adsabs/AstroCLIMB huggingface dataset:
Paper: Sensitivity to Sub-Io-sized Exosatellite Transits in the MIRI LRS Light Curve of the Nearest Substellar Worlds
Authors: Andrew Householder, Mary Anne Limbach, Beth Biller, Brooke Kotten, Mikayla J. Wilson, Johanna M. Vos, Andrew Skemer, Andrew Vanderburg, Ben J. Sutlieff, Xueqing Chen, Ian J. M. Crossfield, Nicolas Crouzet, Trent Dupuy, Jacqueline Faherty, Pengyu Liu, Elena Manjavacas, Allison McCarthy, Caroline V. Morley, Philip S. Muirhead, Natalia Oliveros-Gomez, Genaro Suárez, Xianyu Tan, Yifan Zhou
Figure caption: Top: blended MIRI LRS variability map of WISE J1049 AB: wavelength (x-axis) vs. time (y-axis) and normalized flux (amplitude—color bar). There are two distinct light curve behaviors present, allowing for the construction of two unique light curves distinguished by the change in behavior at 8.5 μm (center dashed line). Bottom: light curves 1 (red) and 2 (blue) constructed from the above data and outlined with an ∼11.77 minutes running median.
Paper: Sensitivity to Sub-Io-sized Exosatellite Transits in the MIRI LRS Light Curve of the Nearest Substellar Worlds
Authors: Andrew Householder, Mary Anne Limbach, Beth Biller, Brooke Kotten, Mikayla J. Wilson, Johanna M. Vos, Andrew Skemer, Andrew Vanderburg, Ben J. Sutlieff, Xueqing Chen, Ian J. M. Crossfield, Nicolas Crouzet, Trent Dupuy, Jacqueline Faherty, Pengyu Liu, Elena Manjavacas, Allison McCarthy, Caroline V. Morley, Philip S. Muirhead, Natalia Oliveros-Gomez, Genaro Suárez, Xianyu Tan, Yifan Zhou
Figure caption: Transit durations calculated for an Io-sized (0.29R⊕) exosatellite across multiple inclination cases. The x-axis begins at the Roche limit (0.0025 au / 6.6 hr) and extends to 144 hr orbits at 0.02 au. An edge-on / equator-on (90﹩\mathop{.}\limits^{\unicode{x000b0}}﹩0, solid black line) case produces transits up to 1 hr. The case of spin–orbit alignment with WISE J1049 B (88﹩\mathop{.}\limits^{\unicode{x000b0}}﹩5, blue line) peaks at roughly 40 minutes transits. The limiting case (80﹩\mathop{.}\limits^{\unicode{x000b0}}﹩1, brown line) shows the minimum possible inclination for which transits may still occur. The dotted vertical lines, from left to right, are the orbital periods / semimajor axes of Io (0.0028 au / 7.8 hr), Europa (0.004 au / 15.9 hr), TRAPPIST 1b (0.01154 au / 64.9 hr), and TRAPPIST 1 c (0.01580 au / 103.9 hr) (E. Agol et al. 2021). These results only apply to the B component of the WISE J1049 AB system, but the small difference in mass between the two implies we would find similar results for the A component.
Paper: Sensitivity to Sub-Io-sized Exosatellite Transits in the MIRI LRS Light Curve of the Nearest Substellar Worlds
Authors: Andrew Householder, Mary Anne Limbach, Beth Biller, Brooke Kotten, Mikayla J. Wilson, Johanna M. Vos, Andrew Skemer, Andrew Vanderburg, Ben J. Sutlieff, Xueqing Chen, Ian J. M. Crossfield, Nicolas Crouzet, Trent Dupuy, Jacqueline Faherty, Pengyu Liu, Elena Manjavacas, Allison McCarthy, Caroline V. Morley, Philip S. Muirhead, Natalia Oliveros-Gomez, Genaro Suárez, Xianyu Tan, Yifan Zhou
Figure caption: Companion radius vs. host mass of the known exoplanet population (black points; includes only confirmed planets with measured radii) as well as the approximate sensitivity of several past or ongoing exosatellite (or moon) surveys of substellar, free-floating planet, and exoplanet hosts. This study demonstrates that JWST is sensitive to exosatellites down to 0.275R⊕ around 30 MJup hosts. JWST is set to observe the light curves of dozens more wide-orbit exoplanets, free-floating planets, and brown dwarfs. If the survey’s sensitivity applies to other host types (see the discussion), the resulting JWST light curves will explore the exosatellite parameter space indicated by the light blue shaded region in this plot. References: (a) M. A. Limbach et al. (2024); (b) P. Tamburo et al. (2022a, 2022b); and (c) D. Kipping et al. (2022).
Paper: Sensitivity to Sub-Io-sized Exosatellite Transits in the MIRI LRS Light Curve of the Nearest Substellar Worlds
Authors: Andrew Householder, Mary Anne Limbach, Beth Biller, Brooke Kotten, Mikayla J. Wilson, Johanna M. Vos, Andrew Skemer, Andrew Vanderburg, Ben J. Sutlieff, Xueqing Chen, Ian J. M. Crossfield, Nicolas Crouzet, Trent Dupuy, Jacqueline Faherty, Pengyu Liu, Elena Manjavacas, Allison McCarthy, Caroline V. Morley, Philip S. Muirhead, Natalia Oliveros-Gomez, Genaro Suárez, Xianyu Tan, Yifan Zhou
Figure caption: Left: a plot of the injected and recovered transit midtimes for three of our nine exosatellite radius cases. The size of each point is scaled to the ﹩{\rm{\Delta }}{\rm{log}}z﹩ value of the test it represents, with the largest points having the largest ﹩{\rm{\Delta }}{\rm{log}}z﹩ and thus the highest favor of a transit-inclusive model. Two “exclusion zones,” corresponding to two variability features in the light curves that create transit-like signals (that are not statistically significant) at t ∼ 3.8 hr and t ∼ 4.5 hr, are marked by the vertical lines. All transits injected into these regions (3% of the total set) are excluded from injection/recovery statistics. Right: a bar chart showing the percentage of recoveries made as a function of satellite radius. A transit is considered to be successfully recovered if it meets two metrics: (1) a recovered transit midtime within 3 minutes of the injected value; and (2) a ﹩{\rm{\Delta }}{\rm{log}}z\gt 1.55﹩.
Paper: Sensitivity to Sub-Io-sized Exosatellite Transits in the MIRI LRS Light Curve of the Nearest Substellar Worlds
Authors: Andrew Householder, Mary Anne Limbach, Beth Biller, Brooke Kotten, Mikayla J. Wilson, Johanna M. Vos, Andrew Skemer, Andrew Vanderburg, Ben J. Sutlieff, Xueqing Chen, Ian J. M. Crossfield, Nicolas Crouzet, Trent Dupuy, Jacqueline Faherty, Pengyu Liu, Elena Manjavacas, Allison McCarthy, Caroline V. Morley, Philip S. Muirhead, Natalia Oliveros-Gomez, Genaro Suárez, Xianyu Tan, Yifan Zhou
Figure caption: The geometric probability of detecting a transit from a random viewing angle around either WISE J1049 A or WISE J1049 B individually as a function of the orbital period of the satellite. Reference lines are given at the orbital periods of Phobos (7.6 hr), Deimos (30 hr), Io (42.5 hr), and Europa (85.2 hr).
Paper: Sensitivity to Sub-Io-sized Exosatellite Transits in the MIRI LRS Light Curve of the Nearest Substellar Worlds
Authors: Andrew Householder, Mary Anne Limbach, Beth Biller, Brooke Kotten, Mikayla J. Wilson, Johanna M. Vos, Andrew Skemer, Andrew Vanderburg, Ben J. Sutlieff, Xueqing Chen, Ian J. M. Crossfield, Nicolas Crouzet, Trent Dupuy, Jacqueline Faherty, Pengyu Liu, Elena Manjavacas, Allison McCarthy, Caroline V. Morley, Philip S. Muirhead, Natalia Oliveros-Gomez, Genaro Suárez, Xianyu Tan, Yifan Zhou
Figure caption: Left: the probability of retrieving a transit for any one injection/recovery test is tracked on the y-axis across the range of injected satellite sizes on the x-axis for the different recovery metrics. The detection rate reaches 20%–50% (depending on the metric) for injected exosatellites of radius 0.275R⊕ (0.96 RIo or ∼1 lunar radius). For satellites >0.35R⊕ (0.85 RGanymede), nearly all transits are detected. The typical error value is calculated by first separating the results of each individual size bin into two sub-bins containing half of the injected transits. The average difference between the number of injected transits that meet metric (1) falling into each sub-bin, for each size bin, is multiplied by ﹩\sqrt{2}﹩ to give the typical error. Right: a comparison between the probability of a transit injection/recovery test meeting metric (1) using our multiband approach (orange curve, matching that in the left panel) vs. using a single-band approach (red curve).
Paper: Sensitivity to Sub-Io-sized Exosatellite Transits in the MIRI LRS Light Curve of the Nearest Substellar Worlds
Authors: Andrew Householder, Mary Anne Limbach, Beth Biller, Brooke Kotten, Mikayla J. Wilson, Johanna M. Vos, Andrew Skemer, Andrew Vanderburg, Ben J. Sutlieff, Xueqing Chen, Ian J. M. Crossfield, Nicolas Crouzet, Trent Dupuy, Jacqueline Faherty, Pengyu Liu, Elena Manjavacas, Allison McCarthy, Caroline V. Morley, Philip S. Muirhead, Natalia Oliveros-Gomez, Genaro Suárez, Xianyu Tan, Yifan Zhou
Figure caption: WISE J1049 data with an injection of a Mars-sized (0.53R⊕; ∼1100 ppm) exosatellite, shown in both light curves 1 and 2 (black points). The red (light curve 1) and blue (light curve 2) curves show the GP+transit fits to the light curves, with the transit centered near 4 hr accurately captured by the transit model. Note that this transit is easily detected by eye, despite the intrinsic variability of WISE J1049 AB, which has a larger amplitude than the transit itself.
Paper: Sensitivity to Sub-Io-sized Exosatellite Transits in the MIRI LRS Light Curve of the Nearest Substellar Worlds
Authors: Andrew Householder, Mary Anne Limbach, Beth Biller, Brooke Kotten, Mikayla J. Wilson, Johanna M. Vos, Andrew Skemer, Andrew Vanderburg, Ben J. Sutlieff, Xueqing Chen, Ian J. M. Crossfield, Nicolas Crouzet, Trent Dupuy, Jacqueline Faherty, Pengyu Liu, Elena Manjavacas, Allison McCarthy, Caroline V. Morley, Philip S. Muirhead, Natalia Oliveros-Gomez, Genaro Suárez, Xianyu Tan, Yifan Zhou
Figure caption: Top: WISE J1049 AB data (black points) with an injected 0.275R⊕ (0.96 RIo or ∼1 lunar radius) exosatellite transit in both light curves 1 and 2 along with the GP+transit model fit (the red and blue lines, respectively). Bottom: detrended (from the GP of the GP+transit fit) light curves highlighting the successful recovery of the injected transit with the GP+transit fit.
Paper: Sensitivity to Sub-Io-sized Exosatellite Transits in the MIRI LRS Light Curve of the Nearest Substellar Worlds
Authors: Andrew Householder, Mary Anne Limbach, Beth Biller, Brooke Kotten, Mikayla J. Wilson, Johanna M. Vos, Andrew Skemer, Andrew Vanderburg, Ben J. Sutlieff, Xueqing Chen, Ian J. M. Crossfield, Nicolas Crouzet, Trent Dupuy, Jacqueline Faherty, Pengyu Liu, Elena Manjavacas, Allison McCarthy, Caroline V. Morley, Philip S. Muirhead, Natalia Oliveros-Gomez, Genaro Suárez, Xianyu Tan, Yifan Zhou
Figure caption: Posterior parameter distributions for the transit model shown in Figure 6. We see well-constrained values on all transit-defining parameters, with the exception of the slope of ingress/egress. The injected transit depth was 0.030% (∼300 ppm), and the retrieved transit depth was 0.032% ± 0.007%.
Paper: Sensitivity to Sub-Io-sized Exosatellite Transits in the MIRI LRS Light Curve of the Nearest Substellar Worlds
Authors: Andrew Householder, Mary Anne Limbach, Beth Biller, Brooke Kotten, Mikayla J. Wilson, Johanna M. Vos, Andrew Skemer, Andrew Vanderburg, Ben J. Sutlieff, Xueqing Chen, Ian J. M. Crossfield, Nicolas Crouzet, Trent Dupuy, Jacqueline Faherty, Pengyu Liu, Elena Manjavacas, Allison McCarthy, Caroline V. Morley, Philip S. Muirhead, Natalia Oliveros-Gomez, Genaro Suárez, Xianyu Tan, Yifan Zhou
Figure caption: The transit depths of the Galilean moons and the planet Mars as they would appear in orbit of WISE J1049 AB. Note that the transit depths computed here are for the unresolved A and B components and would be ﹩\sqrt{2}﹩ times larger if the light curves of the two components were resolved.
Paper: Modeling the “Dark-matter Dominated” Dwarf Galaxy Segue 1 with a Supermassive Black Hole
Authors: Nathaniel Lujan, Karl Gebhardt, Richard Anantua, Owen Chase, Maya H. Debski, Claire Finley, Loraine V. Gomez, Om Gupta, Alex J. Lawson, Izabella Marron, Zorayda Martinez, Connor A. Painter, Yonatan Sklansky, Hayley West
Figure caption: χ2 vs. each of the four parameters. The top left is stellar-mass-to-light ratio, the top right is black hole mass in solar masses, the bottom left is dark matter circular velocity, and bottom right is dark matter scale radius. In each panel, we plot all models, and a contour along the bottom in χ2 determines the best-fit value and the uncertainty. The red points highlight those models that have no dark halo, and the blue points highlight those models that have no black hole. The green points are the other models that vary all four parameters. The shaded horizontal regions indicate σ values ranging from 0 to 3. The dashed line represents a best fit.
Paper: Modeling the “Dark-matter Dominated” Dwarf Galaxy Segue 1 with a Supermassive Black Hole
Authors: Nathaniel Lujan, Karl Gebhardt, Richard Anantua, Owen Chase, Maya H. Debski, Claire Finley, Loraine V. Gomez, Om Gupta, Alex J. Lawson, Izabella Marron, Zorayda Martinez, Connor A. Painter, Yonatan Sklansky, Hayley West
Figure caption: Ratio of internal dispersions σr/σt for three different models. The blue and black lines represent models that include a black hole with a mass of approximately 4.5 ± 1.5 × 105 M⊙. These models show close-to-isotropic dispersions in the central regions of Segue 1. In contrast, the red line represents a model with a dark halo but no black hole, exhibiting significant radial anisotropy. Such high radial anisotropy values are uncommon in other stellar systems.
Paper: Modeling the “Dark-matter Dominated” Dwarf Galaxy Segue 1 with a Supermassive Black Hole
Authors: Nathaniel Lujan, Karl Gebhardt, Richard Anantua, Owen Chase, Maya H. Debski, Claire Finley, Loraine V. Gomez, Om Gupta, Alex J. Lawson, Izabella Marron, Zorayda Martinez, Connor A. Painter, Yonatan Sklansky, Hayley West
Figure caption: Amplitude of the rotation as a function of radius. We use radial bins of 21 stars for most of Segue 1, going to a minimum of 15 stars at the center and outer bins. In each radial bin, we fit a sinusoid as a function of position angle and plot the amplitude of the fit. The thick solid line represents that amplitude, and the dotted lines represent the 68% confidence bands. There is a large rise in the rotation in the central region, significant at over 99%. Beyond 2′, there is no significant rotation.
Paper: Modeling the “Dark-matter Dominated” Dwarf Galaxy Segue 1 with a Supermassive Black Hole
Authors: Nathaniel Lujan, Karl Gebhardt, Richard Anantua, Owen Chase, Maya H. Debski, Claire Finley, Loraine V. Gomez, Om Gupta, Alex J. Lawson, Izabella Marron, Zorayda Martinez, Connor A. Painter, Yonatan Sklansky, Hayley West
Figure caption: The projected number count profile for Segue 1. The open circles are the data from M. Niederste-Ostholt et al. (2009). The solid red circles represent the data after subtraction of the tidal effects. The blue line is the smoothing spline that we use for the deprojection.
Paper: Fine Structures of Tiny Quiet Sun Jets Observed by Solar Orbiter and Big Bear Solar Observatory
Authors: Jeongwoo Lee, Dana Longcope, Junmu Youn, Navdeep K. Panesar, Nengyi Huang, Haimin Wang
Figure caption: Projection effects of the quiet-region EUV jet for multiple instruments. (a) SDO/AIA 171 Å with a small jet enclosed by the dotted box. (b) SolO’s EUI/HRIEUV 174 Å of the same region. The three-color half-circles are meant to show the projection effect. Model loops are constructed in the disk center and projected back to the two locations. Other images in the small FOV around the jets shown in (c)–(e) include a tilt-adjusted EUI/HRIEUV 174 Å (c), the SDO/AIA 171 Å (d), and Hα wing ±0.8 Å images ((e) and (f)). As a reference, we overlay the outline of the AIA 171 Å profile (blue contour from (d)) on other images ((c), (e), and (f)). A composite image of the Hα blue wing image (gray scale) and EUI/HRIEUV in yellow color shades (g) shows different morphologies. The observation time of AIA and GST is delayed by 4.5 minutes from that of EUI/HRIEUV.
Paper: Fine Structures of Tiny Quiet Sun Jets Observed by Solar Orbiter and Big Bear Solar Observatory
Authors: Jeongwoo Lee, Dana Longcope, Junmu Youn, Navdeep K. Panesar, Nengyi Huang, Haimin Wang
Figure caption: The reconnection model illustrated using a thin flux tube simulation. (a) Five snapshots from the initial phase in which the field line (colored curve) relaxes following its formation by reconnection. The pre-reconnection field lines are shown as red and blue curves in the leftmost snapshot. The reverse color scale shows emission measure of hot (T > 106 K) plasma. A dashed diagonal line shows a constant velocity, for reference. (b) The temperature vs. height for the five times using the same colors. The shaded box indicates the hot plasma whose emission is shown in (a). (c) At five later times, a spicule has been launched by the downward Alfvén wave. The green region shows cool (<105 K), dense plasma at each time. (d) The vertical velocity (shaded) in spacetime coordinates. A green dashed parabola shows freefall for reference, and vertical dashed lines show the times of the snapshots.
Paper: Fine Structures of Tiny Quiet Sun Jets Observed by Solar Orbiter and Big Bear Solar Observatory
Authors: Jeongwoo Lee, Dana Longcope, Junmu Youn, Navdeep K. Panesar, Nengyi Huang, Haimin Wang
Figure caption: DEMs of the jet region derived from EUV images. (a) The six panels show one EUI/FSI 174 Å image and five AIA-equivalent images generated by deep learning. The red box indicates the pixels used to calculate the DEM. (b) The DEM derived from the SDO/AIA images (green) with AI-generated EUV images with the observed FSI 174 Å image (purple). The solid lines represent the DEM profiles when the jet activity is strong (19:10:20 UT), while the dashed lines correspond to the profiles when the jet diminished (19:20:50 UT). (c) The net DEM calculated from the difference EUV images between the jet maximum and the jet quiet time.
Paper: Fine Structures of Tiny Quiet Sun Jets Observed by Solar Orbiter and Big Bear Solar Observatory
Authors: Jeongwoo Lee, Dana Longcope, Junmu Youn, Navdeep K. Panesar, Nengyi Huang, Haimin Wang
Figure caption: The evolution of EUI/HRIEUV jet structure at 174 Å (top), the difference between Hα ±0.8 Å wing images (middle), and pseudo-Dopplergrams from five wavelength point GST/VIS images (bottom). They show a preexisting strand (a), a knot-like structure (b), multiple stripes ((b)–(d)), and a rapidly turning or bending structure ((e), (j), (o)) as well as sheath flows (arrows in (f)–(i) and (k)–(n)). The Dopplergrams show strong redshift components concentrated under the EUV jets.
Paper: A Late-time View of the Progenitor Candidates of the Type II-P SN 2009ib and SN 2012ec
Authors: Yi-Han Zhao, Xinyi Hong, Ning-Chen Sun, Zexi Niu, Justyn R. Maund, Jifeng Liu
Figure caption: (a) Preexplosion HST/WFPC2 image of the site of SN 2009ib. (b), (d), (e) Late-time HST/WFC3 images of the SN site with different pixel scales labeled on the images. (c) Difference image obtained by subtracting (b) from (a). All images are in the F814W band. The SN position is marked by a circle in all images with a 1σ uncertainty. Each image has a size of ∼68 × 68 pc and is oriented with north up and east to the left.
Paper: A Late-time View of the Progenitor Candidates of the Type II-P SN 2009ib and SN 2012ec
Authors: Yi-Han Zhao, Xinyi Hong, Ning-Chen Sun, Zexi Niu, Justyn R. Maund, Jifeng Liu
Figure caption: Preexplosion and late-time images of the SN 2012ec site taken with HST/ACS in the F814W filter. The SN position is denoted by the red crosshair, and the Source B position by the white crosshair. Each image has a size of ∼78 × 78 pc and is oriented with north up and east to the left.
Paper: A Late-time View of the Progenitor Candidates of the Type II-P SN 2009ib and SN 2012ec
Authors: Yi-Han Zhao, Xinyi Hong, Ning-Chen Sun, Zexi Niu, Justyn R. Maund, Jifeng Liu
Figure caption: Values of pixels within the SN’s positional error in the difference image shown in Figure 1(c). The solid red line marks the zero level, while the dashed lines indicate ±1σ (teal) and ±3σ (brown) thresholds. As illustrated in the figure, no signal is detected beyond the 3σ level.
Paper: A Late-time View of the Progenitor Candidates of the Type II-P SN 2009ib and SN 2012ec
Authors: Yi-Han Zhao, Xinyi Hong, Ning-Chen Sun, Zexi Niu, Justyn R. Maund, Jifeng Liu
Figure caption: Comparison between the I-band and ﹩{i}^{{\prime} }﹩-band light curves of SN 2012ec from C. Barbarino et al. (2015) and our late-time measurements. The ﹩{i}^{{\prime} }﹩-band magnitudes are subtracted by 0.5 to align with the I-band magnitudes. The Co-56 decay slope is also shown to illustrate the deviation of the observed flux from the expected radioactive decay.
Paper: A Late-time View of the Progenitor Candidates of the Type II-P SN 2009ib and SN 2012ec
Authors: Yi-Han Zhao, Xinyi Hong, Ning-Chen Sun, Zexi Niu, Justyn R. Maund, Jifeng Liu
Figure caption: Histograms of magnitude differences for common stars in the SN 2012ec field (relative to the t = 4 yr epoch). The solid lines are Gaussian fit curves and the dashed lines represent the means of the Gaussian fit. Normalization has been applied to each graph.
Paper: A Late-time View of the Progenitor Candidates of the Type II-P SN 2009ib and SN 2012ec
Authors: Yi-Han Zhao, Xinyi Hong, Ning-Chen Sun, Zexi Niu, Justyn R. Maund, Jifeng Liu
Figure caption: Light curve of Source A. The preexplosion magnitudes measured with WFPC2 and ACS by J. Maund et al. (2013) are also plotted for comparison. The three preexplosion data points are slightly shifted for clarity.
Paper: A Late-time View of the Progenitor Candidates of the Type II-P SN 2009ib and SN 2012ec
Authors: Yi-Han Zhao, Xinyi Hong, Ning-Chen Sun, Zexi Niu, Justyn R. Maund, Jifeng Liu
Figure caption: Comparison of DOLPHOT-derived photometric measurements for the SN 2012ec field across multiple epochs. The black dashed line shows the one-to-one relation. No significant systematic shifts are evident.
Paper: Neural Networks as Surrogate Solvers for Time-dependent Accretion Disk Dynamics
Authors: Shunyuan Mao, Weiqi Wang, Sifan Wang, Ruobing Dong, Lu Lu, Kwang Moo Yi, Paris Perdikaris, Andrea Isella, Sébastien Fabbro, Lile Wang
Figure caption: The training workflow for our PINN. The overall strategy (left) partitions the total simulation time [0, T] into a sequence of overlapping temporal windows (shown in yellow), such as [0, T1], [T1 − ΔT, T2], [T2 − ΔT, T3], etc., each with its own dedicated neural network ﹩{{ \mathcal N }}_{0}﹩, ﹩{{ \mathcal N }}_{1}﹩, ﹩{{ \mathcal N }}_{2}﹩, etc. (Section 2.2.1). The procedure for updating the network within a single window is detailed on the right. The process begins by feeding spatiotemporal coordinates (r, θ, t) into a multilayer perceptron (MLP). A periodic layer then acts on the angular coordinate θ to enforce the required azimuthal boundary conditions (Section 2.2.3). The raw MLP outputs are subsequently scaled by factors, ωi, and combined with initial profiles to construct the final solution variables (Σ, vr, vθ) (Sections 2.2.4, 2.2.5). These variables are then processed via automatic differentiation to compute the residuals of the governing PDEs, which form the PDE loss component (Section 2.2.6). The total loss function, ﹩{ \mathcal L }﹩, combines this PDE loss with a continuity loss. The second loss ensures the network ﹩{{ \mathcal N }}_{i}﹩ gives the same solution as ﹩{{ \mathcal N }}_{i-1}﹩ inside the overlapping region [Ti − ΔT, Ti] for i≥1. Finally, a gradient-based optimizer iteratively updates the network’s parameters to minimize the total loss ﹩{ \mathcal L }﹩.
Paper: Neural Networks as Surrogate Solvers for Time-dependent Accretion Disk Dynamics
Authors: Shunyuan Mao, Weiqi Wang, Sifan Wang, Ruobing Dong, Lu Lu, Kwang Moo Yi, Paris Perdikaris, Andrea Isella, Sébastien Fabbro, Lile Wang
Figure caption: Training loss history for the fiducial model (M2/M1 = 10−3) presented in Section 4.1. The top panel shows the evolution of the unweighted mean squared error for each component of the loss function, including PDE residuals for mass continuity (Equation (4)), radial (Equation (5)), and azimuthal (Equation (6)) components of the Navier–Stokes equations, alongside data-matching losses that enforce continuity across time-marching windows. The bottom panel shows the same components after being scaled by their respective weights (Section 2.2.6), representing their actual contribution to the total loss during optimization.