Related papers: Higher-Order LaSDI: Reduced Order Modeling with Mu…

The numerical treatment of fluid-particle systems is a very challenging problem because of the complex coupling phenomena occurring between the two phases. Although accurate mathematical modelling is available to address this kind of…

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…

Fractional Laplace equations are becoming important tools for mathematical modeling and prediction. Recent years have shown much progress in developing accurate and robust algorithms to numerically solve such problems, yet most solvers for…

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

There are two main strategies for improving the projection-based reduced order model (ROM) accuracy: (i) improving the ROM, i.e., adding new terms to the standard ROM; and (ii) improving the ROM basis, i.e., constructing ROM bases that…

This study concerns the development of a data-based compact model for the prediction of the fluid temperature evolution in district heating (DH) pipeline networks. This so-called "reduced-order model" (ROM) is obtained from reduction of the…

The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods such as the proper orthogonal decomposition (POD). For some nonlinear problems, linear RB…

Reduced-order models (ROMs) are essential for rapid simulation of complex biomechanical systems and for bridging the gap between high fidelity models and clinical application. However, ROMs for tissue growth and remodeling (G&R) remain…

Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and…

POD--Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam…

Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…

In systems governed by nonlinear partial differential equations such as fluid flows, the design of state estimators such as Kalman filters relies on a reduced-order model (ROM) that projects the original high-dimensional dynamics onto a…

Finite element based simulation of phenomena governed by partial differential equations is a standard tool in many engineering workflows today. However, the simulation of complex geometries is computationally expensive. Many engineering…

In order to solve partial differential equations numerically and accurately, a high order spatial discretization is usually needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems…

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…

Reduced order models (ROM) are commonly employed to solve parametric problems and to devise inexpensive response surfaces to evaluate quantities of interest in real-time. There are many families of ROMs in the literature and choosing among…

Continuous monitoring and real-time control of high-dimensional distributed systems are often crucial in applications to ensure a desired physical behavior, without degrading stability and system performances. Traditional feedback control…

Many Hamiltonian systems can be recast in multi-symplectic form. We develop a reduced-order model (ROM) for multi-symplectic Hamiltonian partial differential equations (PDEs) that preserves the global energy. The full-order solutions are…

POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…

Reduced-order models of time-dependent partial differential equations (PDEs) where the solution is assumed as a linear combination of prescribed modes are rooted in a well-developed theory. However, more general models where the reduced…