Related papers: Partition of unity interpolation using stable kern…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
We propose a Fast Fourier Transform based Periodic Interpolation Method (FFT-PIM), a flexible and computationally efficient approach for computing the scalar potential given by a superposition sum in a unit cell of an infinitely periodic…
Range-based set reconciliation is a simple approach to efficiently computing the union of two sets over a network, based on recursively partitioning the sets and comparing fingerprints of the partitions to probabilistically detect whether a…
Ray tracing is increasingly utilized in wireless system simulations to estimate channel paths. In large-scale simulations with complex environments, ray tracing at high resolution can be computationally demanding. To reduce the computation,…
The finite difference time domain method is one of the simplest and most popular methods in computational electromagnetics. This work considers two possible ways of generalising it to a meshless setting by employing local radial basis…
Particle-In-Cell codes are widely used for plasma physics simulations. It is often the case that particles within a computational cell need to be split to improve the statistics or, in the case of non-uniform meshes, to avoid the…
Recent developments have made it possible to overcome grid-based limitations of finite difference (FD) methods by adopting the kernel-based meshless framework using radial basis functions (RBFs). Such an approach provides a meshless…
This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…
A key task in quantum computation is the application of a sequence of gates implementing a specific unitary operation. However, the decomposition of an arbitrary unitary operation into simpler quantum gates is a nontrivial problem. Here we…
Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing…
This work describes a method of approximating matrix permanents efficiently using belief propagation. We formulate a probability distribution whose partition function is exactly the permanent, then use Bethe free energy to approximate this…
In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta…
Flux reconstruction provides a framework for solving partial differential equations in which functions are discontinuously approximated within elements. Typically, this is done by using polynomials. Here, the use of radial basis functions…
A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those…
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…
Random feature maps are used to decrease the computational cost of kernel machines in large-scale problems. The Mondrian kernel is one such example of a fast random feature approximation of the Laplace kernel, generated by a computationally…
PDE-constrained optimization problems have been barely solved by radial basis functions (RBFs) methods [Pearson, 2013]. It is well known that RBF methods can attain an exponential rate of convergence when $C^{\infty}$ kernels are used,…
The particle filter (PF) is a powerful inference tool widely used to estimate the filtering distribution in non-linear and/or non-Gaussian problems. To overcome the curse of dimensionality of PF, the block PF (BPF) inserts a blocking step…
We propose some protocols to implement various classes of bipartite unitary operations on two remote parties with the help of repeater nodes in-between. We also present a protocol to implement a single-qubit unitary with parameters…