Despite great progress in simulating multiphysics problems using the numerical discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate noisy data into existing algorithms, mesh generation remains complex, and high-dimensional problems governed by parameterized PDEs cannot be tackled. Moreover, solving inverse problems with hidden physics is often prohibitively expensive and requires different formulations and elaborate computer codes. Machine learning has emerged as a promising alternative, but training deep neural networks requires big data, not always available for scientific problems. Instead, such networks can be trained from additional information obtained by enforcing the physical laws (for example, at random points in the continuous space-time domain). Such physics-informed learning integrates (noisy) data and mathematical models, and implements them through neural networks or other kernel-based regression networks. Moreover, it may be possible to design specialized network architectures that automatically satisfy some of the physical invariants for better accuracy, faster training and improved generalization. Here, we review some of the prevailing trends in embedding physics into machine learning, present some of the current capabilities and limitations and discuss diverse applications of physics-informed learning both for forward and inverse problems, including discovering hidden physics and tackling high-dimensional problems. The rapidly developing field of physics-informed learning integrates data and mathematical models seamlessly, enabling accurate inference of realistic and high-dimensional multiphysics problems. This Review discusses the methodology and provides diverse examples and an outlook for further developments.

Physics-informed machine learning

The Astropy Project supports and fosters the development of open-source and openly developed Python packages that provide commonly needed functionality to the astronomical community. A key element of the Astropy Project is the core package astropy, which serves as the foundation for more specialized projects and packages. In this article, we summarize key features in the core package as of the recent major release, version 5.0, and provide major updates on the Project. We then discuss supporting a broader ecosystem of interoperable packages, including connections with several astronomical observatories and missions. We also revisit the future outlook of the Astropy Project and the current status of Learn Astropy. We conclude by raising and discussing the current and future challenges facing the Project.

The Astropy Project: Sustaining and Growing a Community-oriented Open-source Project and the Latest Major Release (v5.0) of the Core Package

We report the Transiting Exoplanet Survey Satellite (TESS) discovery of three terrestrial-sized planets transiting L 98-59 (TOI-175, TIC 307210830) -- a bright M dwarf at a distance of 10.6 pc. Using the Gaia-measured distance and broad-band photometry we find that the host star is an M3 dwarf. Combined with the TESS transits from three sectors, the corresponding stellar parameters yield planet radii ranging from 0.8REarth to 1.6REarth. All three planets have short orbital periods, ranging from 2.25 to 7.45 days with the outer pair just wide of a 2:1 period resonance. Diagnostic tests produced by the TESS Data Validation Report and the vetting package DAVE rule out common false positive sources. These analyses, along with dedicated follow-up and the multiplicity of the system, lend confidence that the observed signals are caused by planets transiting L 98-59 and are not associated with other sources in the field. The L 98-59 system is interesting for a number of reasons: the host star is bright (V = 11.7 mag, K = 7.1 mag) and the planets are prime targets for further follow-up observations including precision radial-velocity mass measurements and future transit spectroscopy with the James Webb Space Telescope; the near resonant configuration makes the system a laboratory to study planetary system dynamical evolution; and three planets of relatively similar size in the same system present an opportunity to study terrestrial planets where other variables (age, metallicity, etc.) can be held constant. L 98-59 will be observed in 4 more TESS sectors, which will provide a wealth of information on the three currently known planets and have the potential to reveal additional planets in the system.

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The L 98-59 System: Three Transiting, Terrestrial-Sized Planets Orbiting a Nearby M-dwarf.

We thank the NASA TESS Guest Investigator Program for supporting this work through grant 80NSSC18K1583 (awarded to C.D.D.). S.G. and C.D.D. also appreciate and acknowledge support from the Hellman Fellows Fund, the Alfred P. Sloan Foundation, the David and Lucile Packard Foundation, and the NASA Exoplanets Research Program (XRP) through grant
80NSSC20K0250. This work makes use of observations from the LCOGT network. This material is based on work supported by the National Science Foundation Graduate Research Fellowship Program under grant No. DGE-1650115. The research leading
to these results has received funding from the ARC grant for Concerted Research Actions, financed by the WalloniaBrussels Federation. TRAPPIST is funded by the Belgian Fund for Scientific Research (Fond National de la Recherche Scientifique, FNRS) under the grant FRFC 2.5.594.09.F, with the participation of the Swiss National Science Foundation (SNF). M.G. and E.J. are F.R.S.-FNRS Senior Research Associates. The MEarth Team gratefully acknowledges the David and Lucile Packard Fellowship for Science and Engineering (awarded to D.C.), continued support by the NSF mostly recently under grant AST-1616624, and support by NASA under grant 80NSSC18K0476 (XRP Program). This work is made possible by a grant from the John Templeton
Foundation. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation. J.N.W. thanks the HeisingSimons Foundation for support. Funding for the TESS mission is provided by NASA’s Science Mission directorate. This research has made use of the Exoplanet Follow-up Observation Program website, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This paper includes data collected by the TESS mission, which are publicly available from the Mikulski Archive for Space Telescopes (MAST). We acknowledge the use of public TESS Alert data from pipelines at the TESS Science Office and TESS Science Processing Operations Center. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center for the production of the SPOC data products.

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Vetting of 384 TESS Objects of Interest with TRICERATOPS and Statistical Validation of 12 Planet Candidates

Dippers are a common class of young variable star exhibiting day-long dimmings with depths of up to several tens of per cent. A standard explanation is that dippers host nearly edge-on (id ≈ 70°) protoplanetary discs that allow close-in ( 10 au) disc resolved by ALMA and that inner disc misalignments may be common during the protoplanetary phase. More than one mechanism may contribute to the dipper phenomenon, including accretion-driven warps and ‘broken’ discs caused by inclined (sub-)stellar or planetary companions.

Are inner disc misalignments common? ALMA reveals an isotropic outer disc inclination distribution for young dipper stars

Lightkurve: Kepler and TESS time series analysis in Python

Summary: We study the training process of Deep Neural Networks (DNNs) from the Fourier analysis perspective. We demonstrate a very universal Frequency Principle (F-Principle) – DNNs often ﬁt target functions from low to high frequencies – on high-dimensional benchmark datasets such as MNIST/CIFAR10 and deep neural networks such as VGG16. This F-Principle of DNNs is opposite to the behavior of Jacobi method, a conventional iterative numerical scheme, which exhibits faster convergence for higher frequencies for various scientiﬁc computing problems. With theories under an idealized setting, we illustrate that this F-Principle results from the smoothness/regularity of the commonly used activation functions. The F-Principle implies an implicit bias that DNNs tend to ﬁt training data by a low-frequency function. This understanding provides an explanation of good generalization of DNNs on most real datasets and bad generalization of DNNs on parity function or a randomized dataset.

Johnny Zhang

Papers

Lightkurve: Kepler and TESS time series analysis in Python

Fourier analysis sheds light on deep

KeplerGO/lightkurve: Lightkurve v1.0b29

No Optimal SFF Motion Detrending Parameters for Red Giant Asteroseismology in K2