Eli Turkel
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Attention-based hybrid solvers for linear equations that are geometry aware Open
We present a novel architecture for learning geometry-aware preconditioners for linear partial differential equations (PDEs). We show that a deep operator network (Deeponet) can be trained on a simple geometry and remain a robust precondit…
Fourth-Order Accurate Compact Scheme for First-Order Maxwell’s Equations Open
We construct a compact fourth-order scheme, in space and time, for the time-dependent Maxwell’s equations given as a first-order system on a staggered (Yee) grid. At each time step, we update the fields by solving positive definite second-…
Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problem Open
Three-dimensional target identification using scattering techniques requires high accuracy solutions and very fast computations for real-time predictions in some critical applications. We first train a deep neural operator~(DeepONet) to so…
Real-time Inference and Extrapolation via a Diffusion-inspired Temporal Transformer Operator (DiTTO) Open
Extrapolation remains a grand challenge in deep neural networks across all application domains. We propose an operator learning method to solve time-dependent partial differential equations (PDEs) continuously and with extrapolation in tim…
ViTO: Vision Transformer-Operator Open
We combine vision transformers with operator learning to solve diverse inverse problems described by partial differential equations (PDEs). Our approach, named ViTO, combines a U-Net based architecture with a vision transformer. We apply V…
Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers Open
Neural networks suffer from spectral bias having difficulty in representing the high frequency components of a function while relaxation methods can resolve high frequencies efficiently but stall at moderate to low frequencies. We exploit …
Comparison of the FWI-Adjoint and Time Reversal Methods for the Identification of Elastic Scatterers Open
The paper falls into the category of computational methods for inverse scattering techniques for the identification of scatterers. We consider a linear elastodynamic problem and compare two popular methods for identifying a scatterer in th…
A physically-informed Deep-Learning approach for locating sources in a waveguide Open
Inverse source problems are central to many applications in acoustics, geophysics, non-destructive testing, and more. Traditional imaging methods suffer from the resolution limit, preventing distinction of sources separated by less than th…
A Convolutional Dispersion Relation Preserving Scheme for the Acoustic Wave Equation Open
We propose an accurate numerical scheme for approximating the solution of the two dimensional acoustic wave problem. We use machine learning to find a stencil suitable even in the presence of high wavenumbers. The proposed scheme incorpora…
Non-iterative domain decomposition for the Helmholtz equation using the method of difference potentials Open
We use the Method of Difference Potentials (MDP) to solve a non-overlapping domain decomposition formulation of the Helmholtz equation. The MDP reduces the Helmholtz equation on each subdomain to a Calderon's boundary equation with project…
Non-iterative domain decomposition for the Helmholtz equation using the\n method of difference potentials Open
We use the Method of Difference Potentials (MDP) to solve a non-overlapping\ndomain decomposition formulation of the Helmholtz equation. The MDP reduces the\nHelmholtz equation on each subdomain to a Calderon's boundary equation with\nproj…
Algorithmic handwriting analysis of the Samaria inscriptions illuminates bureaucratic apparatus in biblical Israel Open
Past excavations in Samaria, capital of biblical Israel, yielded a corpus of Hebrew ink on clay inscriptions (ostraca) that documents wine and oil shipments to the palace from surrounding localities. Many questions regarding these early 8t…
Multispectral imaging reveals biblical-period inscription unnoticed for half a century Open
Most surviving biblical period Hebrew inscriptions are ostraca-ink-on-clay texts. They are poorly preserved and once unearthed, fade rapidly. Therefore, proper and timely documentation of ostraca is essential. Here we show a striking examp…
Autonomous Vehicles in Delaware: Analyzing the Impact and Readiness for the First State Open
The sci-fi reality of self-driving, networked, autonomous vehicles is nearly here. Ford claims it will sell these vehicles within five years, and most analysts expect modest sale numbers by the late 2020s and widespread adoption throughout…
Algorithmic handwriting analysis of Judah’s military correspondence sheds light on composition of biblical texts Open
Significance Scholars debate whether the first major phase of compilation of biblical texts took place before or after the destruction of Jerusalem in 586 BCE. Proliferation of literacy is considered a precondition for the creation of such…