arXiv subjects

Michele Alessandro Bucci

Publications and source records attributed to Michele Alessandro Bucci.

11 recordsLinked to original sources

arXiv2026

PLAID: A Unified Data Model for Machine Learning on Heterogeneous Physics Simulations

Machine learning-based surrogate models have emerged as a powerful tool to accelerate simulation-driven scientific workflows, but their adoption is limited by the lack of large-scale, diverse, and standardized datasets for physics-based simulations. Existing benchmarks often focus on narrow domains or rely on simplified data models, and fail to capture the heterogeneity arising from variable geometries, meshes, and topologies, which is critical for assessing generalization in realistic settings. We introduce PLAID (Physics-Learning AI Data model), a unified and extensible data layer for heterogeneous physics simulations. It preserves the full complexity of simulation data while enabling efficient and scalable machine learning workflows, together with a library for dataset construction and manipulation~(\href{https://github.com/PLAID-lib/plaid}{github.com/PLAID-lib/plaid}). We release six datasets covering structural mechanics and computational fluid dynamics, designed to reflect realistic industrial scenarios and provide standardized benchmarks. The framework includes reproducible evaluation protocols and is integrated with Hugging Face to enable open, community-driven benchmarking with active user participation (\href{https://huggingface.co/PLAIDcompetitions}{huggingface.co/PLAIDcompetitions}).

cs.LG↗

arXiv2026

An End-to-End PyTorch Interface for Differentiable PDE Solvers: A RANS Model-Correction Study

This work presents an end-to-end strategy for solving inverse problems constrained by Partial Differential Equations within a fully differentiable Machine Learning framework. The proposed formulation provides a unified and user-friendly methodology applicable to a wide range of problems, from data assimilation to closure modeling. Our approach combines a baseline differentiable PDE solver, which predicts the state w from the nonlinear system $R(w) = 0$, with a generic additive, parametrized, and differentiable correction $f_ϕ(w)$, with trainable parameters $ϕ$. We show how to optimize phi within a fully differentiable Python workflow by reformulating the PDE as an implicit layer, enabling its integration into arbitrary objective functions, while leveraging PyTorch's automatic differentiation graph. The method is demonstrated on the Reynolds-Averaged Navier-Stokes equations for compressible flows, where the closure term, or a portion of it, is modeled using trainable parameters or a Neural Network. The first application considers the 2D NASA Wall-Mounted Hump test case, where a production-term parameter is optimized against time-averaged LES data. A second application is carried out on the VKI LS-59 turbine blade, where the Spalart-Allmaras eddy viscosity field is reconstructed through the optimization of a trainable spatial field. A dataset is generated starting from the VKI LS-59 turbine blade geometry using the differentiable BROADCAST solver with the Spalart-Allmaras turbulence model. The results highlight the flexibility of the framework, showing its applicability beyond turbulence modeling to a broader class of physics-informed PDE-constrained problems with data-driven components.

cs.CE↗

arXiv2025

Active learning of data-assimilation closures using Graph Neural Networks

The spread of machine learning techniques coupled with the availability of high-quality experimental and numerical data has significantly advanced numerous applications in fluid mechanics. Notable among these are the development of data assimilation and closure models for unsteady and turbulent flows employing neural networks (NN). Despite their widespread use, these methods often suffer from overfitting and typically require extensive datasets, particularly when not incorporating physical constraints. This becomes compelling in the context of numerical simulations, where, given the high computational costs, it is crucial to establish learning procedures that are effective even with a limited dataset. Here, we tackle those limitations by developing NN models capable of generalizing over unseen data in low-data limit by: i) incorporating invariances into the NN model using a Graph Neural Networks (GNNs) architecture; and ii) devising an adaptive strategy for the selection of the data utilized in the learning process. GNNs are particularly well-suited for numerical simulations involving unstructured domain discretization and we demonstrate their use by interfacing them with a Finite Elements (FEM) solver for the supervised learning of Reynolds-averaged Navier-Stokes equations. We consider as a test-case the data-assimilation of meanflows past generic bluff bodies, at different Reynolds numbers 50>=Re>=150, characterized by an unsteady dynamics. We show that the GNN models successfully predict the closure term; remarkably, these performances are achieved using a very limited dataset selected through an active learning process ensuring the generalization properties of the RANS closure term. The results suggest that GNN models trained through active learning procedures are a valid alternative to less flexible techniques such as convolutional NN.

physics.flu-dyn↗

arXiv2024

An Implicit GNN Solver for Poisson-like problems

This paper presents $Ψ$-GNN, a novel Graph Neural Network (GNN) approach for solving the ubiquitous Poisson PDE problems with mixed boundary conditions. By leveraging the Implicit Layer Theory, $Ψ$-GNN models an "infinitely" deep network, thus avoiding the empirical tuning of the number of required Message Passing layers to attain the solution. Its original architecture explicitly takes into account the boundary conditions, a critical prerequisite for physical applications, and is able to adapt to any initially provided solution. $Ψ$-GNN is trained using a "physics-informed" loss, and the training process is stable by design, and insensitive to its initialization. Furthermore, the consistency of the approach is theoretically proven, and its flexibility and generalization efficiency are experimentally demonstrated: the same learned model can accurately handle unstructured meshes of various sizes, as well as different boundary conditions. To the best of our knowledge, $Ψ$-GNN is the first physics-informed GNN-based method that can handle various unstructured domains, boundary conditions and initial solutions while also providing convergence guarantees.

cs.LG↗

arXiv2024

Multi-Level GNN Preconditioner for Solving Large Scale Problems

Large-scale numerical simulations often come at the expense of daunting computations. High-Performance Computing has enhanced the process, but adapting legacy codes to leverage parallel GPU computations remains challenging. Meanwhile, Machine Learning models can harness GPU computations effectively but often struggle with generalization and accuracy. Graph Neural Networks (GNNs), in particular, are great for learning from unstructured data like meshes but are often limited to small-scale problems. Moreover, the capabilities of the trained model usually restrict the accuracy of the data-driven solution. To benefit from both worlds, this paper introduces a novel preconditioner integrating a GNN model within a multi-level Domain Decomposition framework. The proposed GNN-based preconditioner is used to enhance the efficiency of a Krylov method, resulting in a hybrid solver that can converge with any desired level of accuracy. The efficiency of the Krylov method greatly benefits from the GNN preconditioner, which is adaptable to meshes of any size and shape, is executed on GPUs, and features a multi-level approach to enforce the scalability of the entire process. Several experiments are conducted to validate the numerical behavior of the hybrid solver, and an in-depth analysis of its performance is proposed to assess its competitiveness against a C++ legacy solver.

cs.LG↗

arXiv2023

Enhancing Data-Assimilation in CFD using Graph Neural Networks

We present a novel machine learning approach for data assimilation applied in fluid mechanics, based on adjoint-optimization augmented by Graph Neural Networks (GNNs) models. We consider as baseline the Reynolds-Averaged Navier-Stokes (RANS) equations, where the unknown is the meanflow and a closure model based on the Reynolds-stress tensor is required for correctly computing the solution. An end-to-end process is cast; first, we train a GNN model for the closure term. Second, the GNN model is introduced in the training process of data assimilation, where the RANS equations act as a physics constraint for a consistent prediction. We obtain our results using direct numerical simulations based on a Finite Element Method (FEM) solver; a two-fold interface between the GNN model and the solver allows the GNN's predictions to be incorporated into post-processing steps of the FEM analysis. The proposed scheme provides an excellent reconstruction of the meanflow without any features selection; preliminary results show promising generalization properties over unseen flow configurations.

physics.flu-dyn↗

arXiv2023

CD-ROM: Complemented Deep-Reduced Order Model

Model order reduction through the POD-Galerkin method can lead to dramatic gains in terms of computational efficiency in solving physical problems. However, the applicability of the method to non linear high-dimensional dynamical systems such as the Navier-Stokes equations has been shown to be limited, producing inaccurate and sometimes unstable models. This paper proposes a deep learning based closure modeling approach for classical POD-Galerkin reduced order models (ROM). The proposed approach is theoretically grounded, using neural networks to approximate well studied operators. In contrast with most previous works, the present CD-ROM approach is based on an interpretable continuous memory formulation, derived from simple hypotheses on the behavior of partially observed dynamical systems. The final corrected models can hence be simulated using most classical time stepping schemes. The capabilities of the CD-ROM approach are demonstrated on two classical examples from Computational Fluid Dynamics, as well as a parametric case, the Kuramoto-Sivashinsky equation.

physics.flu-dyn↗

arXiv2022

Continuous Methods : Adaptively intrusive reduced order model closure

Reduced order modeling methods are often used as a mean to reduce simulation costs in industrial applications. Despite their computational advantages, reduced order models (ROMs) often fail to accurately reproduce complex dynamics encountered in real life applications. To address this challenge, we leverage NeuralODEs to propose a novel ROM correction approach based on a time-continuous memory formulation. Finally, experimental results show that our proposed method provides a high level of accuracy while retaining the low computational costs inherent to reduced models.

cs.LG↗

arXiv2022

Continuous Methods : Hamiltonian Domain Translation

This paper proposes a novel approach to domain translation. Leveraging established parallels between generative models and dynamical systems, we propose a reformulation of the Cycle-GAN architecture. By embedding our model with a Hamiltonian structure, we obtain a continuous, expressive and most importantly invertible generative model for domain translation.

cs.CV↗

arXiv2019

Control of chaotic systems by Deep Reinforcement Learning

Deep Reinforcement Learning (DRL) is applied to control a nonlinear, chaotic system governed by the one-dimensional Kuramoto-Sivashinsky (KS) equation. DRL uses reinforcement learning principles for the determination of optimal control solutions and deep Neural Networks for approximating the value function and the control policy. Recent applications have shown that DRL may achieve superhuman performance in complex cognitive tasks. In this work, we show that using restricted, localized actuations, partial knowledge of the state based on limited sensor measurements, and model-free DRL controllers, it is possible to stabilize the dynamics of the KS system around its unstable fixed solutions, here considered as target states. The robustness of the controllers is tested by considering several trajectories in the phase-space emanating from different initial conditions; we show that the DRL is always capable of driving and stabilizing the dynamics around the target states. The complexity of the KS system, the possibility of defining the DRL control policies by solely relying on the local measurements of the system, and their efficiency in controlling its nonlinear dynamics pave the way for the application of RL methods in control of complex fluid systems such as turbulent boundary layers, turbulent mixers or multiphase flows.

math.OC↗

arXiv2018

Time-stepping and Krylov methods for large-scale instability problems

With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has been become reachable. It must be noted however that the memory capabilities of computers increase at a slower rate than their computational capabilities. Consequently, the traditional matrix-forming approaches wherein the Jacobian matrix of the system considered is explicitly assembled become rapidly intractable. Over the past two decades, so-called matrix-free approaches have emerged as an efficient alternative. The aim of this chapter is thus to provide an overview of well-grounded matrix-free methods for fixed points computations and linear stability analyses of very large-scale nonlinear dynamical systems.

physics.flu-dyn↗