相关论文: Modified Legendre-Gauss Collocation Method for Sol…
In this paper, a third-order compact gas-kinetic scheme is firstly proposed for three-dimensional computation for the compressible Euler and Navier-Stokes solutions. The scheme achieves its compactness due to the time-dependent gas…
Distributed optimization plays an important role in modern large-scale machine learning and data processing systems by optimizing the utilization of computational resources. One of the classical and popular approaches is Local Stochastic…
We present a robust optimisation framework for computing invariant solutions of wall-bounded flows by recasting the Navier-Stokes equations as a variational problem as established in Ashtari and Schneider, JFM (2023). The approach minimises…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a strong convexity property, then the theory yields convergence for…
We present a set-oriented graph-based computational framework for continuous-time optimal transport over nonlinear dynamical systems. We recover provably optimal control laws for steering a given initial distribution in phase space to a…
In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…
While many techniques have been developed for chance constrained stochastic optimal control with Gaussian disturbance processes, far less is known about computationally efficient methods to handle non-Gaussian processes. In this paper, we…
We propose a control-oriented optimal experimental design (cOED) approach for linear PDE-constrained Bayesian inverse problems. In particular, we consider optimal control problems with uncertain parameters that need to be estimated by…
We introduce ODE-GS, a novel approach that integrates 3D Gaussian Splatting with latent neural ordinary differential equations (ODEs) to enable future extrapolation of dynamic 3D scenes. Unlike existing dynamic scene reconstruction methods,…
Reliable controllers with high flexibility and performance are necessary for the control of intricate, advanced, and expensive systems such as aircraft, marine vessels, automotive vehicles, and satellites. Meanwhile, control allocation has…
We propose joining a flexible mesh design with an integrated residual transcription in order to improve the accuracy of numerical solutions to optimal control problems. This approach is particularly useful when state or input trajectories…
The paper concerns optimal control of discontinuous differential inclusions of the normal cone type governed by a generalized version of the Moreau sweeping process with control functions acting in both nonconvex moving sets and additive…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…
This study proposes an extension of the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulation in an arbitrary Lagrangian-Eulerian (ALE) formulation in unstructured mesh. The ALE method is achieved by subdividing…
3D Gaussian Splatting has shown remarkable capabilities in novel view rendering tasks and exhibits significant potential for multi-view optimization.However, the original 3D Gaussian Splatting lacks color representation for inputs in…
In this paper we study a distributed optimal control problem for a nonlocal convective Cahn--Hilliard equation with degenerate mobility and singular potential in three dimensions of space. While the cost functional is of standard tracking…
Stochastic nested optimization, including stochastic compositional, min-max and bilevel optimization, is gaining popularity in many machine learning applications. While the three problems share the nested structure, existing works often…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal…