More Like this

1. Amortized simulation-based frequentist inference for tractable and intractable likelihoods

   https://doi.org/10.1088/2632-2153/ad218e  

   Al Kadhim, Ali ; Prosper, Harrison B. ; Prosper, Olivia F. ( February 2024 , Machine Learning: Science and Technology)

   High-fidelity simulators that connect theoretical models with observations are indispensable tools in many sciences. If the likelihood is known, inference can proceed using standard techniques. However, when the likelihood is intractable or unknown, a simulator makes it possible to infer the parameters of a theoretical model directly from real and simulated observations when coupled with machine learning. We introduce an extension of the recently proposed likelihood-free frequentist inference (LF2I) approach that makes it possible to construct confidence sets with thep-value function and to use the same function to check the coverage explicitly at any given parameter point. LikeLF2I, this extension yields provably valid confidence sets in parameter inference problems for which a high-fidelity simulator is available. The utility of our algorithm is illustrated by applying it to three pedagogically interesting examples: the first is from cosmology, the second from high-energy physics and astronomy, both with tractable likelihoods, while the third, with an intractable likelihood, is from epidemiology³3

   Code to reproduce all of our results is available onhttps://github.com/AliAlkadhim/ALFFI.

   .

    

   more » « less
2. Entanglement entropy of two disjoint intervals separated by one spin in a chain of free fermion*

   https://doi.org/10.1088/1751-8121/ab9cf2  

   Brightmore, L. ; Gehér, G. P. ; Its, A. R. ; Korepin, V. E. ; Mezzadri, F. ; Mo, M. Y. ; Virtanen, J. A. ( August 2020 , Journal of Physics A: Mathematical and Theoretical)

   We calculate the entanglement entropy of a non-contiguous subsystem of a chain of free fermions. The starting point is a formula suggested by Jin and Korepin,arXiv:1104.1004, for the reduced density of states of two disjoint intervals with lattice sitesP= {1, 2, …,m} ∪ {2m+ 1, 2m+ 2, …, 3m}, which applies to this model. As a first step in the asymptotic analysis of this system, we consider its simplification to two disjoint intervals separated just by one site, and we rigorously calculate the mutual information between these two blocks and the rest of the chain. In order to compute the entropy we need to study the asymptotic behaviour of an inverse Toeplitz matrix with Fisher–Hartwig symbol using the the Riemann–Hilbert method.

    

   more » « less
3. The Locations of Features in the Mass Distribution of Merging Binary Black Holes Are Robust against Uncertainties in the Metallicity-dependent Cosmic Star Formation History

   https://doi.org/10.3847/1538-4357/acbf51  

   van Son, L. A. C. ; de Mink, S. E. ; Chruślińska, M. ; Conroy, C. ; Pakmor, R. ; Hernquist, L. ( May 2023 , The Astrophysical Journal)

   New observational facilities are probing astrophysical transients such as stellar explosions and gravitational-wave sources at ever-increasing redshifts, while also revealing new features in source property distributions. To interpret these observations, we need to compare them to predictions from stellar population models. Such models require the metallicity-dependent cosmic star formation history ($\mathit{}(Z,z)$) as an input. Large uncertainties remain in the shape and evolution of this function. In this work, we propose a simple analytical function for$\mathit{}(Z,z)$. Variations of this function can be easily interpreted because the parameters link to its shape in an intuitive way. We fit our analytical function to the star-forming gas of the cosmological TNG100 simulation and find that it is able to capture the main behavior well. As an example application, we investigate the effect of systematic variations in the$\mathit{}(Z,z)$parameters on the predicted mass distribution of locally merging binary black holes. Our main findings are that (i) the locations of features are remarkably robust against variations in the metallicity-dependent cosmic star formation history, and (ii) the low-mass end is least affected by these variations. This is promising as it increases our chances of constraining the physics that govern the formation of these objects (https://github.com/LiekeVanSon/SFRD_fit/tree/7348a1ad0d2ed6b78c70d5100fb3cd2515493f02/).

    

   more » « less
4. Applications of physics informed neural operators

   https://doi.org/10.1088/2632-2153/acd168  

   Rosofsky, Shawn G. ; Al Majed, Hani ; Huerta, E. A. ( May 2023 , Machine Learning: Science and Technology)

   We present a critical analysis of physics-informed neural operators (PINOs) to solve partial differential equations (PDEs) that are ubiquitous in the study and modeling of physics phenomena using carefully curated datasets. Further, we provide a benchmarking suite which can be used to evaluate PINOs in solving such problems. We first demonstrate that our methods reproduce the accuracy and performance of other neural operators published elsewhere in the literature to learn the 1D wave equation and the 1D Burgers equation. Thereafter, we apply our PINOs to learn new types of equations, including the 2D Burgers equation in the scalar, inviscid and vector types. Finally, we show that our approach is also applicable to learn the physics of the 2D linear and nonlinear shallow water equations, which involve three coupled PDEs. We release our artificial intelligence surrogates and scientific software to produce initial data and boundary conditions to study a broad range of physically motivated scenarios. We provide thesource code, an interactivewebsiteto visualize the predictions of our PINOs, and a tutorial for their use at theData and Learning Hub for Science.

    

   more » « less
5. Localizing Sources of Variability in Crowded TESS Photometry

   https://doi.org/10.3847/1538-3881/acb20c  

   Higgins, Michael E. ; Bell, Keaton J. ( March 2023 , The Astronomical Journal)

   The Transiting Exoplanet Survey Satellite (TESS) has an exceptionally large plate scale of 21″ px⁻¹, causing most TESS light curves to record the blended light of multiple stars. This creates a danger of misattributing variability observed by TESS to the wrong source, which would invalidate any analysis. We developed a method that can localize the origin of variability on the sky to better than one fifth of a pixel. Given measured frequencies of variability (e.g., from periodogram analysis), we show that the best-fit sinusoid amplitudes to raw light curves extracted from each pixel are distributed in the same way as light from the variable source. The primary assumption of this method is that other nearby stars are not variable at the same frequencies. Essentially, we are using the high frequency resolution of TESS to overcome limitations from its low spatial resolution. We have implemented our method in an open-source Python package,TESS_localize(github.com/Higgins00/TESS-Localize), that determines the location of a variable source on the sky and the most likely Gaia source given TESS pixel data and a set of observed frequencies of variability. Our method utilizes models of the TESS pixel response function, and we characterize systematics in the residuals of fitting these models to data. We find that even stars more than three pixels outside a photometric aperture can produce significant contaminant signals in the extracted light curves. Given the ubiquity of source blending in TESS light curves, verifying the source of observed variability should be a standard step in TESS analyses.

    

   more » « less