Related papers: Optimal Solution of Linear Ordinary Differential E…
In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and…
We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…
We present a hybrid a-priori/a-posteriori goal oriented error estimator for a combination of dynamic iteration-based solution of ordinary differential equations discretized by finite elements. Our novel error estimator combines estimates…
In high-dimensional statistics, variable selection recovers the latent sparse patterns from all possible covariate combinations. This paper proposes a novel optimization method to solve the exact L0-regularized regression problem, which is…
We present a stable and convergent method for solving initial value problems based on the use of differentiation matrices obtained by Lagrange interpolation. This implicit multistep-like method is easy-to-use and performs pretty well in the…
At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly,…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
We suggest a modification of the operator exponential method for the numerical solving the difference linear initial boundary value problems. The scheme is based on the representation of the difference operator for given boundary conditions…
This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…
It is common practice to apply gradient-based optimization algorithms to numerically solve large-scale ODE constrained optimal control problems. Gradients of the objective function are most efficiently computed by approximate adjoint…
Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…
We are interested in numerically approximating the solution ${\bf U}(t)$ of the large dimensional semilinear matrix differential equation $\dot{\bf U}(t) = { \bf A}{\bf U}(t) + {\bf U}(t){ \bf B} + {\cal F}({\bf U},t)$, with appropriate…
In this paper, it is shown that the solutions of general differentiable constrained optimization problems can be viewed as asymptotic solutions to sets of Ordinary Differential Equations (ODEs). The construction of the ODE associated to the…
In this paper, we propose a conditional gradient method for solving constrained vector optimization problems with respect to a partial order induced by a closed, convex and pointed cone with nonempty interior. When the partial order under…
In this paper, we develop new first-order method for composite non-convex minimization problems with simple constraints and inexact oracle. The objective function is given as a sum of "`hard"', possibly non-convex part, and "`simple"'…
We describe a set of Gaussian Process based approaches that can be used to solve non-linear Ordinary Differential Equations. We suggest an explicit probabilistic solver and two implicit methods, one analogous to Picard iteration and the…
We develop spectral methods for ODEs and operator eigenvalue problems that are based on a least-squares formulation of the problem. The key tool is a method for rectangular generalized eigenvalue problems, which we extend to quasimatrices…
Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…
In this paper, we analyze the accuracy of gradient estimates obtained by linear interpolation when the underlying function is subject to bounded measurement noise. The total gradient error is decomposed into a deterministic component…
The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…