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In many recent applications when new materials and technologies are developed it is important to describe and simulate new nonlinear and nonlocal diffusion transport processes. A general class of such models deals with nonlocal fractional…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
We develop a weak adversarial approach to solving obstacle problems using neural networks. By employing (generalised) regularised gap functions and their properties we rewrite the obstacle problem (which is an elliptic variational…
We develop a single pass method for approximating the solution to an anisotropic eikonal equation related to the anisotropic min-time optimal trajectory problem. Ordered Upwind Method (OUM) solves this equation, which is a single-pass…
Motion Planning (MP) is a critical challenge in robotics, especially pertinent with the burgeoning interest in embodied artificial intelligence. Traditional MP methods often struggle with high-dimensional complexities. Recently neural…
We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., $\ell^1$ or $\ell^2$, such functionals provide more flexibility and allow…
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, and so on. Recently, a new splitting approach has been…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
The three body problem is a special case of the n body problem where one takes the initial positions and velocities of three point masses and attempts to predict their motion over time according to Newtonian laws of motion and universal…
This study presents deep neural network solutions to a time-integrated Smoluchowski equation modeling the mean first passage time of nanoparticles traversing the slit-well microfluidic device. This physical scenario is representative of a…
Computing shortest paths is one of the most researched topics in algorithm engineering. Currently available algorithms compute shortest paths in mere fractions of a second on continental sized road networks. In the presence of…
This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…
We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining…
In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…
In this paper we use a Variational Quantum Algorithm to solve Initial Value Problems with the Implicit Crank-Nicolson and the Method of Lines (MoL) evolution schemes. The unknown functions use a spectral decomposition with the Fourier…
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…
We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the boundary (or initial) conditions…
Travel time tomography for the velocity structure of a medium is a highly non-linear and non-unique inverse problem. Monte Carlo methods are becoming increasingly common choices to provide probabilistic solutions to tomographic problems but…
The variational principle serves as a fundamental framework for describing equilibrium states of physical systems via the minimization or extremization of an energy-like functional. While quantum algorithms have demonstrated promising…
This paper presents a data driven universal ball trajectory prediction method integrated with physics equations. Existing methods are designed for specific ball types and struggle to generalize. This challenge arises from three key factors.…