Related papers: Data-driven model order reduction for wave propaga…
Distributed-order time-fractional wave equations appear in the modeling of wave propagation in viscoelastic media. The material characteristics of the medium are modeled through constitutive functions or distributions in the…
Strongly nonlinear models of internal wave propagation for incompressible stratified Euler fluids are investigated numerically and analytically to determine the evolution of a class of initial conditions of interest in laboratory…
The data-driven techniques have been developed to deal with the output regulation problem of unknown linear systems by various approaches. In this paper, we first extend an existing algorithm from single-input single-output linear systems…
Time-dependent wave equations represent an important class of partial differential equations (PDE) for describing wave propagation phenomena, which are often formulated over unbounded domains. Given a compactly supported initial condition,…
We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…
The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…
Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…
In this work, we introduce a new Hybrid High-Order method for the numerical simulation of fracture propagation based on phase-field models. The proposed method supports general meshes made of polygonal/polyhedral elements, which provides…
This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of…
Clinical oriented applications of computational electrocardiology require efficient and reliable identification of patient-specific parameters of mathematical models based on available measures. In particular, the estimation of cardiac…
Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs,…
In the process of the deep learning, we integrate more integrable information of nonlinear wave models, such as the conservation law obtained from the integrable theory, into the neural network structure, and propose a conservation-law…
The performance of optimization-based robot motion planning algorithms is highly dependent on the initial solutions, commonly obtained by running a sampling-based planner to obtain a collision-free path. However, these methods can be slow…
We consider the effect of an array of plates or beams over a semi-infinite elastic ground on the propagation of elastic waves hitting the interface. The plates/beams are slender bodies with flexural resonances at low frequencies able to…
In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…
In this work, we present a deep collocation method for three dimensional potential problems in nonhomogeneous media. This approach utilizes a physics informed neural network with material transfer learning reducing the solution of the…
Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear…
This paper probes the dispersive shock waves (DSWs) theory in nonlinear optical systems through Whitham modulation theory for the high-order Chen-Lee-Liu (HOCLL) equation. We systematically derived the one-phase periodic solutions and the…
We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…