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Semi-lagrangian schemes for discretization of the dynamic programming principle are based on a time discretization projected on a state-space grid. The use of a structured grid makes this approach not feasible for high-dimensional problems…

Reconstructing category-specific objects using Neural Radiance Field (NeRF) from a single image is a promising yet challenging task. Existing approaches predominantly rely on projection-based feature retrieval to associate 3D points in the…

Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…

One of the most popular methods employed in computational electromagnetics is the Finite Difference Time Domain (FDTD) method. We generalise it to a meshless setting using the Radial Basis Function generated Finite Difference (RBF-FD)…

In this paper, we present a dimension reduction method to reduce the dimension of parameter space and state space and efficiently solve inverse problems. To this end, proper orthogonal decomposition (POD) and radial basis function (RBF) are…

In this work, the divergence and curl operators are obtained using the coordinate free non rigid basis formulation of differential geometry. Although the authors have attempted to keep the presentation self-contained as much as possible,…

This paper presents the rigorous mathematical construction and foundational properties of the Divergence-Free Radiant Transform (DFRT), a spectral transform specifically designed for divergence-free vector fields, with applications in…

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…

Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…

Variational (Rayleigh-Ritz) methods are applied to local quantum field theory. For scalar theories the wave functional is parametrized in the form of a superposition of Gaussians and the expectation value of the Hamiltonian is expressed in…

We introduce a new local meshfree method for the approximation of the Laplace-Beltrami operator on a smooth surface of co-dimension one embedded in $\R^3$. A key element of this method is that it does not need an explicit expression of the…

Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…

The radial basis function (RBF) method is used for the numerical solution of the Poisson problem in high dimension. The approximate solution can be found by solving a large system of linear equations. Here we investigate the extent to which…

Random Fourier Features (RFF) is among the most popular and broadly applicable approaches for scaling up kernel methods. In essence, RFF allows the user to avoid costly computations on a large kernel matrix via a fast randomized…

There is currently a huge effort to understand the potential and limitations of variational quantum machine learning (QML) based on the optimization of parameterized quantum circuits. Recent proposals toward dequantizing variational QML…

In probability theory, the partition function is a factor used to reduce any probability function to a density function with total probability of one. Among other statistical models used to represent joint distribution, Markov random fields…

Fluid-Structure Interaction (FSI) can be investigated by means of non-linear Finite Element Models (FEM), suitable to capture large deflections of structural parts interacting with fluids, and Computational Fluid Dynamics (CFD). High…

This paper studies the numerical approximation of divergence-free vector fields by linearized shallow neural networks, also referred to as random feature models or finite neuron spaces. Combining the stable potential lifting for…

We present adaptive finite difference ENO/WENO methods by adopting infinitely smooth radial basis functions (RBFs). This is a direct extension of the non-polynomial finite volume ENO/WENO method proposed by authors in \cite{GuoJung} to the…

This paper presents an adaptive hyperviscosity stabilisation procedure for the Radial Basis Function-generated Finite Difference (RBF-FD) method, aimed at solving linear and non-linear advection-dominated transport equations on domains…