, once a filter is selected, how should its parameters, such as the filter radius, be determined? Addressing these questions is essential for the reliable design and performance of filter-based stabilization strategies. To answer these questions, we propose a novel strategy that differs fundamentally from current filter-based approaches: we replace traditional spatial filters with a data-driven stabilization operator (StabOp) that yields accurate results for a given resolution, quantity of interest, and stabilization strategy. Although the new StabOp can be used for both classical discretizations and ROMs, and for different types of filter-based stabilization or closure, for clarity we focus on ROMs and the Leray stabilization. To build the new StabOp, we postulate its model form as a linear, quadratic, or nonlinear mapping, and then solve a PDE-constrained optimization problem to minimize a given loss function. Using the resulting StabOp in the Leray ROM (L-ROM) yields a new stabilized ROM, StabOp-L-ROM. To assess the StabOp-L-ROM, we compare it with the L-ROM and the standard ROM in numerical simulations of four flows: 2D flow past a cylinder at Re=500, lid-driven cavity at Re=10000, 3D flow past a hemisphere at Re=2200, and minimal channel flow at Re=5000. Our numerical results show that the StabOp-L-ROM can be orders of magnitude more accurate than the classical L-ROM tuned with an optimal filter radius in the predictive regime. Furthermore, while the new StabOp smooths the input flow fields, its smoothing mechanism differs from that of classical spatial filters.

physics.flu-dyn↗

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

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

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↗

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

Enhancing non-intrusive Reduced Order Models with space-dependent aggregation methods

In this manuscript, we combine non-intrusive reduced order models (ROMs) with space-dependent aggregation techniques to build a mixed-ROM. The prediction of the mixed formulation is given by a convex linear combination of the predictions of some previously-trained ROMs, where we assign to each model a space-dependent weight. The ROMs taken into account to build the mixed model exploit different reduction techniques, such as Proper Orthogonal Decomposition (POD) and AutoEncoders (AE), and/or different approximation techniques, namely a Radial Basis Function Interpolation (RBF), a Gaussian Process Regression (GPR) or a feed-forward Artificial Neural Network (ANN). The contribution of each model is retained with higher weights in the regions where the model performs best, and, vice versa, with smaller weights where the model has a lower accuracy with respect to the other models. Finally, a regression technique, namely a Random Forest, is exploited to evaluate the weights for unseen conditions. The performance of the aggregated model is evaluated on two different test cases: the 2D flow past a NACA 4412 airfoil, with an angle of attack of 5 degrees, having as parameter the Reynolds number varying between 1e5 and 1e6 and a transonic flow over a NACA 0012 airfoil, considering as parameter the angle of attack. In both cases, the mixed-ROM has provided improved accuracy with respect to each individual ROM technique.

math.NA↗

arXiv2024

A Shape Optimization Pipeline for Marine Propellers by means of Reduced Order Modeling Techniques

In this paper, we propose a shape optimization pipeline for propeller blades, applied to naval applications. The geometrical features of a blade are exploited to parametrize it, allowing to obtain deformed blades by perturbating their parameters. The optimization is performed using a genetic algorithm that exploits the computational speed-up of reduced order models to maximize the efficiency of a given propeller. A standard offline-online procedure is exploited to construct the reduced-order model. In an expensive offline phase, the full order model, which reproduces an open water test, is set up in the open-source software OpenFOAM and the same full order setting is used to run the CFD simulations for all the deformed propellers. The collected high-fidelity snapshots and the deformed parameters are used in the online stage to build the non-intrusive reduced-order model. This paper provides a proof of concept of the pipeline proposed, where the optimized propeller improves the efficiency of the original propeller.

math.OC↗

arXiv2022

Hybrid Data-Driven Closure Strategies for Reduced Order Modeling

In this paper, we propose hybrid data-driven ROM closures for fluid flows. These new ROM closures combine two fundamentally different strategies: (i) purely data-driven ROM closures, both for the velocity and the pressure; and (ii) physically based, eddy viscosity data-driven closures, which model the energy transfer in the system. The first strategy consists in the addition of closure/correction terms to the governing equations, which are built from the available data. The second strategy includes turbulence modeling by adding eddy viscosity terms, which are determined by using machine learning techniques. The two strategies are combined for the first time in this paper to investigate a two-dimensional flow past a circular cylinder at Re=50000. Our numerical results show that the hybrid data-driven ROM is more accurate than both the purely data-driven ROM and the eddy viscosity ROM.

math.NA↗

arXiv2022

Pressure Data-Driven Variational Multiscale Reduced Order Models

In this paper, we develop data-driven closure/correction terms to increase the pressure and velocity accuracy of reduced order models (ROMs) for fluid flows. Specifically, we propose the first pressure-based data-driven variational multiscale ROM, in which we use the available data to construct closure/correction terms for both the momentum equation and the continuity equation. Our numerical investigation of the two-dimensional flow past a circular cylinder at Re=50000 in the marginally-resolved regime shows that the novel pressure data-driven variational multiscale ROM yields significantly more accurate velocity and pressure approximations than the standard ROM and, more importantly, than the original data-driven variational multiscale ROM (i.e., without pressure components). In particular, our numerical results show that adding the closure/correction term in the momentum equation significantly improves both the velocity and the pressure approximations, whereas adding the closure/correction term in the continuity equation improves only the pressure approximation.

math.NA↗

arXiv2022

Towards a machine learning pipeline in reduced order modelling for inverse problems: neural networks for boundary parametrization, dimensionality reduction and solution manifold approximation

In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the iterative optimization process. To accelerate such a procedure, we apply a numerical pipeline that involves artificial neural networks to parametrize the boundary conditions of the problem in hand, compress the dimensionality of the (full-order) snapshots, and approximate the parametric solution manifold. It derives a general framework capable to provide an ad-hoc parametrization of the inlet boundary and quickly converges to the optimal solution thanks to model order reduction. We present in this contribution the results obtained by applying such methods to two different CFD test cases.

math.NA↗