Physics-Informed (& -Informative) Generative Modelling in Astronomy

Machine Learning for Physics and the Physics of Learning 2019: IPAM/UCLA

Transcript

1. “I love working with astronomers, since their data is worthless.” - Jim Gray, Microsoft
2. Josh Bloom UC Berkeley (Astronomy), LBNL @profjsb Physics-Informed (& -Informative) Generative Modelling in Astronomy Machine Learning for Physics and the Physics of Learning 2019 Sept 23, IPAM/UCLA Data Driven Discovery Investigator
3. E. Ramirez-Ruiz (UCSC) (cf. Kasen) 50 100 150 200 Days Since Explosion Type Ia NS + NS Mergers Type IIp NS + RSG Collision IMBH + WD Collision Pair Production Supernovae -10 -12 -14 -16 -18 -20 -22 M H z=0.45 200Mpc Rumsfelian Challenge Optimizing Payout over known-knowns, known- unknowns, & unknown- unknowns (Small # of labels of known knowns) ie. Discovery & Classification To Prioritize Followup with Scarce resources
4. Large Synoptic Survey Telescope (LSST)
 • 20 Tb/night (raw imaging) • Track 18 Billion objects • 150 TFLOPS for First Data Release ~ 2022 • 15 PB final catalog September 2019
5. Agenda ๏Intro to ML centrality in astrophysical discovery & inference
 ๏Self- and semi-supervision ‣astronomical time-series ‣Image inpainting
 ๏Physical constraints in VAEs for survey simulation
 ๏Generative Catalogs & Semantic Self-Supervised 
 Models for Remote Sensing Machine Learning for Physics and the Physics of Learning 2019 Sept 23, IPAM/UCLA
6. Bread & Butter ML in Astronomy
7. 4 H. Brink et al. Figure 1. Examples of bogus (top) and real (bottom) thumbnails. Note that the shapes of the bogus sources can be quite varied, values lie between 1 and 1. As the pixel values for real can- didates can take on a wide range of values depending on the astrophysical source and observing conditions, this normal- ization ensures that our features are not overly sensitive to the peak brightness of the residual nor the residual level of background flux, and instead capture the sizes and shapes of the subtraction residual. Starting with the raw subtraction thumbnail, I, normalization is achieved by first subtract- ing the median pixel value from the subtraction thumbnail and then dividing by the maximum absolute value across all median-subtracted pixels via IN (x, y) = ⇢ I(x, y) med[I(x, y)] max{abs[I(x, y)]} . (1) Analysis of the features derived from these normalized real and bogus subtraction images showed that the transfor- mation in (1) is superior to other alternatives, such as the Frobenius norm ( p trace(IT I)) and truncation schemes where extreme pixel values are removed. Using Figure 1 as a guide, our first intuition about real candidates is that their subtractions are typically az- imuthally symmetric in nature, and well-represented by a 2-dimensional Gaussian function, whereas bogus candidates are not well behaved. To this end, we define a spherical 2D Gaussian, G(x, y), over pixels x, y as G(x, y) = A · exp ⇢ 1 2  (cx x)2 + (cy y)2 , (2) which we fit to the normalized PTF subtraction image, IN , of each candidate by minimizing the sum-of-squared di↵er- “bogus” “real” image “subtractions” a real-time framework to discover variable/transient sources without people • fast (compared to people) • parallelizeable • transparent • deterministic • versionable 1000 to 1 needle in the haystack problem Machine Learning Discovery Engine
8. Supernova Discovery in the Pinwheel Galaxy 11 hr after explosion nearest SN Ia in >3 decades ML-assisted “real-bogus” discovery at LBNL ©Peter Nugent Nugent, …, JSB+12 1110.6201
9. Bloom+12 see also Nugent+12, Nature
10. Cosmological Parameters from the Dark matter Distribution Figure 6. The architecture of our 3D conv-net. The model has six convolutional and 3 fully connected layers. The first two convolu- tional layers are followed by average pooling. All layers, except the final layer, use leaky rectified linear units, and all the convo- lutional layers use batch-normalization (b.n.). Figure 7. (top) visualization of inputs that maximize the activa- tion of 7/1024 units (corresponding to seven rows) at the first fully connected layer. In this figure, we have unwrapped the maximiz- ing input sub-cubes for better visualization. (bottom) magnified portion of the top row. vation of a particular unit while treating the input X as the optimization variable (Erhan et al., 2009; Simonyan et al., 2013) X⇤ = arg max X s.t. Xl,i kXk2  ⇣ “Estimating Cosmological Parameters from the Dark Matter Distribution” Ravanbakhsh+ 1711.02033 “Fast Automated Analysis of Strong Gravitational Lenses with Convolutional Neural Networks” Figure 1: Comparison of parameters estimated u true values (x-axis). From left to right, the panels y components of complex ellipticity. The shade Hezaveh, Levasseur, Marshall 1708.08842 Black-Box Cosmological Inference Einstein Radius (model) Einstein Radius (CNN) Williams Center for Cosmology, Department of Physics, Carnegie Mellon University, Carnegie 5000 Forbes Ave., rgh, PA 15213, USA Abstract grand challenge of the 21st century cosmol- gy is to accurately estimate the cosmological arameters of our Universe. A major approach estimating the cosmological parameters is to se the large scale matter distribution of the Uni- erse. Galaxy surveys provide the means to map ut cosmic large-scale structure in three dimen- ons. Information about galaxy locations is typ- ally summarized in a “single” function of scale, uch as the galaxy correlation function or power- pectrum. We show that it is possible to estimate ese cosmological parameters directly from the stribution of matter. This paper presents the pplication of deep 3D convolutional networks volumetric representation of dark-matter sim- ations as well as the results obtained using a Figure 1. Dark matter distribution in three cubes produced using
11. Cosmological Parameters from the Dark matter Distribution Figure 6. The architecture of our 3D conv-net. The model has six convolutional and 3 fully connected layers. The first two convolu- tional layers are followed by average pooling. All layers, except the final layer, use leaky rectified linear units, and all the convo- lutional layers use batch-normalization (b.n.). Figure 7. (top) visualization of inputs that maximize the activa- tion of 7/1024 units (corresponding to seven rows) at the first fully connected layer. In this figure, we have unwrapped the maximiz- ing input sub-cubes for better visualization. (bottom) magnified portion of the top row. vation of a particular unit while treating the input X as the optimization variable (Erhan et al., 2009; Simonyan et al., 2013) X⇤ = arg max X s.t. Xl,i kXk2  ⇣ “Estimating Cosmological Parameters from the Dark Matter Distribution” Ravanbakhsh+ 1711.02033 “Fast Automated Analysis of Strong Gravitational Lenses with Convolutional Neural Networks” Figure 1: Comparison of parameters estimated u true values (x-axis). From left to right, the panels y components of complex ellipticity. The shade Hezaveh, Levasseur, Marshall 1708.08842 Black-Box Cosmological Inference Einstein Radius (model) Einstein Radius (CNN)
12. Self- and Semi- Supervision
13. • 50+ features (colors, frequency domain, …) • Random Forest (+feature selection) • Probability Postprocessing Challenges
 • Hand-coded feature engineering • Prediction time∝ # features • Small # of labels • Transfer learning difficult Traditional Approach to Classification Richards, JSB+11, 12 Armstrong+16
14. 1. Build an autoencoder network to learn to reproduce irregularly sampled light curves using an information bottleneck (B) E( ( → B D → ( ( ≈ 2. Use B as features and learn a traditional classifier (random forest) F. Peréz S. van der Walt Self-Supervised (Autoencoder) Recurrent NN
15. len(B) = 64 Example Reconstructions of the Autoencoder Self-Supervised (Autoencoder) Recurrent NN
16. Results rival best-in-class approaches Code/Data: https://github.com/bnaul/IrregularTimeSeriesAutoencoderPaper Self-Supervised (Autoencoder) Recurrent NN
17. Figure 1: Diagram of an RNN encoder/decoder architecture for irregularly sampled time ser data. This network uses two RNN layers (specifically, bidirectional gated recurrent units (GRU) [6, 2 • Natively handles irregularly sampling • Learning loss accounts for uncertainty • Natural data augmentation with bootstrap resampling Novelties & Improvements Self-Supervised (Autoencoder) Recurrent NN
18. Figure 1: Diagram of an RNN encoder/decoder architecture for irregularly sampled time ser data. This network uses two RNN layers (specifically, bidirectional gated recurrent units (GRU) [6, 2 • self-supervised feature learning → we leverage large corpus of unlabelled light curves • transfer learning appears to work • learning scales linearly in training examples Novelties & Improvements Self-Supervised (Autoencoder) Recurrent NN
19. • Co-training across multiple surveys & multiple bandpasses • Semi-supervised topology + metadata (“Kitchen Sink”) Loss ~ Lts + λ Lclass Source Metadata Source Time series Bottleneck Self-supervised Supervised Classification Time series Reconstruction FC LSTM/TCN LSTM/TCN Extensions/Active Research S. Jamal, JSB+ 2019, in prep Self-Supervised (Autoencoder) Recurrent NN
20. Anomaly Detection with Autoencoders • Goal: find new (sub)classes of variable/transient sources “known classes” “anomalous classes” UMAP’ed, Predict-time Bottleneck layer E. Abrahams, in prep
21. Good reconstruction, Small loss Poor reconstruction, Large loss Anomaly Detection with Autoencoders • Goal: find new (sub)classes of variable/transient sources “known classes” “anomalous classes” UMAP’ed, Predict-time Bottleneck layer E. Abrahams, in prep
22. Denoising Autoencoders for Imaging Pipelines
23. UNet: Ronneberger et al. 2015 deepCR*: Network Architecture * deepCR-mask & deepCR-inpaint Zhang & Bloom 1907.09500 Denoising Autoencoders for Imaging Pipelines
24. UNet: Ronneberger et al. 2015 deepCR*: Network Architecture * deepCR-mask & deepCR-inpaint Zhang & Bloom 1907.09500 Denoising Autoencoders for Imaging Pipelines
25. deepCR-mask LACosmic Convolution Filters Learned in 1st layer Current State of the Art Approach Denoising Autoencoders for Imaging Pipelines
26. Zhang & Bloom 2019 deepCR-mask deepCR-inpaint
27. deepCR-mask: better*, faster * at least on Hubble Space Telescope ACS/WFC Denoising Autoencoders for Imaging Pipelines
28. Evaluation of deepCR-inpaint *average value of 60 iteration through the test set Denoising Autoencoders for Imaging Pipelines
29. Physics Informed ML “although neural networks only work well for an exponentially tiny fraction of all possible inputs, the laws of physics are such that the data sets we care about for machine learning are also drawn from an exponentially tiny fraction of all imaginable data sets…” “Why does deep and cheap learning work so well?” Lin, Tegmark, Rolnick arXiv:1608.08225 (2017)
30. • Computer vision: e.g., Spatial Transformer Network, GVNN (s03 layer Euler,…) • High-energy physics: “QCD-Aware Recursive NN for Jet Physics” • Quantum Chemistry: “Ab-Initio Solution of the Many-Electron 
 Schrödinger Equation with Deep Neural Networks” • Louppe+ 1702.00748 Jaderberg+1506.02025; Handa+1607.07405 Pfau+ 1909.02487 Impart/impose/imbue physical constraints into architecture Euclidean Neural Networks rotation-, translation-, & permutation- equivariant convolutional neural networks for 3D point clouds for emulating ab initio calculations & generating atomic geometries Tess Smidt 2018 Alvarez Postdoctoral Fellow in Computing Sciences cf. "Machine learning and the physical sciences” Carleo+ 1903.10563
31. • Computer vision: e.g., Spatial Transformer Network, GVNN (s03 layer Euler,…) • High-energy physics: “QCD-Aware Recursive NN for Jet Physics” • Quantum Chemistry: “Ab-Initio Solution of the Many-Electron 
 Schrödinger Equation with Deep Neural Networks” • Louppe+ 1702.00748 Jaderberg+1506.02025; Handa+1607.07405 Pfau+ 1909.02487 Impart/impose/imbue physical constraints into architecture Euclidean Neural Networks rotation-, translation-, & permutation- equivariant convolutional neural networks for 3D point clouds for emulating ab initio calculations & generating atomic geometries Tess Smidt 2018 Alvarez Postdoctoral Fellow in Computing Sciences Challenge: Find data embeddings & network architectures that conform to known taxonomies, conservation laws, & symmetries cf. "Machine learning and the physical sciences” Carleo+ 1903.10563
32. Application: Optimization of Telescope Operations Opportunity: Learn how to optimally observe the sky to maximize science returns across multiple (competing initiatives). Ie. Run simulations. Science objectives of LSST: •Constraining Dark Energy & Dark Matter •Taking an Inventory of the Solar System •Exploring the Transient Optical Sky •Mapping the Milky Way Towards OpSim v4 and rolling cadence Main drivers for non-uniform, more frequent, visits: - supernovae: need about three times higher sampling rate - asteroids: tracklet linkage would be easier - short-period variability (e.g. cataclysmic variables)
 r band visit every ~15 days https://github.com/LSSTScienceCollaborations/ObservingStrategy
33. Application: Optimization of Telescope Operations Time [day] Brightness Data Driven, Interpolated Simulations Class: Supernova Challenge: we do not have have ab initio physical models for most events/objects that vary. And if we do, those physical models are expensive to run…and they generally do not capture the intra-class variance as observed.
34. Application: Optimization of Telescope Operations Time [day] Brightness Data Driven, Interpolated Simulations Class: Supernova Challenge: we do not have have ab initio physical models for most events/objects that vary. And if we do, those physical models are expensive to run…and they generally do not capture the intra-class variance as observed. Can we build data-driven non-linear, non- parametric models of astronomical sources that capture the range of physically plausible conditions for each type of source?
35. VAE with Physical Parameters for Astronomical Time Series With Jorge Martínez-Palomera (Berkeley) Input data Reconstructed data Latent Space + Label [RRL, LPV, EB,…] + Physical Params , Period, … T eff , [Fe/H] Real Light Curves Generated Light Curve Latent vector + Label + Physical Params
36. VAE with Physical Parameters for Astronomical Time Series van den Oord+ 1609.03499 (Wavenet) Bai+ 1803.01271 (TCN)
37. VAE with Physical Parameters for Astronomical Time Series Reconstruction Likelihood KL-Divergence between encoder’s distribution and prior latent distribution p(z) ∼ (0,1) ℒ = q(z|x) [log p(x|z)]−β D KL (q(z|x)||p(z)) + D KL ( ̂ σ mag ||σ mag ) KL-Divergence between reconstructed and real errors distributions : tunes the importance of an orthogonal/ disentangled latent space β Objective Function
38. No Physical Param Including T eff T eff Note: reconstruction is insensitive to Period Demo VAE with Physical Parameters for Astronomical Time Series
39. Fast cosmic web simulations with generative adversarial networks Figure 2: Comparison of summary statistics between N-body and GAN simulations, for box size of 500 Mpc. The statistics are: mass density histogram (upper left), peak count (upper right), power spectrum of 2D images (lower left) and cross power spectrum (lower right). The cross power spectrum is calculated between pairs N-body images (blue points), between pairs of GAN images (red points), and between pairs consisting of one GAN and one N-body image (cyan points). The power spectra are shown in units of h 1 Mpc, where h = H0/100 corresponds to the Hubble parameter. The standard errors on the mean of the shown with a shaded region, and are too small to be seen for the first three panels. Rodriguez+ 1801.08070 Enabling Dark Energy Science with Deep Generative Models of Galaxy Images Ravanbaksh+16098.05769 5 ig. 7: Comparison of a C-VAE sample before and after adding noise nd a real COSMOS image with corresponding size, magnitude and dshift. f conditional models with increasing resolution in Denton al. (2015). In these conditional models, the generator (a) Galaxy sizes (b) Galaxy brightness Fig. 8: Comparison of galaxy sizes and brightness between real COSMOS images and C-VAE samples. Colors indicate the value of the relevant variable used to condition the generated images (half-light radius for size and magnitude for brightness) accuracy and therefore the dynamics of this adversarial setting Generative Modeling Validation 0.0 0.2 0.4 0.6 0.8 (deg) Generated 0.0 0.2 0.4 0.6 0.8 (deg) 0.0 0.2 0.4 0.6 0.8 (deg) 10 4 10 3 10 2 10 1 Figure 1: Weak lensing convergence maps for our ⇤CDM cosmological model. Randomly selected maps from validation dataset (top) and GAN generated examples (bottom). Mustafa+ 1706.02390
40. Supernova (Thomas/Nugent); Exoplanets (Ford+11) Surrogate Modeling Chen+ 2016 ApJ 836
41. 4 IG. 2. Parameters of the 1528 NR simulations used in the construction of the surrogate models in this paper. We show the Surrogate Modeling "Surrogate models for precessing binary black hole simulations with unequal masse” Varma+ 1905.09300 Numerical Relativity calculations of black hole merger waveforms 100 4000 3000 2000 1000 t (M) 0.1 0.0 0.1 r h+/M q = 3.6 1 = [ 0.74, 0.20, 0.21] 2 = [ 0.38, 0.25, 0.65] = 1.04 0 = 5.02 NRSur7dq4 SEOBNRv3 NR FIG. 5. The plus polarization of the waveforms for the cases that result in th SEOBNRv3 (bottom) in the left panel of Fig. 4. We also show the correspondi using all available modes for that model, along the direction that results in the in the top (bottom) panel. Note that NRSur7dq4 is evaluated using trial surrog binary parameters and the direction in the source frame are indicated in the fi that the peak of the total amplitude occurs at t = 0 [using all available modes, 1528 full simulations
42. Inverse Problems & Likelihood-Free Inference (a) DRDAE: quasi-circular (b) DRDAE: pure noise (c) DRDAE: eccentric (d) EDRDAE: quasi-circular (e) EDRDAE: pure noise (f) EDRDAE: eccentric signals Fig. 4. Performance on GW signals contaminated by real LIGO detector noise with SNRpeak = 0.5. The plots include reconstructed outputs of DRDAE and EDRDAE on quasi-circular signals, pure noise input, and eccentric gravitational waves. Table 3. Ablation study for major parts in EDRDAE MISSING PARTS W/O SA W/O BA W/O CL resilience of the model to denoise signals that are not used during training, i.e., eccentric GWs. Currently, there is no "Denoising Gravitational Waves with Enhanced Deep Recurrent Denoising Auto-Encoders” Time (sec) Shen+ 1903.03105 cf. ”Fast likelihood-free cosmology with neural density estimators and active learning” Alsing+ 1903.00007 Turn inference into density estimation task using simulated data 20 Simulation Machine Learning Inference x z <latexit 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<latexit 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r(x, z|✓) <latexit 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✓ <latexit 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<latexit 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ˆ r(x|✓) <latexit 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<latexit 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<latexit 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✓j <latexit 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parameter latent observable augmented data approximate likelihood ratio Figure 2 A schematic of machine learning based approaches to likelihood-free inference in which the simulation provides training data for a neural network that is subsequently used as a surrogate for the intractable likelihood during inference. Reproduced from (Brehmer et al., 2018b). techniques (Brehmer et al., 2018c). In addition, an inference compilation technique has been applied to inference of a tau-lepton decay. This proof-of-concept effort required developing probabilistic programming protocol that can be integrated into exist- ing domain-specific simulation codes such as SHERPA and GEANT4 (Baydin et al., 2018; Casado et al., 2017). This approach provides Bayesian inference on the latent vari- ables p(Z|X = x) and deep interpretability as the pos- the Hubble parameter evolution from type Ia supernova measurements. These experiences motivated the devel- opment of tools such as CosmoABC to streamline the ap- plication of the methodology in cosmological applica- tions (Ishida et al., 2015). More recently, likelihood-free inference methods based on machine learning have also been developed motivated by the experiences in cosmology. To confront the chal- lenges of ABC for high-dimensional observations X, a Brehmer+ 1805.00013 cf. Nachman, later this week
43. Gaia Catalog (1.7B stars) 200 TB raw data 1.2 TB compressed catalog
44. Tidal Streams & Galactic Cannibalism – 19 – Fig. 1.— Luminance filter images of nearby galaxies from our pilot survey (see Sec. 2 for discussion) showing large, di↵use light substructures in their outskirts: (a) a possible Sgr-like stream in Messier Martinez-Delgado+ 1003.4860 Malhan, Ibata, & Martin 1804+11339
45. Generative Catalogs Preserving Physical Distributions ̂ x x Encoder Decoder z μ σ Catalog Inputs x = r k [mini batch] s k [true] ℒ = D KL [q(z|x)∥p(z)] + λ 1 /N∑ i ∥(x i − ̂ x i )∥2 2 − λ 2 /N∑ i ∑n classes j x i,j log ̂ x i,j k Derived Mini-batch distributions + ∑ k λ k D KL [r k ∥s k ] Latent space regularization Numerical Columns Categorical Columns Ensure Distributions Make physical sense } } } }
46. Generative Catalogs Preserving Physical Distributions ̂ x x Encoder Decoder z μ σ Catalog Inputs x = r k [mini batch] s k [true] ℒ = D KL [q(z|x)∥p(z)] + λ 1 /N∑ i ∥(x i − ̂ x i )∥2 2 − λ 2 /N∑ i ∑n classes j x i,j log ̂ x i,j k Derived Mini-batch distributions + ∑ k λ k D KL [r k ∥s k ] Latent space regularization Numerical Columns Categorical Columns Ensure Distributions Make physical sense } } } } Utility ‣ Enable anomaly detection and uncovering of data quality issues ‣ Lots of mock catalogs consistent with the data to compare to theory ‣ Obfuscation could lower the barrier to (earlier) data releases, affording the development of 3rd party science At what level of compression can we preserve scientific inquiry?
47. Raw Data Preprocessing Batch Predictions ɠ Featurization & Embedding Convert raw data to features & embed following our understanding of the physical system Baking Physical Constraints into the Entire Learning Process ɡ Symmetry preserving layers ɢ Bottlenecks & Model Capacity Sparsity imposition ɣ Loss Function Curation Enforce physically meaningful instance-level predictions ɤ Distributional Loss Enforce ensemble-level predictions conform to expectations
48. James Webb Space Telescope (JWST - 2021) ~ 2 MB/s effective download rate from L2 (56 GB/day max) vs. A single instrument could produce 680 GB/day at full throttle Semantic Self-Supervised Models for Remote Sensing Application to space-based time-domain imaging surveys
49. Semantic Self-Supervised Models for Remote Sensing Application to space-based time-domain imaging surveys 1. Train a denoising autoencoder on all-sky simulations (including meta- data), with enough bottleneck capacity (and overall network capacity) to reach Poisson noise limit at some brightness threshold
 2. Fly the model into space!
 3. Send down bottleneck encoding instead of raw images
 4. Periodically send down weight updates (on-the-fly transfer learning) JWST Mock Image Credit: Williams+ 1802.05272
50. Summary ‣ML is already central to astrophysical discovery & inference at the scale ‣ Self- and semi-supervised approaches are becoming key for astronomers: small label problem ‣ Emerging Opportunity to Accelerate Learning (with less) on Physical Systems w/ Physics-based constraints ‣Growing symbiosis: 
 first-principles simulations ⟷ generative/surrogate/likelihood-free inference ‣New interest: Generative models for compressed sensing & data sharing
51. Josh Bloom UC Berkeley (Astronomy), LBNL @profjsb Data Driven Discovery Investigator Thanks! Physics-Informed (& -Informative) Generative Modelling in Astronomy Machine Learning for Physics and the Physics of Learning 2019 Sept 23, IPAM/UCLA