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Optimal prediction approximates the average solution of a large system of ordinary differential equations by a smaller system. We present how optimal prediction can be applied to a typical problem in the field of molecular dynamics, in…
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…
The variational approach to fracture is effective for simulating the nucleation and propagation of complex crack patterns, but is computationally demanding. The model is a strongly nonlinear non-convex variational inequality that demands…
When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…
We propose an efficient way of solving optimal control problems for rigid-body systems on the basis of inverse dynamics and the multiple-shooting method. We treat all variables, including the state, acceleration, and control input torques,…
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…
This paper constructs a predictor-corrector technique with orthogonal spline collocation finite element method for simulating a FitzHugh-Nagumo system subject to suitable initial and boundary conditions. The developed computational…
We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…
Optimal prediction methods compensate for a lack of resolution in the numerical solution of time-dependent differential equations through the use of prior statistical information. We present a new derivation of the basic methodology, show…
Projection-based model order reduction on nonlinear manifolds has been recently proposed for problems with slowly decaying Kolmogorov n-width such as advection-dominated ones. These methods often use neural networks for manifold learning…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
We consider optimization algorithms that successively minimize simple Taylor-like models of the objective function. Methods of Gauss-Newton type for minimizing the composition of a convex function and a smooth map are common examples. Our…
In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…
Given 2D point correspondences between an image pair, inferring the camera motion is a fundamental issue in the computer vision community. The existing works generally set out from the epipolar constraint and estimate the essential matrix,…
In this work, we present an efficient gradient projection method for solving a class of stochastic optimal control problem with expected integral state constraint. The first order optimality condition system consisting of forward-backward…
We propose an energy-optimized invariant energy quadratization method to solve the gradient flow models in this paper, which requires only one linear energy-optimized step to correct the auxiliary variables on each time step. In addition to…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
This letter proposes a predictor-corrector method to strike a balance between simulation accuracy and efficiency by appropriately tuning the numerical integration step length of a power system time-domain simulation. Numerical tests…
In this work we adapt a prediction-correction algorithm for continuous time-varying convex optimization problems to solve dynamic programs arising from Model Predictive Control. In particular, the prediction step tracks the evolution of the…
We study the acceleration of steady-state computation for microflow, which is modeled by the high-order moment models derived recently from the steady-state Boltzmann equation with BGK-type collision term. By using the lower-order model…