Related papers: Enhancing Dynamic-Mode Decomposition via Multi-Sca…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
Estimating accurate high-dimensional transformations remains very challenging, especially in a clinical setting. In this paper, we introduce a multiscale parameterization of deformations to enhance registration and atlas estimation in the…
Multiresolution decomposition is commonly understood as a procedure to capture scale-dependent features in random signals. Such methods were first established for image processing and typically rely on raster or regularly gridded data. In…
The data driven extrapolation requires the definition of a functional model depending on the available data and has the application scope of providing reliable predictions on the unknown dynamics. Since data might be scattered, we drive our…
This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action…
Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string,…
We formulate a low-storage method for performing dynamic mode decomposition that can be updated inexpensively as new data become available; this formulation allows dynamical information to be extracted from large datasets and data streams.…
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…
This paper introduces a new series of methods which combine modal decomposition algorithms, such as singular value decomposition and high-order singular value decomposition, and deep learning architectures to repair, enhance, and increase…
Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the Triebel-Lizorkin and Besov spaces on $\R^d$ induced by Hermite expansions can be characterized in…
We present the applications of methods from nonlinear local harmonic analysis for calculations in nonlinear collective dynamics described by different forms of Vlasov-Maxwell-Poisson equations. Our approach is based on methods provided the…
Deep image registration has demonstrated exceptional accuracy and fast inference. Recent advances have adopted either multiple cascades or pyramid architectures to estimate dense deformation fields in a coarse-to-fine manner. However, due…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
In this paper we propose a new adaptive wavelet denoising methodology using complex wavelets. The method is based on a fully Bayesian hierarchical model in the complex wavelet domain that uses a bivariate mixture prior on the wavelet…
Irrespective of the fact that Machine learning has produced groundbreaking results, it demands an enormous amount of data in order to perform so. Even though data production has been in its all-time high, almost all the data is unlabelled,…
Profile decompositions for "critical" Sobolev-type embeddings are established, allowing one to regain some compactness despite the non-compact nature of the embeddings. Such decompositions have wide applications to the regularity theory of…
We consider multilevel decompositions of piecewise constants on simplicial meshes that are stable in $H^{-s}$ for $s\in (0,1)$. Proofs are given in the case of uniformly and locally refined meshes. Our findings can be applied to define…
Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
To solve large-scale or high-resolution topology optimization problem, a novel algorithm is developed based on modified bi-directional evolutionary structure optimization (BESO) and extended finite element method (XFEM). Within XFEM, a set…