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Emulating Individual Mode Frequencies of Solar-Like Oscillators with a Branching Neural Network

Scutt, Owen; Davies, Guy; Stokholm, Amalie; Lyttle, Alexander; Nielsen, Martin Bo; Hatt, Emily; Li, Tanda; Lund, Mikkel Nørup; Bedding, Tim

Publisher
Zenodo
DOI
10.5281/zenodo.17251415
Repository
zenodo.org
Language
en

Abstract

Accurately measuring the ages and internal structures of stars is challenging. Including asteroseismic observables in the inference of stellar fundamental properties can improve precision. However, the resulting increase in dimensions in grids of stellar models mean this can come at a high computational cost when using standard interpolation methods. Furthermore, without quantifying the random uncertainties in grid-based modelling, treating the systematics in the stellar models we rely on is impossible. In this talk, we present an extension to the current state-of-the-art methods in the modelling of solar-like oscillators. We present Pitchfork– a neural network with a branching architecture capable of rapid and precise emulation of both classical stellar observables and asteroseismic individual oscillation modes. Pitchfork is used in tandem with a vectorised Bayesian inference pipeline capable of sampling the posterior distributions of stellar fundamental properties in just minutes. With an extensive hare-and-hounds exercise, we demonstrate the rigorous treatment of the random uncertainties present across multiple stages of stellar parameter inference – such as emulation error, observational noise, and the asteroseismic surface effect. Using this method, we infer the stellar properties of benchmark stars - namely, the Sun-as-a-star and the binary stars 16 Cygni A and B. This work is a significant step in the development of computationally scalable and statistically sound methods for stellar parameter inference using asteroseismology, and paves the way for treatment of systematics in preparation for the imminent abundance of asteroseismic data from future missions.

Full text

Emulating Individual Mode Frequencies of Solar-Like Oscillators with a Branching Neural Network Owen J. Scutt, Guy R. Davies (supervisor), Amalie Stokholm, Alexander J. Lyttle, Martin B. Nielsen, Emily Hatt, Tanda Li, Mikkel N. Lund, and Timothy R. Bedding Model grids are discrete... [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 1 @ojscutt T L Our grid points don’t match observations Grid spacing error reduced with more points, but... Model grids are discrete... [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 1 @ojscutt T L Our grid points don’t match observations Grid spacing error reduced with more points, but... Simulations take time! Especially if we want to: Consider more dimensions Compete with observational noise Model many stars at once ...but stars are continuous! [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 2 @ojscutt Z τ M f(M,Z,τ) This is the continuous function we discretely sample: For continuous sampling, we could interpolate, but... T L ...but stars are continuous! [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 2 @ojscutt Z Y α τ M f(M,Z,Y,α,τ) T L This is the continuous function we discretely sample: For continuous sampling, we could interpolate, but... ...this becomes slow with many dimensions[1] [1]: Maltsev et al. (2024) We need an alternative that: [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 3 @ojscutt 1) Can sample f(M,Z,Y,a,t) continuously f(M,Z,Y,α,τ) 2) Scales well to many dimensions 3) Is precise! We need an alternative that: [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 3 @ojscutt Neural Networks are capable of: 1) Can sample f(M,Z,Y,a,t) continuously 2) Scales well to many dimensions 3) Is precise! f(M,Z,Y,α,τ)1) Emulating complex functions continuously when trained on discrete data 2) Rapid predictions even at high dimensions 3) Optimisation for precise predictions Neural Network Emulators [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 4 @ojscutt Z Y α τ MT L Obscure diagrams, simple maths What is a neuron? [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 5 @ojscutt f(M,Z,Y,α,τ) ≠ f(W⋅X+b) With one neuron, and a linear activation function, we are just optimising a linear fit Inference Pipeline Surface Correction 35 radial modes Error budget [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 9 @ojscutt PRIOR Pitchfork prior samples Likelihood Function 3 classical observables repeated x100,000 during vectorised nested sampling with UltraNest[3] stellar observables [[1]: Kjeldsen et al. (2008), [2]: Li et al. (2023), [3]: Buchner, J. (2021) [1][2] Inference Pipeline Surface Correction 35 radial modes Error budget [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 9 @ojscutt PRIOR POSTERIOR Pitchfork prior samples Likelihood Function 3 classical observables repeated x100,000 during vectorised nested sampling with UltraNest[3] stellar observables [1][2] [[1]: Kjeldsen et al. (2008), [2]: Li et al. (2023), [3]: Buchner, J. (2021) Benchmark: Hare-and-Hounds [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 10 @ojscutt We sample 7 parameters for all stars... Hares: Simulated stars from the grid Check recovery of truth values Benchmark: Hare-and-Hounds [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 10 @ojscutt Z τ M Hares: Simulated stars from the grid Check recovery of truth values We sample 7 parameters for all stars... ... but I’ll show 3 parameters from now on Benchmark: Hare-and-Emu-and-Hounds Hares: Fundamental properties from the grid Observables from the grid [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 11 @ojscutt Emus: Fundamental properties from the grid Observables from the Emulator Benchmark: the Sun [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 12 @ojscutt Using L, Teff , and [Fe/H] , and 23 BiSON radial modes [1] [2] [3][4][5] Posteriors are: Well sampled Fully marginalised Returned in minutes [1]: Scott et al. (2015) [2]: Asplund et al. (2009) [3]: Hale et al. (2016) [4]: Davies et al. (2014) [5]: Broomhall et al. (2009) Solar Posterior Predictive [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 13 @ojscutt Pass posterior samples back through Pitchfork Predictions on all trained modes (not just observed) Compare to observed frequency spectrum with and without surface correction Benchmark: 16 Cygni A 16 Cygni B [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 14 @ojscutt Using L , Teff , [Fe/H] [1] [2] [3] 16 and 15 radial modes[4] Agreement in Zini and Age despite entirely independent modelling! [1]: Metcalfe et al. (2012) [2]: White et al. (2013) [3]: Ramirez et al (2009) [4]: Lund et al. 2017 Posterior Predictive: [email protected]Owen J. Scutt, Neural Network Emulators talk for TASC9/KASC16 Page: 15 @ojscutt 16 Cygni A 16 Cygni B Summary: Future Work: Contact Me: @ojscutt [email protected] NN emulators are promising alternatives to interpolation Pitchfork predicts precisely on 38 observables in milliseconds This makes for efficient likelihood evaluation This proof-of-concept method is demonstrated on benchmark stars Benchmark posteriors are: Well sampled Fully marginalised Returned in minutes! Reduced uncertainty on a pointby-point basis? Ensemble! Better constraints on fundamentals? More frequencies! Better understanding of systematics? Mixture model! Owen J. Scutt, 3rd Year PhD student, University of Birmingham Solar Results: 16Cyg Results: