相关论文: SPIRAL: An Efficient Algorithm for the Integration…

The SecularMultiple code, presented in two previous papers of this series, integrates the long-term dynamical evolution of multiple systems with any number of bodies and hierarchical structure, provided that the system is composed of nested…

We present a method for efficient differentiable simulation of articulated bodies. This enables integration of articulated body dynamics into deep learning frameworks, and gradient-based optimization of neural networks that operate on…

Three-dimensional rigid-body transforms, i.e. rotations and translations, are central to modern differentiable machine learning pipelines in robotics, vision, and simulation. However, numerically robust and mathematically correct…

This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…

For many problems, some of which are reviewed in the paper, popular algorithms like Douglas--Rachford (DR), ADMM, and FISTA produce approximating sequences that show signs of spiraling toward the solution. We present a meta-algorithm that…

Simulation engines are widely adopted in robotics. However, they lack either full simulation control, ROS integration, realistic physics, or photorealism. Recently, synthetic data generation and realistic rendering has advanced tasks like…

Interventional C-arm systems allow flexible 2-D imaging of a 3-D scene while being capable of cone beam computed tomography. Due to the flexible structure of the C-arm, the rotation speed is limited, increasing the acquisition time compared…

We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…

We propose an algorithm for rotational sparse coding along with an efficient implementation using steerability. Sparse coding (also called dictionary learning) is an important technique in image processing, useful in inverse problems,…

Learning dexterous and agile policy for humanoid and dexterous hand control requires large-scale demonstrations, but collecting robot-specific data is prohibitively expensive. In contrast, abundant human motion data is readily available…

The conventional spin dynamics simulations are performed in direct products of state spaces of individual spins. In a general system of n spins, the total number of elements in the state basis is >4^n. A system propagation step requires an…

This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…

We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…

Simflowny is an open platform which automatically generates efficient parallel code of scientific dynamical models for different simulation frameworks. Here we present major upgrades on this software to support simultaneously a quite…

Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…

By combining a standard symmetric, symplectic integrator with a new step size controller, we provide an integration scheme that is symmetric, reversible and conserves the values of the constants of motion. This new scheme is appropriate for…

Granular materials are of critical interest to many robotic tasks in planetary science, construction, and manufacturing. However, the dynamics of granular materials are complex and often computationally very expensive to simulate. We…

The phase-integral method (PIM) is an asymptotic method of the geometrical optics or semi-classical type for solving approximately, but in many cases very accurately, a wide class of differential equations in physics. Unlike the related…

For many applications of pulsed radiation, the time-history of the radiation intensity must be optimized to induce a desired time-history of conditions. This optimization is normally performed using multi-physics simulations of the system.…

We consider the problem of numerically integrating functions with hyperplane discontinuities over the entire Euclidean space in many dimensions. We describe a simple process through which the Euclidean space is partitioned into simplices on…