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A neural-network warm start makes exoplanet orbit fitting up to 365 times faster while reproducing full posteriors.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-04 09:01 UTC pith:SQGOGNBU

load-bearing objection Sensible hybrid sampler idea, but the headline speedup/accuracy claims are undercut by the paper's own inconsistent likelihood numbers. the 4 major comments →

arxiv 2510.17459 v3 pith:SQGOGNBU submitted 2025-10-20 astro-ph.EP astro-ph.GAcs.LG

Estimating Orbital Parameters of Direct Imaging Exoplanet Using Neural Network

Bo Liang , Hanlin Song , Chang Liu , Tianyu Zhao , Yuxiang Xu , Zihao Xiao , Manjia Liang , Minghui Du
show 4 more authors
Wei-Liang Qian Li-e Qiang Peng Xu Ziren Luo
This is my paper
classification astro-ph.EP astro-ph.GAcs.LG
keywords exoplanet orbit fittingdirect imagingflow matchingMarkov chain Monte Carlonormalizing flowsBayesian inferenceBeta Pictoris bsimulation-based inference
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper claims that a hybrid sampler—a flow-matching neural network that proposes starting parameters, followed by a tempered MCMC chain—infers the orbital elements of directly imaged exoplanets just as accurately as standard Bayesian samplers while running tens to hundreds of times faster. Applied to β Pictoris b, the method reaches posteriors consistent with parallel-tempered MCMC and nested sampling in about 5.8 minutes instead of 7.5 or 35.4 hours, and reports a higher mean log-likelihood. The authors argue this makes the approach suitable for the large data volumes expected from upcoming surveys and for daily orbit updates during observing campaigns.

Core claim

The central claim is that a proposal distribution learned by flow matching can be injected into a parallel-tempered MCMC sampler to eliminate most of its burn-in, so that the sampler converges to the true posterior in a fraction of the wall-clock time. For the single-planet direct-imaging case of β Pictoris b, the flow network is trained on 16 million simulated astrometric observations drawn from Keplerian orbits with Gaussian noise; its outputs seed a PTMCMC chain with 20 temperature tiers and 1,000 chains. The resulting posterior medians and credible intervals for all eight orbital parameters (semi-major axis, eccentricity, inclination, argument of periastron, longitude of ascending node,

What carries the argument

Flow-matching posterior estimation (FMPE) trains a continuous normalizing flow—an invertible neural network parametrizing a time-dependent velocity field that transports a simple base distribution to the posterior—by regressing on conditional velocity targets rather than backpropagating through an ODE solver. The trained flow is then used as the proposal and initialization for a parallel-tempered MCMC sampler, reducing burn-in to about 1% of its normal length. The key work the flow does is to place the MCMC chains near the high-probability region of parameter space immediately, so the sampler spends its iterations refining rather than exploring.

Load-bearing premise

The trained flow network gives an unbiased warm start for the real β Pictoris b data, which depends on the synthetic training set—Keplerian orbits plus Gaussian noise calibrated to that star—and on the prior ranges being wide enough to contain the true parameters; if the real noise or astrometric calibration differs from the simulation, the fast chains could converge to a biased posterior.

What would settle it

Take the same β Pictoris b astrometric data, remove the flow warm start (so PTMCMC starts from random draws), and compare the resulting posteriors to the FM-MCMC ones; if they differ by more than the Monte Carlo noise at identical chain lengths, the flow warm start is not just accelerating but also changing the target. Alternatively, apply FM-MCMC to a synthetic dataset with non-Gaussian noise (e.g., Student-t) and check whether posterior coverage falls below the nominal 68%.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Posterior distributions for β Pictoris b's eight orbital parameters are reproduced within the same 1σ credible regions as PTMCMC and nested sampling, so claims made from the fast posteriors carry the same statistical weight.
  • Orbit fits that once took 7.5 hours (PTMCMC) or 35.4 hours (nested sampling) can be done in under 6 minutes on a consumer-class CPU/GPU setup, enabling same-day updates during observing runs.
  • With a mean log-likelihood higher than either baseline while the maximum likelihood matches, the sampler explores at least as well as the baselines, suggesting the speed-up does not come at the cost of missing high-probability regions.
  • The method is targeted to single-planet direct-imaging systems, the dominant confirmed population, so it applies immediately to most known directly imaged planets, not just β Pictoris b.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the flow's proposal quality degrades as the true parameters move outside the synthetic training distribution (e.g., a wider prior or different noise model), the apparent convergence after a 1%-burn-in could mask bias; a useful test would be to run FM-MCMC with the prior ranges widened substantially and compare against a fully converged PTMCMC run.
  • The framework generalizes to any likelihood that is cheap to evaluate; the same flow-seeding trick should carry over to radial-velocity + astrometry joint fits or multi-planet systems, where the proposal distribution would need to encode the stronger degeneracies.
  • The reported likelihood gain may partly reflect the narrow, system-centered priors used in training; on a truly unknown system, the amortized flow would provide less of an advantage, so the speed-up is likely prior-dependent.
  • One could test the claim that burn-in shrinks to 1% by measuring the autocorrelation time and the Gelman-Rubin statistic as a function of chain length on the real data; if the chains are not at stationarity, the posteriors, though overlapping the baselines here, might diverge for other systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes FM-MCMC, a two-stage inference method for orbital parameter estimation of directly imaged exoplanets. First, a continuous normalizing flow is trained via flow matching on 16 million simulated astrometric datasets drawn from priors tailored to β Pictoris b. Second, the trained flow generates initial proposals that are injected into a parallel-tempered MCMC sampler, with the claim that burn-in can be reduced to 1% of the traditional requirement. Applying this to β Pictoris b, the authors report posterior distributions consistent with PTMCMC and nested sampling (Fig. 3), a 77.8× speedup over PTMCMC and 365.4× over nested sampling, and the highest mean log-likelihood among the three methods (Table 2). The paper also compares against NPE and concludes that FM-MCMC yields more concentrated posteriors.

Significance. The application is timely: direct-imaging orbit fitting is computationally expensive, and a learned-proposal plus MCMC hybrid is a plausible route to acceleration. The paper does train a large simulation set, uses a physically motivated Keplerian simulator via orbitize!, and provides a P-P calibration plot for the flow (Fig. 4). If the central claims held, the method would be a useful contribution to exoplanet orbit fitting and to the broader learned-MCMC literature. However, the current manuscript does not establish equivalence of the FM-MCMC posterior with reference samplers: Table 2 contains an internal inconsistency in reported mean log-likelihoods that cannot be reconciled with all three samplers targeting the same posterior, and no convergence diagnostics are provided. The significance of the contribution therefore hinges on whether the FM-MCMC chains are actually converged; as presented, this is not demonstrated.

major comments (4)
  1. [Section 2.2, Table 2] For any two correctly converged samplers targeting the same posterior, the Monte Carlo mean of a fixed function (here log-likelihood) must agree to within sampling error. Table 2 reports mean log-likelihoods of -133.0 (FM-MCMC), -285.4 (PTMCMC), and -234.3 (nested sampling), with maxima all near -129.6. These differences, of order 50-150 nats, are wildly incompatible with the hypothesis that all three outputs are draws from the same posterior. The likely explanation is that the FM-MCMC chain has not converged after the claimed 1% burn-in and remains in the high-likelihood region seeded by the flow. Please provide trace plots, effective sample sizes, and Gelman-Rubin statistics for every parameter and sampler, and recompute all likelihood statistics on properly thinned, post-burn-in samples. The '53.4% better' and '43.2% better' statements in the text are not meaningful for negative log-l
  2. [Sections 2.2 and 5.2] The speedup comparison is not apples-to-apples. FM-MCMC's reported 348.9 s excludes the 22-minute flow training time (Sec. 5.2) and uses warm starts produced by the trained flow, whereas PTMCMC and nested sampling are run from cold starts. Including the one-time training for a single analysis gives about 1669 s, which changes the speedups from 77.8×/365.4× to roughly 16×/76×. If the training is intended to be amortized over many objects, state that assumption explicitly. Please also report the number of likelihood evaluations, the exact burn-in lengths, and whether the PTMCMC/nested-sampling settings were identical (temperature ladder, number of walkers, stopping criteria) for all three methods.
  3. [Section 5.1, Table 1, Section 3] The training priors are tightly centered on the known β Pictoris b solution: i is restricted to 81°-99°, Ω to 25°-85°, π to N(51.44, 0.12) mas, and M_T to N(1.75, 0.05) M_sun. The posterior medians for π and M_T in Table 3 essentially coincide with the prior means, indicating that part of the reported agreement reflects prior information rather than data information. The claim in Sec. 3 that the flow is 'trained once on simulated astrometric datasets covering extensive parameter spaces' and can work 'with limited prior knowledge' is not supported by these narrow, system-specific priors. Please state the noise scales ϵ_RA and ϵ_Dec used in the training set, report a sensitivity test with wider priors, or at minimum remove the over-general claim.
  4. [Fig. 4 and Section 4.2] The P-P plot in Fig. 4 validates the calibration of the flow network on simulated training data; it does not validate the full FM-MCMC pipeline on real observations. The assertion that burn-in is 'reduced to 1% of the original requirement' is asserted without any quantitative definition or diagnostic support. Please provide simulation-based calibration or coverage checks for the full FM-MCMC algorithm on held-out synthetic datasets, and report whether the real-data run passes any such consistency test. Without this, the 'comparable accuracy' claim rests on the qualitative overlap in Fig. 3 only, which is contradicted by the Table 2 likelihood discrepancy.
minor comments (5)
  1. [Introduction, last paragraph] Text reads 'up to a 77.8× speedup over nested sampling, and a 365.4×speedup over nested sampling.' The first speedup is over PTMCMC according to the Abstract and Table 2; this is a typo.
  2. [Section 5.1] Typo: '12sisting' should be 'consisting'; 'Kapler's law' should be 'Kepler's law'.
  3. [Section 2.2] Percentage improvements of negative log-likelihoods are not interpretable; report raw differences in nats or use a proper accuracy metric such as expected log posterior score.
  4. [Table 1] The sine prior for inclination should be defined explicitly, e.g., p(i) ∝ sin i over [81°,99°], so the reader knows the normalization.
  5. [Section 4.2 vs 5.1] Section 4.2 says the network is trained on O(10^6) simulated observations, while Section 5.1 says 16 million. These should be made consistent.

Circularity Check

0 steps flagged

No significant circularity: the flow network only provides warm-start proposals for PTMCMC, so the central derivation does not reduce to its inputs; prior-centered training is a limitation, not a definitional circularity.

full rationale

The paper's chain is: simulate 16M astrometric datasets from Keplerian orbits plus Gaussian noise using the priors in Table 1; train a flow-matching CNF to estimate the posterior; use CNF samples only as initial proposals for a PTMCMC sampler; report the resulting PTMCMC-based posterior as FM-MCMC's output. The final posterior is not defined as the flow output — it is produced by PTMCMC likelihood evaluations, with the flow serving only to shorten burn-in. Thus there is no specific equation or fitted parameter that is renamed as a prediction. The priors in Table 1 are centered on known Beta Pic b values (e.g., pi ~ N(51.44,0.12), M_T ~ N(1.75,0.05)), so the posteriors for those parameters partially reflect prior information; Section 5.1 states this explicitly: 'Since our ultimate goal is to estimate the orbital parameters of Beta Pictoris b with the trained neural network, it is essential to construct a training dataset consisting of simulated observations that closely resemble systems analogous to Beta Pictoris b.' That is a legitimate system-specific SBI setup, not a circular reduction, especially because the real data are not used to train the network and the same priors are used by the comparison samplers. The self-citations [31-33] are prior applications of flow-matching to gravitational-wave inference and are not load-bearing for the central claim. The Table 2 mean log-likelihoods (FM-MCMC -133.0, PTMCMC -285.4, nested -234.3) are mutually incompatible for converged samplers targeting the same posterior, which is a serious non-convergence/correctness concern, but it is not circularity. No load-bearing step reduces to its own inputs, so the circularity score is 0.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The central claim rests on a system-specific training setup: narrow hand-chosen priors (Table 1), Gaussian noise calibrated to β Pic b, and a flow network whose hyperparameters are arbitrary. The convergence-after-1%-burn-in assumption is central to the speedup but unverified.

free parameters (5)
  • Prior hyperparameters for a,e,i,ω,Ω,τ (Table 1) = a: Log-uniform(4,40) au; e: Uniform(1e-5,0.99); i: Sine(81°,99°); ω: Uniform(0°,360°); Ω: Uniform(25°,85°); τ: Uniform(0
    Chosen by hand from previous β Pic b works; the narrow ranges strongly inform the posterior and are system-specific.
  • Parallax prior mean and std = N(51.44,0.12) mas
    Set to the known β Pic b parallax; posterior medians in Table 3 essentially reproduce the prior mean, so π is prior-dominated.
  • Total mass prior mean and std = N(1.75,0.05) M_sun
    Set to the known system mass; posterior medians (1.78) barely move from the prior.
  • Astrometric noise scales ϵ_RA, ϵ_Dec = not reported
    Calibrated from β Pic b observations (Section 5.1); exact values are needed to reproduce the training data.
  • Network hyperparameters = 21 residual blocks, 68-dim embedding, LR 1e-4, 46 epochs
    Chosen by hand; affect proposal quality and thus the speedup claim.
axioms (5)
  • domain assumption Keplerian orbital model (Kepler's laws) maps eight parameters to ΔRA/ΔDec
    Used to generate 16M training samples via orbitize! (Section 5.1). If the model is wrong, the network learns the wrong forward map.
  • domain assumption Gaussian noise N(0,ϵ) added to synthetic astrometry
    Section 5.1; real astrometric noise is assumed Gaussian with scales from β Pic b observations.
  • standard math Flow matching loss (Eq. 4) yields a valid posterior proposal
    Borrowed from Dax et al. [47]; assumed to hold for this architecture.
  • ad hoc to paper PTMCMC warm-started from flow proposals is converged after 1% burn-in
    Section 4.2 states burn-in is reduced to 1% but gives no convergence diagnostics; this is an unverified assumption central to the speedup claim.
  • domain assumption Priors in Table 1 are appropriate for β Pic b
    The priors on π and M_tot are narrow Gaussians centered on the known system values, so the posterior inference is partly prior-driven.

pith-pipeline@v1.3.0-alltime-deepseek · 16446 in / 15369 out tokens · 115490 ms · 2026-08-04T09:01:45.385900+00:00 · methodology

0 comments
read the original abstract

In this work, we propose a flow-matching Markov chain Monte Carlo (FM-MCMC) algorithm for estimating the orbital parameters of exoplanetary systems, especially for those only one exoplanet is involved. Compared to traditional methods that rely on random sampling within the Bayesian framework, our approach first leverages flow matching posterior estimation (FMPE) to efficiently constrain the prior range of physical parameters, and then employs MCMC to accurately infer the posterior distribution. For example, in the orbital parameter inference of beta Pictoris b, our model achieved a substantial speed-up while maintaining comparable accuracy-running 77.8 times faster than Parallel Tempered MCMC (PTMCMC) and 365.4 times faster than nested sampling. Moreover, our FM-MCMC method also attained the highest average log-likelihood among all approaches, demonstrating its superior sampling efficiency and accuracy. This highlights the scalability and efficiency of our approach, making it well-suited for processing the massive datasets expected from future exoplanet surveys. Beyond astrophysics, our methodology establishes a versatile paradigm for synergizing deep generative models with traditional sampling, which can be adopted to tackle complex inference problems in other fields, such as cosmology, biomedical imaging, and particle physics.

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Reference graph

Works this paper leans on

70 extracted references · 4 canonical work pages

  1. [1]

    Nature355(6356), 145–147 (1992) https://doi.org/10.1038/355145a0

    Wolszczan, A., Frail, D.A.: A planetary system around the millisecond pulsar PSR1257+12. Nature355(6356), 145–147 (1992) https://doi.org/10.1038/355145a0

    doi:10.1038/355145a0 1992

  2. [2]

    Nature378(6555), 355–359 (1995) https: //doi.org/10.1038/378355a0

    Mayor, M., Queloz, D.: A Jupiter-mass companion to a solar-type star. Nature378(6555), 355–359 (1995) https: //doi.org/10.1038/378355a0

    doi:10.1038/378355a0 1995

  3. [3]

    https://science.nasa.gov/exoplanets/

    NASA Exoplanet Archive: NASA Exoplanet Archive by the data 2025.07.09. https://science.nasa.gov/exoplanets/. Accessed: 2025-09-05 (2025)

    2025

  4. [4]

    arXiv preprint arXiv:2501.08191 (2025)

    Howe, A.R., Becker, J.C., Stark, C.C., Adams, F.C.: Architecture classification for extrasolar planetary systems. arXiv preprint arXiv:2501.08191 (2025)

    Pith/arXiv arXiv 2025

  5. [5]

    The Astronomical Journal162(5), 186 (2021) https://doi.org/10.3847/1538-3881/ac042e

    Brandt, T.D., Dupuy, T.J., Li, Y ., Brandt, G.M., Zeng, Y ., Michalik, D., Bardalez Gagliuffi, D.C., Raposo-Pulido, V .: orvara: An efficient code to fit orbits using radial velocity, absolute, and/or relative astrometry. The Astronomical Journal162(5), 186 (2021) https://doi.org/10.3847/1538-3881/ac042e

    doi:10.3847/1538-3881/ac042e 2021

  6. [6]

    The Astronomical Journal159(3), 89 (2020) https://doi.org/10.3847/1538-3881/ ab6663

    Blunt, S., Wang, J.J., Angelo, I., Ngo, H., Cody, D., De Rosa, R.J., Graham, J.R., Hirsch, L., Nagpal, V ., Nielsen, E.L., Pearce, L., Rice, M., Tejada, R.: orbitize!: A comprehensive orbit-fitting software package for the high- contrast imaging community. The Astronomical Journal159(3), 89 (2020) https://doi.org/10.3847/1538-3881/ ab6663

    doi:10.3847/1538-3881/ 2020

  7. [7]

    https://arxiv.org/abs/2410.12905

    Winn, J.N.: The Transiting Exoplanet Survey Satellite (2024). https://arxiv.org/abs/2410.12905

    Pith/arXiv arXiv 2024

  8. [8]

    https://arxiv.org/abs/2406.01716

    Fortier, A., Simon, A.E., Broeg, C., Olofsson, G., Deline, A., Wilson, T.G., Maxted, P.F.L., Brandeker, A., Cameron, A.C., Beck, M., Bekkelien, A., Billot, N., Bonfanti, A., Bruno, G., Cabrera, J., Delrez, L., Demory, B.-O., Futyan, D., Flor´en, H.-G., G¨unther, M.N., Heitzmann, A., Hoyer, S., Isaak, K.G., Sousa, S.G., Stalport, M., Turin, A., Ver- hoeve,...

    Pith/arXiv arXiv 2024

  9. [9]

    Advances in Space Research65(1), 1–10 (2020) https://doi.org/10.1016/j.asr.2019.11.007

    Pancino, E.: Gaia: The galaxy in six (and more) dimensions. Advances in Space Research65(1), 1–10 (2020) https://doi.org/10.1016/j.asr.2019.11.007

    work page doi:10.1016/j.asr.2019.11.007 2020

  10. [10]

    Astronomy & Astrophysics 631, 155 (2019)

    Beuzit, J.-L., Vigan, A., Mouillet, D., Dohlen, K., Gratton, R., Boccaletti, A., Sauvage, J.-F., Schmid, H.M., Lan- glois, M., Petit, C.,et al.: Sphere: the exoplanet imager for the very large telescope. Astronomy & Astrophysics 631, 155 (2019)

    2019

  11. [11]

    https://arxiv.org/abs/2406.05447

    Rauer, H., Aerts, C., Cabrera, J., Deleuil, M., Erikson, A., Gizon, L., Goupil, M., Heras, A., Lorenzo-Alvarez, J., Marliani, F., Martin-Garcia, C., Mas-Hesse, J.M., O’Rourke, L., Osborn, H., Pagano, I., Piotto., G.: The PLATO Mission (2024). https://arxiv.org/abs/2406.05447

    Pith/arXiv arXiv 2024

  12. [12]

    https://arxiv.org/abs/2206.14633

    Changeat, Q., Yip, K.H.: ESA-Ariel Data Challenge NeurIPS 2022: Introduction to exo-atmospheric studies and presentation of the Atmospheric Big Challenge (ABC) Database (2023). https://arxiv.org/abs/2206.14633

    Pith/arXiv arXiv 2022

  13. [13]

    Experimental Astronomy46, 67–100 (2017) 10

    Zingales, T., Tinetti, G., Pillitteri, I., Leconte, J., Micela, G., Sarkar, S.: The ariel mission reference sample. Experimental Astronomy46, 67–100 (2017) 10

    2017

  14. [14]

    arXiv e-prints, 2003–05714 (2020) https://doi.org/10.48550/arXiv.2003.05714 arXiv:2003.05714 [astro-ph.EP]

    Boccaletti, A., Chauvin, G., Mouillet, D., Absil, O., Allard, F., Antoniucci, S., Augereau, J.-C., Barge, P., Baruf- folo, A., Baudino, J.-L., Baudoz, P., Beaulieu, M., Benisty, M., Beuzit, J.-L., Bianco, A., Biller, B., Bonavita, B., Bonnefoy, M., Bos, S., Bouret, J.-C., Brandner, W., Buchschache, N., Carry, B., Cantalloube, F., Cascone, E., Carlotti, A....

    Pith/arXiv arXiv doi:10.48550/arxiv.2003.05714 2003

  15. [15]

    https://arxiv.org/abs/2309.08672

    Bailey, V .P., Bendek, E., Monacelli, B., Baker, C., Bedrosian, G., Cady, E., Douglas, E.S., Groff, T., Hildebrandt, S.R., Kasdin, N.J., Krist, J., Macintosh, B., Mennesson, B., Morrissey, P., Poberezhskiy, I., Subedi, H.B., Rhodes, J., Roberge, A., Ygouf, M., Zellem, R.T., Zhao, F., Zimmerman, N.T.: Nancy Grace Roman Space Telescope Coronagraph Instrumen...

    Pith/arXiv arXiv 2023

  16. [16]

    Publications of the Astronomical Society of the Pacific135(1052), 106001 (2023)

    Maire, A.-L., Delrez, L., Pozuelos, F.J., Becker, J., Espinoza, N., Lillo-Box, J., Revol, A., Absil, O., Agol, E., Almenara, J.M.,et al.: Workshop summary: Exoplanet orbits and dynamics. Publications of the Astronomical Society of the Pacific135(1052), 106001 (2023)

    2023

  17. [17]

    In: Beuther, H., Klessen, R.S., Dullemond, C.P., Henning, T

    Fischer, D.A., Howard, A.W., Laughlin, G.P., Macintosh, B., Mahadevan, S., Sahlmann, J., Yee, J.C.: Exoplanet Detection Techniques. In: Beuther, H., Klessen, R.S., Dullemond, C.P., Henning, T. (eds.) Protostars and Planets VI, pp. 715–737 (2014). https://doi.org/10.2458/azu uapress 9780816531240-ch031

    doi:10.2458/azu 2014

  18. [18]

    https://doi.org/10.1007/978-3-319-55333-7

    Deeg, H.J., Belmonte, J.A.: Handbook of Exoplanets, (2018). https://doi.org/10.1007/978-3-319-55333-7

    doi:10.1007/978-3-319-55333-7 2018

  19. [19]

    Astronomy & Astrophysics602, 94 (2017)

    Abuter, R., Accardo, M., Amorim, A., Anugu, N., Avila, G., Azouaoui, N., Benisty, M., Berger, J.-P., Blind, N., Bonnet, H.,et al.: First light for gravity: Phase referencing optical interferometry for the very large telescope interferometer. Astronomy & Astrophysics602, 94 (2017)

    2017

  20. [20]

    Optical Engineering51(1), 011003–011003 (2012)

    Lightsey, P.A., Atkinson, C., Clampin, M., Feinberg, L.D.: James webb space telescope: large deployable cryogenic telescope in space. Optical Engineering51(1), 011003–011003 (2012)

    2012

  21. [21]

    https://arxiv.org/abs/astro-ph/9909342

    Forveille, T., Beuzit, J.L., Delfosse, X., Segransan, D., Beck, F., Mayor, M., Perrier, C., Tokovini, A., Udry, S.: Accurate masses of very low mass stars: I Gl 570BC (0.6+0.4 Msol) (1999). https://arxiv.org/abs/astro-ph/9909342

    Pith/arXiv arXiv 1999

  22. [22]

    AJ153(5), 229 (2017) https: //doi.org/10.3847/1538-3881/aa6930 arXiv:1703.10653 [astro-ph.EP]

    Blunt, S., Nielsen, E.L., De Rosa, R.J., Konopacky, Q.M., Ryan, D., Wang, J.J., Pueyo, L., Rameau, J., Marois, C., Marchis, F., Macintosh, B., Graham, J.R., Duchˆene, G., Schneider, A.C.: Orbits for the Impatient: A Bayesian Rejection-sampling Method for Quickly Fitting the Orbits of Long-period Exoplanets. AJ153(5), 229 (2017) https: //doi.org/10.3847/15...

    Pith/arXiv arXiv 2017

  23. [23]

    PASP125(925), 306 (2013) https://doi.org/10.1086/670067 arXiv:1202.3665 [astro-ph.IM]

    Foreman-Mackey, D., Hogg, D.W., Lang, D., Goodman, J.: emcee: The MCMC Hammer. PASP125(925), 306 (2013) https://doi.org/10.1086/670067 arXiv:1202.3665 [astro-ph.IM]

    Pith/arXiv arXiv 2013

  24. [24]

    MNRAS455(2), 1919–1937 (2016) https://doi.org/10.1093/mnras/stv2422 arXiv:1501.05823 [astro-ph.IM]

    V ousden, W.D., Farr, W.M., Mandel, I.: Dynamic temperature selection for parallel tempering in Markov chain Monte Carlo simulations. MNRAS455(2), 1919–1937 (2016) https://doi.org/10.1093/mnras/stv2422 arXiv:1501.05823 [astro-ph.IM]

    Pith/arXiv arXiv 1919

  25. [25]

    Speagle, J.S.: dynesty: a dynamic nested sampling package for estimating bayesian posteriors and evidences. Monthly Notices of the Royal Astronomical Society493(3), 3132–3158 (2020) https://doi.org/10.1093/mnras/ staa278 https://academic.oup.com/mnras/article-pdf/493/3/3132/32890730/staa278.pdf

    doi:10.1093/mnras/ 2020

  26. [26]

    The Astrophysical Journal932(2), 99 (2022) https://doi.org/10.3847/1538-4357/ac6be9 11

    Sun, H., Bouman, K.L., Tiede, P., Wang, J.J., Blunt, S., Mawet, D.: Alpha-deep probabilistic inference (alpha-dpi): Efficient uncertainty quantification from exoplanet astrometry to black hole feature extraction. The Astrophysical Journal932(2), 99 (2022) https://doi.org/10.3847/1538-4357/ac6be9 11

    work page doi:10.3847/1538-4357/ac6be9 2022

  27. [27]

    PhD thesis, University of Li `ege, Li`ege, Belgium (June 2024)

    Ruth, M.: Exoplanet Orbital Characterization Using Simulation-Based Inference. PhD thesis, University of Li `ege, Li`ege, Belgium (June 2024). https://matheo.uliege.be/handle/2268.2/20393

    2024

  28. [28]

    arXiv preprint arXiv:2409.04557 (2024)

    Chen, C., Kong, L., Li, G., Tao, M.: Deepttv: Deep learning prediction of hidden exoplanet from transit timing variations. arXiv preprint arXiv:2409.04557 (2024)

    Pith/arXiv arXiv 2024

  29. [29]

    Publications of the Astronomical Society of the Pacific135(2023)

    Sithajan, S., Meethong, S.: Applied machine-learning models to identify spectral sub-types of m dwarfs from photometric surveys. Publications of the Astronomical Society of the Pacific135(2023)

    2023

  30. [30]

    ArXiv abs/2102.10326(2021)

    Ofman, L., Averbuch, A., Shliselberg, A., Benaun, I., Segev, D., Rissman, A.: Automated identification of transiting exoplanet candidates in nasa transiting exoplanets survey satellite (tess) data with machine learning methods. ArXiv abs/2102.10326(2021)

    Pith/arXiv arXiv 2021

  31. [31]

    Science China Physics, Mechanics & Astronomy67(3), 230412 (2024)

    Du, M., Liang, B., Wang, H., Xu, P., Luo, Z., Wu, Y .: Advancing space-based gravitational wave astronomy: Rapid parameter estimation via normalizing flows. Science China Physics, Mechanics & Astronomy67(3), 230412 (2024)

    2024

  32. [32]

    Machine Learning: Science and Technology5(4), 045040 (2024) https://doi.org/10.1088/2632-2153/ad8da9

    Liang, B., Du, M., Wang, H., Xu, Y ., Liu, C., Wei, X., Xu, P., Qiang, L.-e., Luo, Z.: Rapid parameter estima- tion for merging massive black hole binaries using continuous normalizing flows. Machine Learning: Science and Technology5(4), 045040 (2024) https://doi.org/10.1088/2632-2153/ad8da9

    doi:10.1088/2632-2153/ad8da9 2024

  33. [33]

    https://arxiv.org/abs/2412.19169

    Liang, B., Liu, C., Zhao, T., Du, M., Liang, M., Shi, R., Guo, H., Xu, Y ., Qiang, L.-e., Xu, P., Qian, W.-L., Luo, Z.: Accelerating Stochastic Gravitational Wave Backgrounds Parameter Estimation in Pulsar Timing Arrays with Flow Matching (2024). https://arxiv.org/abs/2412.19169

    Pith/arXiv arXiv 2024

  34. [34]

    Wang, K., Ge, J., Willis, K., Wang, K., Zhao, Y .: The gpu phase folding and deep learning method for detecting exoplanet transits. Monthly Notices of the Royal Astronomical Society528(3), 4053–4067 (2024) https://doi.org/ 10.1093/mnras/stae245 https://academic.oup.com/mnras/article-pdf/528/3/4053/56617446/stae245.pdf

    doi:10.1093/mnras/stae245 2024

  35. [35]

    Pan, J.-S., Ting, Y .-S., Yu, J.: Astroconformer: The prospects of analysing stellar light curves with transformer- based deep learning models. Monthly Notices of the Royal Astronomical Society528(4), 5890–5903 (2024) https: //doi.org/10.1093/mnras/stae068 https://academic.oup.com/mnras/article-pdf/528/4/5890/56707271/stae068.pdf

    doi:10.1093/mnras/stae068 2024

  36. [36]

    ArXiv abs/2305.09596(2023)

    Prithivraj, G., Kumari, A.: Identification and classification of exoplanets using machine learning techniques. ArXiv abs/2305.09596(2023)

    Pith/arXiv arXiv 2023

  37. [37]

    https://arxiv.org/abs/2501.17538

    Ulas ¸, B., Szklen´ar, T., Szab ´o, R.: Detection of Oscillation-like Patterns in Eclipsing Binary Light Curves using Neural Network-based Object Detection Algorithms (2025). https://arxiv.org/abs/2501.17538

    Pith/arXiv arXiv 2025

  38. [38]

    https://arxiv.org/abs/2405.18278

    Poleo, V .T., Eisner, N., Hogg, D.W.: NotPlaNET: Removing False Positives from Planet Hunters TESS with Machine Learning (2024). https://arxiv.org/abs/2405.18278

    Pith/arXiv arXiv 2024

  39. [39]

    https: //arxiv.org/abs/2501.16839

    Wald, C., Steidl, G.: Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans (2025). https: //arxiv.org/abs/2501.16839

    Pith/arXiv arXiv 2025

  40. [40]

    Advances in neural information processing systems32(2019)

    Durkan, C., Bekasov, A., Murray, I., Papamakarios, G.: Neural spline flows. Advances in neural information processing systems32(2019)

    2019

  41. [41]

    In: International Conference on Learning Representations (2017).https://openreview.net/forum?id=HkpbnH9lx

    Dinh, L., Sohl-Dickstein, J., Bengio, S.: Density estimation using real NVP. In: International Conference on Learning Representations (2017).https://openreview.net/forum?id=HkpbnH9lx

    2017

  42. [42]

    arXiv: Learning (2014)

    Dinh, L., Krueger, D., Bengio, Y .: Nice: Non-linear independent components estimation. arXiv: Learning (2014)

    2014

  43. [43]

    In: Neural Information Processing Systems (2018).https://api.semanticscholar.org/CorpusID:49310446

    Chen, T.Q., Rubanova, Y ., Bettencourt, J., Duvenaud, D.K.: Neural ordinary differential equations. In: Neural Information Processing Systems (2018).https://api.semanticscholar.org/CorpusID:49310446

    2018

  44. [44]

    Interna- tional Conference on Learning Representations (2021)

    Chen, R.T.Q., Amos, B., Nickel, M.: Learning neural event functions for ordinary differential equations. Interna- tional Conference on Learning Representations (2021)

    2021

  45. [45]

    International Conference on Machine Learning (2021)

    Kidger, P., Chen, R.T.Q., Lyons, T.J.: ”hey, that’s not an ode”: Faster ode adjoints via seminorms. International Conference on Machine Learning (2021)

    2021

  46. [46]

    https://github.com/rtqichen/torchdiffeq 12

    Chen, R.T.Q.: torchdiffeq (2018). https://github.com/rtqichen/torchdiffeq 12

    2018

  47. [47]

    https://arxiv.org/abs/2305.17161

    Dax, M., Wildberger, J., Buchholz, S., Green, S.R., Macke, J.H., Sch ¨olkopf, B.: Flow Matching for Scalable Simulation-Based Inference (2023). https://arxiv.org/abs/2305.17161

    Pith/arXiv arXiv 2023

  48. [48]

    Journal of Open Source Software5(52), 2505 (2020) https://doi.org/10.21105/joss.02505

    Tejero-Cantero, A., Boelts, J., Deistler, M., Lueckmann, J.-M., Durkan, C., Gonc ¸alves, P.J., Greenberg, D.S., Macke, J.H.: sbi: A toolkit for simulation-based inference. Journal of Open Source Software5(52), 2505 (2020) https://doi.org/10.21105/joss.02505

    doi:10.21105/joss.02505 2020

  49. [49]

    Viscasillas V ´azquez, C., Solano, E., Ulla, A., Ambrosch, M.,´Alvarez, M. A., Manteiga, M., Magrini, L., Santove˜na- G´omez, R., Dafonte, C., P ´erez-Fern´andez, E., Aller, A., Drazdauskas, A., Mikolaitis, ˇS., Rodrigo, C.: Advanced classification of hot subdwarf binaries using artificial intelligence techniques and gaia dr3 data. A& A691, 223 (2024) htt...

    work page doi:10.1051/0004-6361/202451247 2024

  50. [50]

    A & A652, 107 (2021) https://doi.org/10.1051/0004-6361/202141068

    Vida, Kriszti ´an, B ´odi, Attila, Szklen ´ar, Tam´as, Seli, B ´alint: Finding flares in kepler and tess data with recurrent deep neural networks. A & A652, 107 (2021) https://doi.org/10.1051/0004-6361/202141068

    doi:10.1051/0004-6361/202141068 2021

  51. [51]

    ArXivabs/2409.09563(2024)

    Smith, J.: Astrometric binary classification via artificial neural networks. ArXivabs/2409.09563(2024)

    Pith/arXiv arXiv 2024

  52. [52]

    Sahlmann, J., G ´omez, P.: Machine learning-based identification of gaia astrometric exoplanet orbits. Monthly Notices of the Royal Astronomical Society537(2), 1130–1145 (2025) https://doi.org/10.1093/mnras/staf018 https://academic.oup.com/mnras/article-pdf/537/2/1130/61382466/staf018.pdf

    doi:10.1093/mnras/staf018 2025

  53. [53]

    In: The Eleventh International Conference on Learning Representations (2023)

    Liu, X., Gong, C., liu: Flow straight and fast: Learning to generate and transfer data with rectified flow. In: The Eleventh International Conference on Learning Representations (2023). https://openreview.net/forum?id=XVjTT1nw5z

    2023

  54. [54]

    In: The Eleventh International Conference on Learning Representations (2023)

    Lipman, Y ., Chen, R.T.Q., Ben-Hamu, H., Nickel, M., Le, M.: Flow matching for genera- tive modeling. In: The Eleventh International Conference on Learning Representations (2023). https://openreview.net/forum?id=PqvMRDCJT9t

    2023

  55. [55]

    Advances in neural information processing systems29(2016)

    Papamakarios, G., Murray, I.: Fastε-free inference of simulation models with bayesian conditional density estimation. Advances in neural information processing systems29(2016)

    2016

  56. [56]

    https://arxiv.org/abs/1711.01861

    Lueckmann, J.-M., Goncalves, P.J., Bassetto, G., ¨Ocal, K., Nonnenmacher, M., Macke, J.H.: Flexible statistical inference for mechanistic models of neural dynamics (2017). https://arxiv.org/abs/1711.01861

    Pith/arXiv arXiv 2017

  57. [57]

    Proceedings of the National Academy of Sciences119(10), 2109420119 (2022) https://doi.org/10.1073/pnas

    Gabri ´e, M., Rotskoff, G.M., Vanden-Eijnden, E.: Adaptive monte carlo augmented with normalizing flows. Proceedings of the National Academy of Sciences119(10), 2109420119 (2022) https://doi.org/10.1073/pnas. 2109420119 https://www.pnas.org/doi/pdf/10.1073/pnas.2109420119

    doi:10.1073/pnas 2022

  58. [58]

    Wong, K.W.k., Gabri ´e, M., Foreman-Mackey, D.: flowMC: Normalizing flow enhanced sampling package for probabilistic inference in JAX. J. Open Source Softw.8(83), 5021 (2023) https://doi.org/10.21105/joss.05021 arXiv:2211.06397 [astro-ph.IM]

    Pith/arXiv arXiv 2023

  59. [59]

    Gabri ´e, M., Rotskoff, G.M., Vanden-Eijnden, E.: Adaptive Monte Carlo augmented with normalizing flows. Proc. Nat. Acad. Sci.119(10), 2109420119 (2022) https://doi.org/10.1073/pnas.2109420119 arXiv:2105.12603 [physics.data-an]

    Pith/arXiv arXiv 2022

  60. [60]

    Lagrange, A.-M.,et al.: A probable giant planet imaged in the Beta Pictoris disk. Astron. Astrophys.493, 21 (2009) https://doi.org/10.1051/0004-6361:200811325 arXiv:0811.3583 [astro-ph]

    Pith/arXiv arXiv 2009

  61. [61]

    Science329, 57 (2010) https://doi.org/10.1126/science.1187187 arXiv:1006.3314 [astro-ph.EP]

    Lagrange, A.-M.,et al.: A giant planet imaged in the disk of the young star Beta Pictoris. Science329, 57 (2010) https://doi.org/10.1126/science.1187187 arXiv:1006.3314 [astro-ph.EP]

    Pith/arXiv arXiv 2010

  62. [62]

    Astronomy & Astrophysics678(2023) https://doi.org/ 10.1051/0004-6361/202245752

    Hayoz, J., Cugno, G., Quanz, S.P., Patapis, P., Alei, E., Bonse, M.J., Dannert, F.A., Garvin, E.O., Gebhard, T.D., Konrad, B.S., Sartori, L.F.: Crocodile: Incorporating medium-resolution spectroscopy of close-in directly imaged exoplanets into atmospheric retrievals via cross-correlation. Astronomy & Astrophysics678(2023) https://doi.org/ 10.1051/0004-636...

    doi:10.1051/0004-6361/202245752 2023

  63. [63]

    New Astronomy13(2), 103–112 (2008) https://doi.org/ 10.1016/j.newast.2007.07.004

    Belleman, R.G., B ´edorf, J., Portegies Zwart, S.F.: High performance direct gravitational n-body simulations on graphics processing units ii: An implementation in cuda. New Astronomy13(2), 103–112 (2008) https://doi.org/ 10.1016/j.newast.2007.07.004

    work page doi:10.1016/j.newast.2007.07.004 2008

  64. [64]

    Astronomy & Astrophysics694, 236 (2025) https://doi.org/10.1051/0004-6361/ 202452632

    Lacquement, A., Beust, H., Faramaz-Gorka, V ., Duchˆene, G.: Dynamics of the beta pictoris planetary system and 13 possibility of an additional planet. Astronomy & Astrophysics694, 236 (2025) https://doi.org/10.1051/0004-6361/ 202452632

    doi:10.1051/0004-6361/ 2025

  65. [65]

    Astronomy & Astrophysics654, 2 (2021) https://doi.org/10.1051/0004-6361/202141889

    Lacour, S., Wang, J.J., Rodet, L., Nowak, M., Shangguan, J., Beust, H., Lagrange, A.-M., Abuter, R., Amorim, A., Asensio-Torres, R., Benisty, M., Berger, J.-P., Blunt, S., Boccaletti, A., Bohn, A., Bolzer, M.-L., Bonnefoy, M., Bonnet, H., Bourdarot, G., Brandner, W., Cantalloube, F., Caselli, P., Charnay, B., Chauvin, G., Choquet, E., Christiaens, V ., Cl...

    2021

  66. [66]

    ApJ794(2), 158 (2014) https://doi.org/ 10.1088/0004-637X/794/2/158 arXiv:1403.7195 [astro-ph.EP]

    Nielsen, E.L., Liu, M.C., Wahhaj, Z., Biller, B.A., Hayward, T.L., Males, J.R., Close, L.M., Morzinski, K.M., Skemer, A.J., Kuchner, M.J., Rodigas, T.J., Hinz, P.M., Chun, M., Ftaclas, C., Toomey, D.W.: The Gemini NICI Planet-Finding Campaign: The Orbit of the Young ExoplanetβPictoris b. ApJ794(2), 158 (2014) https://doi.org/ 10.1088/0004-637X/794/2/158 a...

    Pith/arXiv arXiv 2014

  67. [67]

    A&A621, 8 (2019) https://doi.org/10.1051/0004-6361/201834302 arXiv:1809.08354 [astro-ph.EP]

    Lagrange, A.-M., Boccaletti, A., Langlois, M., Chauvin, G., Gratton, R., Beust, H., Desidera, S., Milli, J., Bonnefoy, M., Cheetham, A., Feldt, M., Meyer, M., Vigan, A., Biller, B., Bonavita, M., Baudino, J.-L., Cantalloube, F., Cudel, M., Daemgen, S., Delorme, P., D’Orazi, V ., Girard, J., Fontanive, C., Hagelberg, J., Janson, M., Keppler, M., Koypitova,...

    Pith/arXiv arXiv 2019

  68. [68]

    AJ159(2), 71 (2020) https://doi.org/10.3847/1538-3881/ab5b92 arXiv:1911.11273 [astro-ph.EP]

    Nielsen, E.L., De Rosa, R.J., Wang, J.J., Sahlmann, J., Kalas, P., Duchˆene, G., Rameau, J., Marley, M.S., Saumon, D., Macintosh, B., Millar-Blanchaer, M.A., Nguyen, M.M., Ammons, S.M., Bailey, V .P., Barman, T., Bulger, J., Chilcote, J., Cotten, T., Doyon, R., Esposito, T.M., Fitzgerald, M.P., Follette, K.B., Gerard, B.L., Goodsell, S.J., Graham, J.R., G...

    Pith/arXiv arXiv 2020

  69. [69]

    Nature Astronomy3, 1135–1142 (2019) https://doi.org/10.1038/ s41550-019-0857-1

    Lagrange, A.-M., Meunier, N., Rubini, P., Keppler, M., Galland, F., Chapellier, E., Michel, E., Balona, L., Beust, H., Guillot, T., Grandjean, A., Borgniet, S., M ´ekarnia, D., Wilson, P.A., Kiefer, F., Bonnefoy, M., Lillo-Box, J., Pantoja, B., Jones, M., Iglesias, D.P., Rodet, L., Diaz, M., Zapata, A., Abe, L., Schmider, F.-X.: Evidence for an additional...

    2019

  70. [70]

    Cambridge University Press, ??? (1985) 14

    Green, R.M.: Spherical Astronomy. Cambridge University Press, ??? (1985) 14

    1985