相关论文: Convergence proof for first-order position-based d…
Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is…
Autonomous driving systems are typically verified based on scenarios. To represent the positions and movements of cars in these scenarios, diagrams that utilize icons are typically employed. However, the interpretation of such diagrams is…
The notion of lambda-symmetries, originally introduced by C. Muriel and J.L. Romero, is extended to the case of systems of first-order ODE's (and of dynamical systems in particular). It is shown that the existence of a symmetry of this type…
Inverse dynamics is used extensively in robotics and biomechanics applications. In manipulator and legged robots, it can form the basis of an effective nonlinear control strategy by providing a robot with both accurate positional tracking…
We describe a novel constructive technique for devising efficient first-order methods for a wide range of large-scale convex minimization settings, including smooth, non-smooth, and strongly convex minimization. The technique builds upon a…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
High-accuracy, high-efficiency physics-based fluid-solid interaction is essential for reality modeling and computer animation in online games or real-time Virtual Reality (VR) systems. However, the large-scale simulation of incompressible…
We propose AEGD, a new algorithm for first-order gradient-based optimization of non-convex objective functions, based on a dynamically updated energy variable. The method is shown to be unconditionally energy stable, irrespective of the…
Many existing region-of-attraction (ROA) analysis tools find difficulty in addressing feedback systems with large-scale neural network (NN) policies and/or high-dimensional sensing modalities such as cameras. In this paper, we tailor the…
Following the seminal work of Nesterov, accelerated optimization methods have been used to powerfully boost the performance of first-order, gradient-based parameter estimation in scenarios where second-order optimization strategies are…
The basis generation in reduced order modeling usually requires multiple high-fidelity large-scale simulations that could take a huge computational cost. In order to accelerate these numerical simulations, we introduce a FOM/ROM hybrid…
Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…
Predictive simulations of complex systems are essential for applications ranging from weather forecasting to drug design. The veracity of these predictions hinges on their capacity to capture the effective system dynamics. Massively…
Gradient compression is of growing interests for solving constrained optimization problems including compressed sensing, noisy recovery and matrix completion under limited communication resources and storage costs. Convergence analysis of…
We introduce new optimized first-order methods for smooth unconstrained convex minimization. Drori and Teboulle recently described a numerical method for computing the $N$-iteration optimal step coefficients in a class of first-order…
In this work the standard kinetic theory assumption of instantaneous collisions is lifted. As a continuation of of a previous paper by Kanzler, Schmeiser, and Tora [KRM, 2024], a model for higher order non-instantaneous alignment collisions…
Perspective distortion (PD) causes unprecedented changes in shape, size, orientation, angles, and other spatial relationships of visual concepts in images. Precisely estimating camera intrinsic and extrinsic parameters is a challenging task…
This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…
Physical processes evolving in both time and space are often modeled using Partial Differential Equations (PDEs). Recently, it has been shown how stability analysis and control of coupled PDEs in a single spatial variable can be more…
We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results…