Related papers: Discovery of physically interpretable wave equatio…
The article explores the acoustic equations in inhomogeneous media and the linearized shallow water equations. Two methods for integrating these equations are proposed. The first method is based on the of the Laplace cascade method, while…
Discovering compact governing equations from experimental observations is one of the defining objectives of quantitative science, yet practical discovery pipelines routinely fail when measurements are noisy, relevant state variables are…
Dielectric is considered in the electric field that has equal to zero the first moment and different from zero the second moment of strength in an equilibrium. The equations of ideal hydrodynamics are obtained in such a field for the case…
We present a lightweight, flexible, and high-performance framework for inferring the properties of gravitational-wave events. By combining likelihood heterodyning, automatically-differentiable and accelerator-compatible waveforms, and…
Recent advances in electron, scanning probe, optical, and chemical imaging and spectroscopy yield bespoke data sets containing the information of structure and functionality of complex systems. In many cases, the resulting data sets are…
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second…
A world-wide array of highly sensitive interferometers stands poised to usher in a new era in astronomy with the first direct detection of gravitational waves. The data from these instruments will provide a unique perspective on extreme…
Continuous gravitational wave signals, like those expected by asymmetric spinning neutron stars, are among the most promising targets for LIGO and Virgo detectors. The development of fast and robust data analysis methods is crucial to…
Time-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective $d$-dimensional spatial domains that share a common $(d-1)$-dimensional interface…
Gravitational waves from a phase transition associated with the generation of the masses of elementary particles are within the reach of future space-based detectors such as LISA. A key determinant of the resulting power spectrum, not…
This is a continuation of our study [Uhlmann-Zhai, JMPA, 2021] on an inverse boundary value problem for a nonlinear elastic wave equation. We prove that all the linear and nonlinear coefficients can be recovered from the…
We introduce a "loosely coherent" method for detection of continuous gravitational waves that bridges the gap between semi-coherent and purely coherent methods. Explicit control over accepted families of signals is used to increase…
A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…
The search for solutions to the theory of weakly non-linear internal gravity wave turbulence is an active research topic. It is notably stimulated by the fact that this regime could drive fine-scale ocean dynamics for which the…
The interaction of a gravitational wave (GW) with an elastic body is usually described in terms of a GW "force" driving the oscillations of the body's normal modes. However, this description is only possible for GW frequencies for which the…
The purpose of this mock data and science challenge is to prepare the data analysis and science interpretation for the second generation of gravitational-wave experiments Advanced LIGO-Virgo in the search for a stochastic gravitational-wave…
We propose a flexible yet interpretable model for high-dimensional data with time-varying second order statistics, motivated and applied to functional neuroimaging data. Motivated by the neuroscience literature, we factorize the covariances…
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…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
Many real-world systems can be described by mathematical models that are human-comprehensible, easy to analyze and help explain the system's behavior. Symbolic regression is a method that can automatically generate such models from data.…