Related papers: A holistic approach to computing first-arrival tra…
In this paper, a new weighted first-order formulation is proposed for solving the anisotropic diffusion equations with deep neural networks. For many numerical schemes, the accurate approximation of anisotropic heat flux is crucial for the…
First formulated by Sir Isaac Newton in his work "Philosophiae Naturalis Principia Mathematica", the concept of the Three-Body Problem was put forth as a study of the motion of the three celestial bodies within the Earth-Sun-Moon system. In…
Seismic tomography has long been an effective tool for constructing reliable subsurface structures. However, simultaneous inversion of P- and S-wave velocities presents a significant challenge for conventional seismic tomography methods,…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
This paper proposes a novel inverse kinematics (IK) solver of articulated robotic systems for path planning. IK is a traditional but essential problem for robot manipulation. Recently, data-driven methods have been proposed to quickly solve…
Constrained Motion Planning (CMP) aims to find a collision-free path between the given start and goal configurations on the kinematic constraint manifolds. These problems appear in various scenarios ranging from object manipulation to…
The paper represents an algorithm for planning safe and optimal routes for transport facilities with unrestricted movement direction that travel within areas with obstacles. Paper explains the algorithm using a ship as an example of such a…
The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…
Recently, message-passing graph neural networks (MPNNs) have shown potential for solving combinatorial and continuous optimization problems due to their ability to capture variable-constraint interactions. While existing approaches leverage…
Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…
We apply physics-informed machine learning (PIML) to solve inverse problems in holography and classical mechanics, focusing on neural ordinary differential equations (Neural ODEs) and physics-informed neural networks (PINNs) for solving…
The derivation by Alan Hodgkin and Andrew Huxley of their famous neuronal conductance model relied on experimental data gathered using neurons of the giant squid. It becomes clear that determining experimentally the conductances of neurons…
We review some recent work in fast, efficient and accurate methods to compute viscosity solutions and non-viscosity solutions to static Hamilton-Jacobi equations which arise in optimal control, anisotropic front propagation, and multiple…
This paper studies path synthesis for nonholonomic mobile robots moving in two-dimensional space. We first address the problem of interpolating paths expressed as sequences of straight line segments, such as those produced by some planning…
Various traditional numerical methods for solving initial value problems of differential equations often produce local solutions near the initial value point, despite the problems having larger interval solutions. Even current popular…
In this work we present an application of modern deep learning methodologies to the numerical solution of partial differential equations in transport models. More specifically, we employ a supervised deep neural network that takes into…
The ARRIVAL problem is to decide the fate of a train moving along the edges of a directed graph, according to a simple (deterministic) pseudorandom walk. The problem is in $NP \cap coNP$ but not known to be in $P$. The currently best…
We present a scalable algorithm for solving the transport equation in two and three spatial dimensions for variable grid sizes and discrete velocities on a fault-tolerant universal quantum computer. As a proof of concept of our quantum…
Topological solitons, which are stable, localized solutions of nonlinear differential equations, are crucial in various fields of physics and mathematics, including particle physics and cosmology. However, solving these solitons presents…
We propose a volumetric formulation for computing the Optimal Transport problem defined on surfaces in $\mathbb{R}^3$, found in disciplines like optics, computer graphics, and computational methodologies. Instead of directly tackling the…