Shallow. Deep. Transits Learning

Transcription

1 Shallow Deep Transits Learning

2 Shay Zucker, Raja Giryes Elad Dvash (Tel Aviv University) Yam Peleg (Deep Trading)

3 Red Noise and Transit Detection Deep transits: traditional methods (BLS) work well BLS: Kovács, Zucker & Mazeh 2002, A&A, 391, 369 Shallow transits: inter-temporal correlations might mask the signal Pont, Zucker & Queloz 2006, MNRAS, 373, 231

4 Gaussian Processes An elegant way to model inter-temporal correlations Use a kernel function to model the correlation A kernel is parameterized by a few hyperparameters k t i t j = A s 2 exp t i t j λ s 2 +A q 2 exp sin2 π t i t j /T q 2 t i t j λ q 2 + A w 2 δ t i t j Fitting is very hard (involves inversion of huge matrices) Simultaneous GP fitting and transit search even harder Rasmussen & Williams 2006 (textbook) Aigrain et al (application to K2 light curves) Foreman-Mackey et al (approximate fast fitting)

5 Deep Learning Neural Networks a set of computational heuristics to train highly nonlinear parametric functions structured in a layered form to perform a certain task

6 Biological Neuron

7 McCulloch-Pitts Neuron

8 Deep Learning in a Nutshell Supervised learning: given examples with ground truth ( training set ) Loss function (error quantification) Loss function depends analytically on the synaptic weights Backpropagation of derivatives (chain rule) through layers Slowly update the synaptic weights (e.g. gradient descent, Metropolis-Hastings, etc.) to minimize loss function Essential ingredients: Non linearity and layered structure A growing multitude of neural network architectures

9 Feasibility Study Zucker & Giryes 2018, AJ, 155, 4 Fictitious planet-hunting space telescope Noise simulated by GP White noise Red noise (squared exponential) Quasi periodic noise Hyperparameters drawn randomly

10 Feasibility Study

11 Feasibility Study Deep Learning HPF+BLS Receiver Operating Characteristic (ROC) curve

12 Feasibility Study Deep Learning Outlier removal +HPF+BLS Adding outliers and discontinuities

13 Sample detections (FPR=0.01)

14 Sample detections (FPR=0.01)

15 Sample false detections (FPR=0.01)

16 TESS ETE-6-based test Time sampling provided in ETE-6 (with gaps) White noise more dominant Red noise, same as in previous study DL still outperforms BLS, but less convincingly First attempts in estimating period and detrending

17 TESS ETE-6-based test DL BLS+HPF DL still outperforms BLS, but less convincingly

18 Estimating period First attempts TESS ETE-6-based test

19 Estimating period First attempts TESS ETE-6-based test

20 What next? Work in progress: use DL to: - Detrend light curves - Characterize transit signals - Identify individual transits Introduce complications (gaps, TTV, multis etc.) Mine old data for hidden planets (Kepler, CoRoT) Use DL to fit GPs Apply Deep Learning to RV (to overcome activity) Prepare for PLATO

21 Related Works Vanderburg & Shallue 2018, AJ, 155, 94 - Identifying not detecting - Traditional approach to detect TCEs in resonant systems - Deep learning for vetting, not detecting Pearson, Palafox & Griffith 2017, MNRAS, 474, Discrete grid of transit parameters (not distributions) - Quasi-periodicity+white noise, not GP

22 Summary Deep learning neural networks are the future! May achieve unprecedented performance, specifically for small planets, with long periods, around G-type stars A fundamentally different approach (nonlinear) Zucker & Giryes 2018, AJ, 155, 4