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 endtoend by matching the higherorder 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.
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Abstract 
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 PanSTARRS1 Medium Deep Survey (PS1MDS), classified photometrically with our
SuperRAENN andSuperphot algorithms. 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 spindown model using the Modular OpenSource Fitter for Transients (MOSFiT ). Comparing the magnetar engine and ejecta parameter distributions of the photometric sample to those of the PS1MDS 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 lowerluminosity events, as expected for photometric selection. While our PS1MDS photometric sample is still smaller than the overall SLSN spectroscopic sample, our methodology paves the way for an ordersofmagnitude increase in the SLSNmore » 
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 lineofsight 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 galaxygalaxy 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 thinlens 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 lineofsight halo with a gravitational lensing method.

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 pixelwise 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 opticalIR 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 >3
σ outliers 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 postprocessing nature of our implementation of LPI photometry allows it to easily improvemore » 
Abstract In a recent work (Halverson
et al 2021Mach. Learn.: Sci. Technol. 2 035002), Halverson, Maiti and Stoner proposed a description of neural networks (NNs) in terms of a Wilsonian effective field theory. The infinitewidth limit is mapped to a free field theory while finiteN corrections are taken into account by interactions (nonGaussian terms in the action). In this paper, we study two related aspects of this correspondence. First, we comment on the concepts of locality and powercounting in this context. Indeed, these usual spacetime 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. 2 035002) by providing an analysis in terms of the nonperturbative RG using the WetterichMorris equation. An important difference with usual nonperturbative RG analysis is that only the effective infrared 2point function is known, which requires setting the problem with care. Our aim is to provide a useful formalism to investigate NNs behavior beyondmore » 
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 fourfolds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by stateoftheart computer vision architectures, we improve earlier benchmarks and demonstrate that all four nontrivial Hodge numbers can be learned at the same time using a multitask architecture. With 30% (80%) training ratio, we reach an accuracy of 100% for
and 97% for ${h}^{(1,1)}$ (100% for both), 81% (96%) for ${h}^{(2,1)}$ , and 49% (83%) for ${h}^{(3,1)}$ . 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. ${h}^{(2,2)}$ 
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 datascarce 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 invarianceboosted contrastive learning (SIBCL), 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 nearzero cost. We demonstrate SIBCL’s effectiveness and generality on various scientific problems, e.g., predicting the densityofstates of 2D photonic crystals and solving the 3D timeindependent Schrödinger equation. SIBCL consistently results in orders of magnitude reduction in the number of labels needed to achieve the same network accuracies.Free, publiclyaccessible full text available December 1, 2023

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 infraredandcollinear 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 quarkgluon tagging and regression.Free, publiclyaccessible full text available September 1, 2023

Free, publiclyaccessible full text available August 1, 2023

Free, publiclyaccessible full text available August 1, 2023