相关论文: Affine differential geometry and smoothness maximi…

Deep learning optimization exhibits structure that is not captured by worst-case gradient bounds. Empirically, gradients along training trajectories are often temporally predictable and evolve within a low-dimensional subspace. In this work…

The generation of 3D molecules requires simultaneously deciding the categorical features~(atom types) and continuous features~(atom coordinates). Deep generative models, especially Diffusion Models (DMs), have demonstrated effectiveness in…

Molecular dynamics (MD) has long been the de facto choice for simulating complex atomistic systems from first principles. Recently deep learning models become a popular way to accelerate MD. Notwithstanding, existing models depend on…

Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the…

In this paper we consider discrete gradient methods for approximating the solution and preserving a first integral (also called a constant of motion) of autonomous ordinary differential equations. We prove under mild conditions for a large…

In this paper, we consider the minimization of a $C^2-$smooth and strongly convex objective depending on a given parameter, which is usually found in many practical applications. We suppose that we desire to solve the problem with some…

Single particle tracking allows probing how biomolecules interact physically with their natural environments. A fundamental challenge when analysing recorded single particle trajectories is the inverse problem of inferring the physical…

We present a new method for motion planning for control systems. The method aims to provide a natural computational framework in which a broad class of motion planning problems can be cast; including problems with holonomic and…

Recently, it has been shown that Absolute Parallelism (AP) geometry admits paths that are naturally quantized. These paths have been used to describe the motion of spinning particles in a background gravitational field. In case of a weak…

To reduce the computational cost of humanoid motion generation, we introduce a new approach to representing robot kinematic reachability: the differentiable reachability map. This map is a scalar-valued function defined in the task space…

Using the method of moving frames we analyze the algebra of differential invariants for surfaces in three-dimensional affine geometry. For elliptic, hyperbolic, and parabolic points, we show that if the algebra of differential invariants is…

This paper is concerned with determining the shortest path for a pursuer aiming to intercept a moving target travelling at a constant speed. To address this challenge, we introduce an efficient mathematical model outlined as an optimal…

Implicit Neural Representations (INRs) have emerged as a powerful tool for geometric representation, yet their suitability for physics-based simulation remains underexplored. While metrics like Hausdorff distance quantify surface…

A $\mathit{\text{moving frame}}$ at a rational curve is a basis of vectors moving along the curve. When the rational curve is given parametrically by a row vector $\mathbf{a}$ of univariate polynomials, a moving frame with important…

Joint space trajectory optimization under end-effector task constraints leads to a challenging non-convex problem. Thus, a real-time adaptation of prior computed trajectories to perturbation in task constraints often becomes intractable.…

The performance of optimization-based robot motion planning algorithms is highly dependent on the initial solutions, commonly obtained by running a sampling-based planner to obtain a collision-free path. However, these methods can be slow…

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…

Shape matching has been a long-studied problem for the computer graphics and vision community. The objective is to predict a dense correspondence between meshes that have a certain degree of deformation. Existing methods either consider the…

We study invariant surfaces generated by one-parameter subgroups of simply and pseudo isotropic rigid motions. Basically, the simply and pseudo isotropic geometries are the study of a three-dimensional space equipped with a rank 2 metric of…

We present a new microscopic ODE-based model for pedestrian dynamics: the Gradient Navigation Model. The model uses a superposition of gradients of distance functions to directly change the direction of the velocity vector. The velocity is…