Related papers: One or Two Components? The Scattering Transform An…
With the aim of constructing a biologically plausible model of machine listening, we study the representation of a multicomponent stationary signal by a wavelet scattering network. First, we show that renormalizing second-order nodes by…
Recent advances in machine learning establish the ability of certain neural-network architectures called neural operators to approximate maps between function spaces. Motivated by a prospect of employing them in fundamental physics, we…
Patra and Sen (2016) consider a two-component mixture model, where one component plays the role of background while the other plays the role of signal, and propose to estimate the background component by simply "maximizing" its weight.…
In this work, we develop machine learning techniques to study nonperturbative scattering amplitudes. We focus on the two-to-two scattering amplitude of identical scalar particles, setting the double discontinuity to zero as a simplifying…
Scattering methods are widely used in many research areas to analyze and resolve material structures. Given the importance, a large number of full textbooks are devoted to this topic. However, technical details in experiments and…
The Iterative Filtering method is a technique aimed at the decomposition of non-stationary and non-linear signals into simple oscillatory components. This method, proposed a decade ago as an alternative technique to the Empirical Mode…
This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by…
The need of mathematically formulate relations between composite materials' properties and its resonance response is growing. This is due the fast technological advancement in micro-material manufacturing, present in chips for instance. In…
A general machine learning architecture is introduced that uses wavelet scattering coefficients of an inputted three dimensional signal as features. Solid harmonic wavelet scattering transforms of three dimensional signals were previously…
The spatial structure of the inhomogeneity in a disordered medium determines how waves scatter and propagate in it. We present a theoretical model of how the Fourier components of the disorder control wave scattering in a two-dimensional…
We measure the transmission and reflection amplitudes of microwaves in a resonator coupled to two antennas at room temperature in the regime of weakly overlapping resonances and in a frequency range of 3 to 16 GHz. Below 10.1 GHz the…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…
Disentangling and recovering physical attributes, such as shape and material, from a few waveform examples is a challenging inverse problem in audio signal processing, with numerous applications in musical acoustics as well as structural…
This work presents a multiple scattering formulation of two dimensional acoustic metamaterials. It is shown that in the low frequency limit multiple scattering allows us to define frequency-dependent effective acoustic parameters for arrays…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the…
The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…
In this work, we focus on an analogical reasoning task that contains rich compositional structures, Raven's Progressive Matrices (RPM). To discover compositional structures of the data, we propose the Scattering Compositional Learner (SCL),…
A general one-loop scattering amplitude may be expanded in terms of master integrals. The coefficients of the master integrals can be obtained from tree-level input in a two-step process. First, use known formulas to write the coefficients…