Related papers: Efficient Computation of Higher-Order Variational …
We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of…
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. Variational integrators are an important class of geometric integrators. The general idea…
We present both the Lagrangian and Hamiltonian procedures for treating higher-order equations of motion for mechanical models by adopting the Riemann-Liouville Fractional integral to describe their action. We point out and discuss its…
A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…
The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schr\"{o}dinger equations. However, when applied to certain nonlinear time-dependent Schr\"{o}dinger equations, this algorithm loses…
The dynamic formulation of optimal transport has attracted growing interests in scientific computing and machine learning, and its computation requires to solve a PDE-constrained optimization problem. The classical Eulerian discretization…
The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover,…
We are considering differential-algebraic equations with embedded optimization criteria (DAEOs) in which the embedded optimization problem is solved by global optimization. This actually leads to differential inclusions for cases in which…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
This research explores the development and application of the High-Order Dynamic Integration Method for solving integro-differential equations, with a specific focus on turbulent fluid dynamics. Traditional numerical methods, such as the…
Gradient-descent based iterative algorithms pervade a variety of problems in estimation, prediction, learning, control, and optimization. Recently iterative algorithms based on higher-order information have been explored in an attempt to…
We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…
An algorithm for planning near time-optimal trajectories for systems with an oscillatory internal dynamics has been developed in previous work. It is based on assembling a complete trajectory from motion primitives called jerk segments,…
Optimal control in general, and flatness-based control in particular, of robotic arms necessitate to compute the first and second time derivatives of the joint torques/forces required to achieve a desired motion. In view of the required…
A transient magneto-quasistatic vector potential formulation involving nonlinear material is spatially discretized using the finite element method of first and second polynomial order. By applying a generalized Schur complement the…
Providing smooth reference trajectories can effectively increase performance and accuracy of tracking control applications while overshoot and unwanted vibrations are reduced. Trajectory planning computations can often be simplified…
We introduce Spiral, a third-order integration algorithm for the rotational motion of extended bodies. It requires only one force calculation per time step, does not require quaternion normalization at each time step, and can be formulated…
In this paper, we present a new adaptive rank approximation technique for computing solutions to the high-dimensional linear kinetic transport equation. The approach we propose is based on a macro-micro decomposition of the kinetic model in…
Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…