Related papers: Discrete empirical interpolation in the tensor t-p…

The Empirical Interpolation Method (EIM) and its generalized version (GEIM) can be used to approximate a physical system by combining data measured from the system itself and a reduced model representing the underlying physics. In presence…

One of the major challenges of coupled problems is to manage nonconforming meshes at the interface between two models and/or domains, due to different numerical schemes or domains discretizations employed. Moreover, very often complex…

The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this…

We propose AIM, a new algorithm for differentially private synthetic data generation. AIM is a workload-adaptive algorithm within the paradigm of algorithms that first selects a set of queries, then privately measures those queries, and…

We propose a parametric sampling strategy for the reduction of large-scale PDE systems with multidimensional input parametric spaces by leveraging models of different fidelity. The design of this methodology allows a user to adaptively…

A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems are presented. First, the Galerkin reduced basis (RB) formulation is presented which…

The combination of the Reduced Basis and the Empirical Interpolation Method (EIM) approaches have produced outstanding results in many disciplines. In particular, in gravitational wave (GW) science these results range from building…

The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…

This paper proposes two new algorithms related to the Tucker tensor format. The first method is a new cross approximation for Tucker tensors, which we call Cross$^2$-DEIM. Cross$^2$-DEIM is an iterative method that uses a fiber sampling…

For a nonlinear dynamical system that depends on parameters, the paper introduces a novel tensorial reduced-order model (TROM). The reduced model is projection-based, and for systems with no parameters involved, it resembles proper…

SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been focused on the exponential Euler discretization, showing…

Physics-informed neural networks (PINNs) have gained significant attention for solving forward and inverse problems related to partial differential equations (PDEs). While advancements in loss functions and network architectures have…

The promise of machine learning has been explored in a variety of scientific disciplines in the last few years, however, its application on first-principles based computationally expensive tools is still in nascent stage. Even with the…

Stochastic reduced-order modeling based on time-dependent bases (TDBs) has proven successful for extracting and exploiting low-dimensional manifold from stochastic partial differential equations (SPDEs). The nominal computational cost of…

In this paper, a reduced-order model (ROM) based on the proper orthogonal decomposition and the discrete empirical interpolation method is proposed for efficiently simulating time-fractional partial differential equations (TFPDEs). Both…

In this paper we develop the Greedy Recombination Interpolation Method (GRIM) for finding sparse approximations of functions initially given as linear combinations of some (large) number of simpler functions. In a similar spirit to the…

In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time formulation is used to develop a certified a-posteriori error estimator. This error estimator…

Time-dependent basis reduced order models (TDB ROMs) have successfully been used for approximating the solution to nonlinear stochastic partial differential equations (PDEs). For many practical problems of interest, discretizing these PDEs…

We present a novel tensor interpolation algorithm for the time integration of nonlinear tensor differential equations (TDEs) on the tensor train and Tucker tensor low-rank manifolds, which are the building blocks of many tensor network…

This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal involves constructing the solution explicitly as a linear…