83 citations · 173 across the 26 of their papers we have counts for
24 papers · 1 filter
A Dynamical Approximation Scheme on the Stiefel manifold for Wasserstein Gradient Flows
Isabella Carla Gonnella, Olga Mula, Federico Pichi +1
We propose a meshless Lagrangian dynamical method for approximating Wasserstein gradient flows (WGFs). The evolving measure is represented as the pushforward of the initial measure…
Stochastic bifurcation analysis via polynomial chaos: consistency and convergence of branch-approximating solutions
Giacomo Venier, Isabella Carla Gonnella, Federico Pichi +1
Parameter-dependent dynamical systems that exhibit bifurcations pose significant computational challenges, as traditional continuation methods require repeated, costly simulations…
A Multi-Fidelity Parametric Framework for Reduced-Order Modeling using Optimal Transport-based Interpolation: Applications to Diffused-Interface Two-Phase Flows
Moaad Khamlich, Niccolò Tonicello, Federico Pichi +1
This work introduces a data-driven, non-intrusive reduced-order modeling (ROM) framework that leverages Optimal Transport (OT) for multi-fidelity and parametric problems in two-pha…
Bifurcation curve detection with deflation for multiparametric PDEs
Nitin Kumar, Federico Pichi, Gianluigi Rozza
This work presents a comprehensive framework for capturing bifurcating phenomena and detecting bifurcation curves in nonlinear multiparametric partial differential equations, where…
ROM for Viscous, Incompressible Flow in Polygons -- exponential -width bounds and convergence rate
Francesco Romor, Federico Pichi, Giovanni Stabile +2
We demonstrate exponential convergence of Reduced Order Model (ROM) approximations for mixed boundary value problems of the stationary, incompressible Navier-Stokes equations in pl…
Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decomposition
Yuanhong Chen, Federico Pichi, Zhen Gao +1
Graph autoencoders have gained attention in nonlinear reduced-order modeling of parameterized partial differential equations defined on unstructured grids. Despite they provide a g…
Convergence and Sketching-Based Efficient Computation of Neural Tangent Kernel Weights in Physics-Based Loss
Max Hirsch, Federico Pichi
In multi-objective optimization, multiple loss terms are weighted and added together to form a single objective. These weights are chosen to properly balance the competing losses a…
Sparse Identification for bifurcating phenomena in Computational Fluid Dynamics
Lorenzo Tomada, Moaad Khamlich, Federico Pichi +1
This work investigates model reduction techniques for nonlinear parameterized and time-dependent PDEs, specifically focusing on bifurcating phenomena in Computational Fluid Dynamic…
Nonlinear reduction strategies for data compression: a comprehensive comparison from diffusion to advection problems
Isabella Carla Gonnella, Federico Pichi, Gianluigi Rozza
This work presents an overview of several nonlinear reduction strategies for data compression from various research fields, and a comparison of their performance when applied to pr…
Deflation-based certified greedy algorithm and adaptivity for bifurcating nonlinear PDEs
Federico Pichi, Maria Strazzullo
This work deals with tailored reduced order models for bifurcating nonlinear parametric partial differential equations, where multiple coexisting solutions arise for a given parame…
Optimal Transport-Based Displacement Interpolation with Data Augmentation for Reduced Order Modeling of Nonlinear Dynamical Systems
Moaad Khamlich, Federico Pichi, Michele Girfoglio +2
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 comp…
Projection-based Reduced Order Modelling for Unsteady Parametrized Optimal Control Problems in 3D Cardiovascular Flows
Surabhi Rathore, Pasquale Claudio Africa, Francesco Ballarin +3
This paper presents a projection-based reduced order modelling (ROM) framework for unsteady parametrized optimal control problems (OCPs) arising from cardiovascular (CV) ap…
GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications
Oisín M. Morrison, Federico Pichi, Jan S. Hesthaven
This work presents a novel resolution-invariant model order reduction strategy for multifidelity applications. We base our architecture on a novel neural network layer developed in…
Neural empirical interpolation method for nonlinear model reduction
Max Hirsch, Federico Pichi, Jan S. Hesthaven
In this paper, we introduce the neural empirical interpolation method (NEIM), a neural network-based alternative to the discrete empirical interpolation method for reducing the tim…
A stochastic perturbation approach to nonlinear bifurcating problems
Isabella Carla Gonnella, Moaad Khamlich, Federico Pichi +1
Incorporating probabilistic terms in mathematical models is crucial for capturing and quantifying uncertainties in real-world systems, especially when the solution is not unique or…
Optimal Transport-inspired Deep Learning Framework for Slow-Decaying Kolmogorov n-width Problems: Exploiting Sinkhorn Loss and Wasserstein Kernel
Moaad Khamlich, Federico Pichi, Gianluigi Rozza
Reduced order models (ROMs) are widely used in scientific computing to tackle high-dimensional systems. However, traditional ROM methods may only partially capture the intrinsic ge…
Reduced order models for the buckling of hyperelastic beams
Federico Pichi, Gianluigi Rozza
In this paper, we discuss reduced order modelling approaches to bifurcating systems arising from continuum mechanics benchmarks. The investigation of the beam's deflection is a rel…
A graph convolutional autoencoder approach to model order reduction for parametrized PDEs
Federico Pichi, Beatriz Moya, Jan S. Hesthaven
The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is…
Model order reduction for bifurcating phenomena in Fluid-Structure Interaction problems
Moaad Khamlich, Federico Pichi, Gianluigi Rozza
This work explores the development and the analysis of an efficient reduced order model for the study of a bifurcating phenomenon, known as the Coandă effect, in a multi-physics se…
Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier-Stokes equations with model order reduction
Federico Pichi, Maria Strazzullo, Francesco Ballarin +1
This work deals with optimal control problems as a strategy to drive bifurcating solution of nonlinear parametrized partial differential equations towards a desired branch. Indeed,…
Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method
Moreno Pintore, Federico Pichi, Martin Hess +2
The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities…
A Reduced Order Modeling technique to study bifurcating phenomena: application to the Gross-Pitaevskii equation
Federico Pichi, Annalisa Quaini, Gianluigi Rozza
We propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varie…
Reduced basis approaches for parametrized bifurcation problems held by non-linear Von Kármán equations
Federico Pichi, Gianluigi Rozza
This work focuses on the detection of the buckling phenomena and bifurcation analysis of the parametric Von Kármán plate equations based on reduced order methods and spectral analy…
Reduced basis approximation and a posteriori error estimation: applications to elasticity problems in several parametric settings
Dinh Bao Phuong Huynh, Federico Pichi, Gianluigi Rozza
In this work we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for elasticity problems in affinley parametrized geometries. The ess…