Related papers: Wave Physics-informed Matrix Factorizations
We consider the problem of matrix completion with side information (\textit{inductive matrix completion}). In real-world applications many side-channel features are typically non-informative making feature selection an important part of the…
Existing nonnegative matrix factorization methods focus on learning global structure of the data to construct basis and coefficient matrices, which ignores the local structure that commonly exists among data. In this paper, we propose a new…
Diffusion models are capable of generating photo-realistic images that combine elements which likely do not appear together in the training set, demonstrating the ability to \textit{compositionally generalize}. Nonetheless, the precise…
Full-wave simulations are indispensable for nanophotonics and electromagnetics but are severely constrained on large systems, especially multi-channel ones such as disordered media, aperiodic metasurfaces, and densely packed photonic…
The constant center frequency to bandwidth ratio (Q-factor) of wavelet transforms provides a very natural representation for audio data. However, invertible wavelet transforms have either required non-uniform decimation -- leading to…
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…
Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in…
A prominent goal of representation learning research is to achieve representations which are factorized in a useful manner with respect to the ground truth factors of variation. The fields of disentangled and equivariant representation…
Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…
This study presents PRISM, a probabilistic simplex component analysis approach to identifying the vertices of a data-circumscribing simplex from data. The problem has a rich variety of applications, the most notable being hyperspectral…
We propose a method that meta-learns a knowledge on matrix factorization from various matrices, and uses the knowledge for factorizing unseen matrices. The proposed method uses a neural network that takes a matrix as input, and generates…
We propose a general method for optimizing periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators based on phase reduction and nonlinear programming. We derive averaged phase dynamics from the mathematical…
Biological signals of interest in high-dimensional data are often masked by dominant variation shared across conditions. This variation, arising from baseline biological structure or technical effects, can prevent standard dimensionality…
In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…
Wave equations are fundamental to describing a vast array of physical phenomena, yet their simulation in inhomogeneous media poses a computational challenge due to the highly oscillatory nature of the solutions. To overcome the high costs…
One of the major problems in modeling natural signals is that signals with very similar structure may locally have completely different measurements, e.g., images taken under different illumination conditions, or the speech signal captured…
Modern power systems are now in continuous process of massive changes. Increased penetration of distributed generation, usage of energy storage and controllable demand require introduction of a new control paradigm that does not rely on…
Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization…