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Learning a continuous and reliable representation of physical fields from sparse sampling is challenging and it affects diverse scientific disciplines. In a recent work, we present a novel model called MMGN (Multiplicative and Modulated Gabor Network) with implicit neural networks. In this work, we design additional studies leveraging explainability methods to complement the previous experiments and further enhance the understanding of latent representations generated by the model. The adopted methods are general enough to be leveraged for any latent space inspection. Preliminary results demonstrate the contextual information incorporated in the latent representations and their impact on the model performance. As a work in progress, we will continue to verify our findings and develop novel explainability approaches.

Reliably reconstructing physical fields from sparse sensor data is a challenge that frequently arises in many scientific domains. In practice, the process generating the data often is not understood to sufficient accuracy. Therefore, there is a growing interest in using the deep neural network route to address the problem. This work presents a novel approach that learns a continuous representation of the physical field using implicit neural representations (INRs). Specifically, after factorizing spatiotemporal variability into spatial and temporal components using the separation of variables technique, the method learns relevant basis functions from sparsely sampled irregular data points to develop a continuous representation of the data. In experimental evaluations, the proposed model outperforms recent INR methods, offering superior reconstruction quality on simulation data from a state-of-the-art climate model and a second dataset that comprises ultra-high resolution satellite-based sea surface temperature fields., Comment: 25 pages,21 figures

Modeling is crucial to understanding the effect of greenhouse gases, warming, and ice sheet melting on the ocean. At the same time, ocean processes affect phenomena such as hurricanes and droughts. Parameters in the models that cannot be physically measured have a significant effect on the model output. For an idealized ocean model, we generated perturbed parameter ensemble data and trained surrogate neural network models. The neural surrogates accurately predicted the one-step forward dynamics, of which we then computed the parametric sensitivity.

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims to explain the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM's quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations., Comment: ACM Transactions on Quantum Computing

We present a new clustering algorithm that is based on searching for natural gaps in the components of the lowest energy eigenvectors of the Laplacian of a graph. In comparing the performance of the proposed method with a set of other popular methods (KMEANS, spectral-KMEANS, and an agglomerative method) in the context of the Lancichinetti-Fortunato-Radicchi (LFR) Benchmark for undirected weighted overlapping networks, we find that the new method outperforms the other spectral methods considered in certain parameter regimes. Finally, in an application to climate data involving one of the most important modes of interannual climate variability, the El Nino Southern Oscillation phenomenon, we demonstrate the ability of the new algorithm to readily identify different flavors of the phenomenon., Comment: 12 pages, 9 figures

We study the modulational instability of geophysical Rossby and plasma drift waves within the Charney-Hasegawa-Mima (CHM) model both theoretically, using truncated (four-mode and three-mode) models, and numerically, using direct simulations of CHM equation in the Fourier space. The linear theory predicts instability for any amplitude of the primary wave. For strong primary waves the most unstable modes are perpendicular to the primary wave, which correspond to generation of a zonal flow if the primary wave is purely meridional. For weaker waves, the maximum growth occurs for off-zonal inclined modulations. For very weak primary waves the unstable waves are close to being in three-wave resonance with the primary wave. The nonlinear theory predicts that the zonal flows generated by the linear instability experience pinching into narrow zonal jets. Our numerical simulations confirm the theoretical predictions of the linear theory as well as of the nonlinear pinching. We find that, for strong primary waves, these narrow zonal jets further roll up into Karman-like vortex streets. On the other hand, for weak primary waves, the growth of the unstable mode reverses and the system oscillates between a dominant jet and a dominate primary wave. The 2D vortex streets appear to be more stable than purely 1D zonal jets, and their zonal-averaged speed can reach amplitudes much stronger than is allowed by the Rayleigh-Kuo instability criterion for the 1D case. We find that the truncation models work well for both the linear stage and and often even for the medium-term nonlinear behavior. In the long term, the system transitions to turbulence helped by the vortex-pairing instability (for strong waves) and by the resonant wave-wave interactions (for weak waves)., Comment: 26 pages, 30 figures

We find that in parameter regimes relevant to the recently observed alternating zonal jets in oceans, the formation of these jets can be explained as due to an arrest of the turbulent inverse-cascade of energy by {\em free} Rossby waves (as opposed to Rossby {\em basin} modes) and a subsequent redirection of that energy into zonal modes. This mechanism, originally studied in the context of alternating jets in Jovian atmospheres and two dimensional turbulence in zonally-periodic configurations survives in spite of the presence of the meridional boundaries in the oceanic context.

For a particular choice of the smoothing kernel, it is shown that the system of partial differential equations governing the vortex-blob method corresponds to the averaged Euler equations. These latter equations have recently been derived by averaging the Euler equations over Lagrangian fluctuations of length scale $\a$, and the same system is also encountered in the description of inviscid and incompressible flow of second-grade polymeric (non-Newtonian) fluids. While previous studies of this system have noted the suppression of nonlinear interaction between modes smaller than $\a$, we show that the modification of the nonlinear advection term also acts to enhance the inverse-cascade of energy in two-dimensional turbulence and thereby affects scales of motion larger than $\a$ as well. This latter effect is reminiscent of the drag-reduction that occurs in a turbulent flow when a dilute polymer is added.

A new discrete-velocity model is presented to solve the three-dimensional Euler equations. The velocities in the model are of an adaptive nature---both the origin of the discrete-velocity space and the magnitudes of the discrete-velocities are dependent on the local flow--- and are used in a finite volume context. The numerical implementation of the model follows the near-equilibrium flow method of Nadiga and Pullin [1] and results in a scheme which is second order in space (in the smooth regions and between first and second order at discontinuities) and second order in time. (The three-dimensional code is included.) For one choice of the scaling between the magnitude of the discrete-velocities and the local internal energy of the flow, the method reduces to a flux-splitting scheme based on characteristics. As a preliminary exercise, the result of the Sod shock-tube simulation is compared to the exact solution., Comment: 17 pages including 2 figures and CMFortran code listing. All in one postscript file (adv.ps) compressed and uuencoded (adv.uu). Name mail file `adv.uu'. Edit so that `#!/bin/csh -f' is the first line of adv.uu On a unix machine say `csh adv.uu'. On a non-unix machine: uudecode adv.uu; uncompress adv.tar.Z; tar -xvf adv.tar

We present a simulation scheme for discrete-velocity gases based on {\em local thermodynamic equilibrium}. Exploiting the kinetic nature of discrete-velocity gases, in that context, results in a natural splitting of fluxes, and the resultant scheme strongly resembles the original processes. The kinetic nature of the scheme and the modeling of the {\em infinite collision rate} limit, result in a small value of the coefficient of (numerical)-viscosity, the behavior of which is remarkably physical [18]. A first order method, and two second order methods using the total variation diminishing principle are developed and an example application presented. Given the same computer resources, it is expected that with this approach, much higher Reynold's number will be achievable than presently possible with either lattice gas automata or lattice Boltzmann approaches. The ideas being general, the scheme is applicable to any discrete-velocity model, and to lattice gases as well., Comment: 19 pages including 4 figures. All in one postscript file (flw.ps) compressed and uuencoded (flw.uu). Name mail file `flw.uu'. Edit so that `#!/bin/csh -f' is the first line of flw.uu On a unix machine say `csh flw.uu'. On a non-unix machine: uudecode flw.uu; uncompress flw.tar.Z; tar -xvf flw.tar

The exact structure of a shock is computed in a multiple-speed discrete-velocity gas, the nine-velocity gas, wherein the multiplicity of speeds ensures nontrivial thermodynamics. Obtained as a solution of the model Boltzmann equations, the procedure consists of tracking the shock as a trajectory of a three dimensional dynamical system connecting an equilibrium upstream state to an equilibrium downstream state. The two equilibria satisfy the jump conditions obtained from the model Euler equations. Comparison of the shock structure to that in a monatomic perfect gas, as given by the Navier-Stokes equation, shows excellent agreement. The shock in the nine-velocity gas has an overshoot in entropy alone, like in a monatomic gas. The near-equilibrium flow technique for discrete-velocity gases (Nadiga \& Pullin [2]), a kinetic flux-splitting method based on the local thermodynamic equilibrium, is also seen to capture the shock structure remarkably well., Comment: 16 pages including 4 figures and 1 table. All in one postscript file (shck.ps). Compressed and uuencoded (shck.uu). Name mail file `shck.uu'. Edit so that `#!/bin/csh -f' is the first line of shck.uu. On a unix machine say `csh shck.uu'. On a non-unix machine: uudecode adv.uu; uncompress adv.tar.Z; tar -xvf adv.tar