Related papers: Fast Hyperbolic Wavelet Regression meets ANOVA
We introduce a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$ - $\Omega$ a…
Collective variable-based enhanced sampling methods are routinely used on systems with metastable states, where high free energy barriers impede proper sampling of the free energy landscapes when using conventional molecular dynamics…
Hyperbolic manifolds for visual representation learning allow for effective learning of semantic class hierarchies by naturally embedding tree-like structures with low distortion within a low-dimensional representation space. The highly…
We propose two algorithms for boosting random Fourier feature models for approximating high-dimensional functions. These methods utilize the classical and generalized analysis of variance (ANOVA) decomposition to learn low-order functions,…
A system of high-order adaptive multiresolution wavelet collocation upwind schemes are developed for the solution of hyperbolic conservation laws. A couple of asymmetrical wavelet bases with interpolation property are built to realize the…
In this paper we consider the reconstruction problem of photoacoustic tomography (PAT) with a flat observation surface. We develop a direct reconstruction method that employs regularization with wavelet sparsity constraints. To that end, we…
This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for…
We study the numerical integration problem for functions with infinitely many variables. The function spaces of integrands we consider are weighted reproducing kernel Hilbert spaces with norms related to the ANOVA decomposition of the…
In the present paper we consider the problem of estimating a periodic $(r+1)$-dimensional function $f$ based on observations from its noisy convolution. We construct a wavelet estimator of $f$, derive minimax lower bounds for the $L^2$-risk…
Generating highly detailed, complex data is a long-standing and frequently considered problem in the machine learning field. However, developing detail-aware generators remains an challenging and open problem. Generative adversarial…
Diffusion models are rising as a powerful solution for high-fidelity image generation, which exceeds GANs in quality in many circumstances. However, their slow training and inference speed is a huge bottleneck, blocking them from being used…
The length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine learning algorithms to develop…
This paper argues that curvelets provide a powerful tool for representing very general linear symmetric systems of hyperbolic differential equations. Curvelets are a recently developed multiscale system in which the elements are highly…
In this work we present an adaptive boundary element method for computing the electromagnetic response of wave interactions in hyperbolic metamaterials. One unique feature of hyperbolic metamaterial is the strongly directional wave in its…
Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…
We consider a variant of regression problem, where the correspondence between input and output data is not available. Such shuffled data is commonly observed in many real world problems. Taking flow cytometry as an example, the measuring…
A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive…
We develop an adjoint approach for recovering the topographical function included in the source term of one-dimensional hyperbolic balance laws. We focus on a specific system, namely the shallow water equations, in an effort to recover the…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…
In this work, we consider the approximate reconstruction of high-dimensional periodic functions based on sampling values. As sampling schemes, we utilize so-called reconstructing multiple rank-1 lattices, which combine several preferable…