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  1. Abstract

    Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. Achieving this kind of interpretable system identification is even more difficult for partially observed systems. We propose a machine learning framework for discovering the governing equations of a dynamical system using only partial observations, combining an encoder for state reconstruction with a sparse symbolic model. The entire architecture is trained end-to-end by matching the higher-order symbolic time derivatives of the sparse symbolic model with finite difference estimates from the data. Our tests show that this method can successfully reconstruct the full system state and identify the equations of motion governing the underlying dynamics for a variety of ordinary differential equation (ODE) and partial differential equation (PDE) systems.

  2. Abstract

    With the upcoming Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), it is expected that only ∼0.1% of all transients will be classified spectroscopically. To conduct studies of rare transients, such as Type I superluminous supernovae (SLSNe), we must instead rely on photometric classification. In this vein, here we carry out a pilot study of SLSNe from the Pan-STARRS1 Medium Deep Survey (PS1-MDS), classified photometrically with ourSuperRAENNandSuperphotalgorithms. We first construct a subsample of the photometric sample using a list of simple selection metrics designed to minimize contamination and ensure sufficient data quality for modeling. We then fit the multiband light curves with a magnetar spin-down model using the Modular Open-Source Fitter for Transients (MOSFiT). Comparing the magnetar engine and ejecta parameter distributions of the photometric sample to those of the PS1-MDS spectroscopic sample and a larger literature spectroscopic sample, we find that these samples are consistent overall, but that the photometric sample extends to slower spins and lower ejecta masses, which correspond to lower-luminosity events, as expected for photometric selection. While our PS1-MDS photometric sample is still smaller than the overall SLSN spectroscopic sample, our methodology paves the way for an orders-of-magnitude increase in the SLSNmore »sample in the LSST era through photometric selection and study.

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  3. ABSTRACT

    Observations of structure at subgalactic scales are crucial for probing the properties of dark matter, which is the dominant source of gravity in the universe. It will become increasingly important for future surveys to distinguish between line-of-sight haloes and subhalos to avoid wrong inferences on the nature of dark matter. We reanalyse a subgalactic structure (in lens JVAS B1938 + 666) that has been previously found using the gravitational imaging technique in galaxy-galaxy lensing systems. This structure has been assumed to be a satellite in the halo of the main lens galaxy. We fit the redshift of the perturber of the system as a free parameter, using the multiplane thin-lens approximation, and find that the redshift of the perturber is $z_\mathrm{int} = 1.42^{+0.10}_{-0.15}$ (with a main lens redshift of z = 0.881). Our analysis indicates that this structure is more massive than the previous result by an order of magnitude. This constitutes the first dark perturber shown to be a line-of-sight halo with a gravitational lensing method.

  4. Abstract

    Photometric pipelines struggle to estimate both the flux and flux uncertainty for stars in the presence of structured backgrounds such as filaments or clouds. However, it is exactly stars in these complex regions that are critical to understanding star formation and the structure of the interstellar medium. We develop a method, similar to Gaussian process regression, which we term local pixel-wise infilling (LPI). Using a local covariance estimate, we predict the background behind each star and the uncertainty of that prediction in order to improve estimates of flux and flux uncertainty. We show the validity of our model on synthetic data and real dust fields. We further demonstrate that the method is stable even in the crowded field limit. While we focus on optical-IR photometry, this method is not restricted to those wavelengths. We apply this technique to the 34 billion detections in the second data release of the Dark Energy Camera Plane Survey. In addition to removing many >3σoutliers and improving uncertainty estimates by a factor of ∼2–3 on nebulous fields, we also show that our method is well behaved on uncrowded fields. The entirely post-processing nature of our implementation of LPI photometry allows it to easily improvemore »the flux and flux uncertainty estimates of past as well as future surveys.

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  5. Abstract

    In a recent work (Halversonet al2021Mach. Learn.: Sci. Technol.2035002), Halverson, Maiti and Stoner proposed a description of neural networks (NNs) in terms of a Wilsonian effective field theory. The infinite-width limit is mapped to a free field theory while finiteNcorrections are taken into account by interactions (non-Gaussian terms in the action). In this paper, we study two related aspects of this correspondence. First, we comment on the concepts of locality and power-counting in this context. Indeed, these usual space-time notions may not hold for NNs (since inputs can be arbitrary), however, the renormalization group (RG) provides natural notions of locality and scaling. Moreover, we comment on several subtleties, for example, that data components may not have a permutation symmetry: in that case, we argue that random tensor field theories could provide a natural generalization. Second, we improve the perturbative Wilsonian renormalization from Halversonet al(2021Mach. Learn.: Sci. Technol.2035002) by providing an analysis in terms of the non-perturbative RG using the Wetterich-Morris equation. An important difference with usual non-perturbative RG analysis is that only the effective infrared 2-point function is known, which requires setting the problem with care. Our aim is to provide a useful formalism to investigate NNs behavior beyondmore »the large-width limit (i.e. far from Gaussian limit) in a non-perturbative fashion. A major result of our analysis is that changing the standard deviation of the NN weight distribution can be interpreted as a renormalization flow in the space of networks. We focus on translations invariant kernels and provide preliminary numerical results.

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  6. Abstract

    We continue earlier efforts in computing the dimensions of tangent space cohomologies of Calabi–Yau manifolds using deep learning. In this paper, we consider the dataset of all Calabi–Yau four-folds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by state-of-the-art computer vision architectures, we improve earlier benchmarks and demonstrate that all four non-trivial Hodge numbers can be learned at the same time using a multi-task architecture. With 30% (80%) training ratio, we reach an accuracy of 100% forh(1,1)and 97% forh(2,1)(100% for both), 81% (96%) forh(3,1), and 49% (83%) forh(2,2). Assuming that the Euler number is known, as it is easy to compute, and taking into account the linear constraint arising from index computations, we get 100% total accuracy.

  7. Abstract Deep learning techniques have been increasingly applied to the natural sciences, e.g., for property prediction and optimization or material discovery. A fundamental ingredient of such approaches is the vast quantity of labeled data needed to train the model. This poses severe challenges in data-scarce settings where obtaining labels requires substantial computational or labor resources. Noting that problems in natural sciences often benefit from easily obtainable auxiliary information sources, we introduce surrogate- and invariance-boosted contrastive learning (SIB-CL), a deep learning framework which incorporates three inexpensive and easily obtainable auxiliary information sources to overcome data scarcity. Specifically, these are: abundant unlabeled data, prior knowledge of symmetries or invariances, and surrogate data obtained at near-zero cost. We demonstrate SIB-CL’s effectiveness and generality on various scientific problems, e.g., predicting the density-of-states of 2D photonic crystals and solving the 3D time-independent Schrödinger equation. SIB-CL consistently results in orders of magnitude reduction in the number of labels needed to achieve the same network accuracies.
    Free, publicly-accessible full text available December 1, 2023
  8. A bstract Power counting is a systematic strategy for organizing collider observables and their associated theoretical calculations. In this paper, we use power counting to characterize a class of jet substructure observables called energy flow polynomials (EFPs). EFPs provide an overcomplete linear basis for infrared-and-collinear safe jet observables, but it is known that in practice, a small subset of EFPs is often sufficient for specific jet analysis tasks. By applying power counting arguments, we obtain linear relationships between EFPs that hold for quark and gluon jets to a specific order in the power counting. We test these relations in the parton shower generator Pythia, finding excellent agreement. Power counting allows us to truncate the basis of EFPs without affecting performance, which we corroborate through a study of quark-gluon tagging and regression.
    Free, publicly-accessible full text available September 1, 2023
  9. Free, publicly-accessible full text available August 1, 2023
  10. Free, publicly-accessible full text available August 1, 2023