Related papers: Variational Integrators and Graph-Based Solvers fo…
In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the…
Differentiable physics simulation provides an avenue to tackle previously intractable challenges through gradient-based optimization, thereby greatly improving the efficiency of solving robotics-related problems. To apply differentiable…
A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in…
In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques…
Potential disagreement in the result induced by discontinuities is revealed in this paper between a novel power system transient simulation scheme using numerical integrators considering second order derivative and conventional ones using…
Real-world multibody systems are often subject to phenomena like friction, joint clearances, and external events. These phenomena can significantly impact the optimal design of the system and its controller. This work addresses the…
This paper invites the reader to experiment with an easy-to-use MATLAB implementation of Metropolis integrators for Molecular Dynamics (MD) simulation. These integrators are analysis-based, in the sense that they can rigorously simulate…
The development of physical simulators, called Ising machines, that sample from low energy states of the Ising Hamiltonian has the potential to drastically transform our ability to understand and control complex systems. However, most of…
Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to the…
The stability of integrators dealing with high order Differential Algebraic Equations (DAEs) is a major issue. The usual procedures give rise to instabilities that are not predicted by the usual linear analysis, rendering the common checks…
Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We…
We present a new time integrator for articulated body dynamics. We formulate the governing equations of the dynamics using only the position variables and recast the position-based articulated dynamics as an optimization problem. Our…
A fixed time-step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive…
Building upon recent developments of force-based estimators with a reduced variance for the computation of densities, radial distribution functions or local transport properties from molecular simulations, we show that the variance can be…
We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire…
An articulated body is defined as a finite number of rigid bodies connected by a set of arbitrary constraints that limit the relative motion between pairs of bodies. Such a general definition encompasses a wide variety of situations in the…
The standard paradigm for state preparation on quantum computers for the simulation of physical systems in the near term has been widely explored with different algorithmic methods. One such approach is the optimization of parameterized…
We study numerically classical 1-dimensional Hamiltonian lattices involving inter-particle long range interactions that decay with distance like 1/r^alpha, for alpha>=0. We demonstrate that although such systems are generally characterized…
Nonlinear programming targets nonlinear optimization with constraints, which is a generic yet complex methodology involving humans for problem modeling and algorithms for problem solving. We address the particularly hard challenge of…
Collaborative robots should ideally use low torque actuators for passive safety reasons. However, some applications require these collaborative robots to reach deep into confined spaces while assisting a human operator in physically…