Related papers: Metric-driven numerical methods
Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…
This work recasts time-dependent optimal control problems governed by partial differential equations in a Dynamic Mode Decomposition with control framework. Indeed, since the numerical solution of such problems requires a lot of…
We present a framework enabling variational data assimilation for gradient flows in general metric spaces, based on the minimizing movement (or Jordan-Kinderlehrer-Otto) approximation scheme. After discussing stability properties in the…
We present an approach for variational regularization of inverse and imaging problems for recovering functions with values in a set of vectors. We introduce regularization functionals, which are derivative-free double integrals of such…
We are interested in the approximation of partial differential equations with a data-driven approach based on the reduced basis method and machine learning. We suppose that the phenomenon of interest can be modeled by a parametrized partial…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
The energy preserving discrete gradient methods are generalized to finite-dimensional Riemannian manifolds by definition of a discrete approximation to the Riemannian gradient, a retraction, and a coordinate center function. The resulting…
We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…
This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…
The numerical integration method has been routinely used to produce global standard gravitational models from satellite tracking measurements of CHAMP/GRACE types. It is implemented by solving the differential equations of the partial…
We propose a novel Riemannian method for solving the Extreme multi-label classification problem that exploits the geometric structure of the sparse low-dimensional local embedding models. A constrained optimization problem is formulated as…
The problem of finding roots or solutions of a nonlinear partial differential equation may be formulated as the problem of minimizing a sum of squared residuals. One then defines an evolution equation so that in the asymptotic limit a…
We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
We propose three iterative methods for solving the Moser-Veselov equation, which arises in the discretization of the Euler-Arnold differential equations governing the motion of a generalized rigid body. We start by formulating the problem…
Modeling physical phenomena like heat transport and diffusion is crucially dependent on the numerical solution of partial differential equations (PDEs). A PDE solver finds the solution given coefficients and a boundary condition, whereas an…
In this article, we describe a function fitting method that has potential applications in machine learning and also prove relevant theorems. The described function fitting method is a convex minimization problem and can be solved using a…
We introduce an algebraic multiscale method for two--dimensional problems. The method uses the generalized multiscale finite element method based on the quadrilateral nonconforming finite element spaces. Differently from the…
Solutions of certain partial differential equations (PDEs) are often represented by the steepest descent curves of corresponding functionals. Minimizing movement scheme was developed in order to study such curves in metric spaces.…