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Found 12 papers, 5 papers with code
Implicit Neural Representations and the Algebra of Complex Wavelets
Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains.
High-Rate Phase Association with Travel Time Neural Fields
Existing techniques relying on coarsely approximated, fixed wave speed models fail in this unexplored dense regime where the complexity of unknown wave speed cannot be ignored.
Martian time-series unraveled: A multi-scale nested approach with factorial variational autoencoders
This problem is inherently ill-posed and is further challenged by the variety of timescales exhibited by sources.
An Approximation Theory for Metric Space-Valued Functions With A View Towards Deep Learning
Motivated by the developing mathematics of deep learning, we build universal functions approximators of continuous maps between arbitrary Polish metric spaces $\mathcal{X}$ and $\mathcal{Y}$ using elementary functions between Euclidean spaces as building blocks.
Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation
We conclude by proposing a hypernetwork version of the subfamily of NOs as a surrogate model for the mentioned forward operator.
Unearthing InSights into Mars: Unsupervised Source Separation with Limited Data
Source separation involves the ill-posed problem of retrieving a set of source signals that have been observed through a mixing operator.
Convergence Rates for Learning Linear Operators from Noisy Data
This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces.
Stable reconstruction of simple Riemannian manifolds from unknown interior sources
If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a Riemannian manifold with boundary?
Differential Geometry Analysis of PDEs Metric Geometry
Deep learning architectures for nonlinear operator functions and nonlinear inverse problems
Lastly, we discuss how operator recurrent networks can be viewed as a deep learning analogue to deterministic algorithms such as boundary control for reconstructing the unknown wavespeed in the acoustic wave equation from boundary measurements.
Attention network forecasts time-to-failure in laboratory shear experiments
Our data were generated in a laboratory setting using a biaxial shearing device with granular fault gouge intended to mimic the conditions of tectonic faults.
A non-perturbative approach to computing seismic normal modes in rotating planets
A Continuous Galerkin method-based approach is presented to compute the seismic normal modes of rotating planets.
Computational Physics Earth and Planetary Astrophysics Geophysics 86-08, 86-04, 85-04, 85-08, 85-10, 15A18, 65N25, 65N30
Random mesh projectors for inverse problems
We show that in this case the common approach to directly learn the mapping from the measured data to the reconstruction becomes unstable.
