He Wang (王赫)

Institute of Theoretical Physics, CAS

Beijing Normal University

on behalf of the KAGRA collaboration

The 8\(^\text{th}\) KAGRA International Workshop , 14:30-14:45 KST on July 9\(^\text{th}\), 2021

Part of works as a pre-print.

hewang@mail.bnu.edu.cn / hewang@itp.ac.cn

Collaborators:

Zhoujian Cao (BNU)

Yue Zhou (PCL)

Zong-Kuan Guo (ITP-CAS)

Zhixiang Ren (PCL)

Outline

• Opportunity in Gravitational-Wave Data Analysis
• Trends in Gravitational-Wave Signal Detection
• Curse of Dimensionality
• Motivation: Prior Sampling
• Normalizing Flow
• Results

Matched-filtering for waveform features

• Machine learning algorithms present features that make them particularly suitable for gravitational waves astrophysics

• Highlight:
  • Now we can extract our target features by matched-filtering technique or machine learning from feature space of GW.
  • 
     

• Review article: Enhancing Gravitational-Wave Science with Machine Learning, Machine Learning: Science and Technology, arXiv:2005.03745 （also in Survey4GWML）

GW150914

Phys.Rev.D 101 (2020) 10, 104003

• Machine learning algorithms present features that make them particularly suitable for gravitational waves astrophysics

• Highlight:
  • Now we can extract our target features by matched-filtering technique or machine learning from feature space of GW.
  • 
     

• Review article: Enhancing Gravitational-Wave Science with Machine Learning, Machine Learning: Science and Technology, arXiv:2005.03745 （also in Survey4GWML）

• Machine learning algorithms present features that make them particularly suitable for gravitational waves astrophysics

• Highlight:
  • Now we can extract our target features by matched-filtering technique or machine learning from feature space of GW.
  • Can we achieve more by exploiting the whole feature space for parameter estimation?

• Review article: Enhancing Gravitational-Wave Science with Machine Learning, Machine Learning: Science and Technology, arXiv:2005.03745 （also in Survey4GWML）

• Phys.Rev.D 97 (2018) 4, 044039 
  • The first attempt
• Phys.Rev.Lett 120 (2019) 14, 141103
  • Matched-filtering vs CNN
• Phys.Rev.D 101, 083006 (2020)
  • GstLAL vs DNN by ranking candidates...

• Phys.Rev.D 100 (2019) 6, 063015
  • GW events for BBH in GWTC-1
• Phys.Rev.D 101 (2020) 10, 104003
  • All GW events in GWTC-1
• Phys.Lett.B 812 (2021) 136029
  • GWTC-1 & GW190412, GW190521
• 2011.10425
  • GWTC-1 & 34/37 in GWTC-2
• Phys.Rev.D 103, 062004 (2021)
  • 8/11 in GWTC-1
• Phys.Lett.B 815 (2021) 136161
  • All GW events in GWTC-1

Proof-of-principle studies

Production search studies

Last updated on April. 2021

Detection of early inspiral of GW

• Phys.Rev.D 103 (2021), 063034
• Wei et al. (2012.03963)
• Baltus et al. (2104.00594)
• Yu et al. (2104.09438)

• Use Bayes’ theorem to estimate the posterior distribution of the source parameters.
• Stochastically sampling the posterior is a time-consuming process:
  • One parameter estimation run requires collecting tens of thousands of samples from the posterior.
  • Each sample is found by conducting thousands of random walks.
  • Each random walk involves one waveform generation.
  • One parameter estimation run requires more than millions of waveform calculations.
• May take several days to several weeks to run parameter estimation on a single event.

• Traditional statistical methods scale poorly in time / accuracy for
  datasets described by many parameters.
   
• Machine learning algorithms perform very well in exploiting
  correlations across a large number of dimensions

• We tackle this issue by thinking out of the box and directly use the information from the "future", as opposed to the others' work by exploring network structure.

• In many high-dimensional cases, the dataset is normally limited relative to the prior physical dimensions and the feature space can not be sufficiently covered by data points.
• Without representations, it would be challenging and even impossible to learn the subtle features.
• Therefore the key question is how to effectively sample the feature space.
• This is essentially equivalent to incorporate the physical domain knowledge into the high-dimensional training data.

• In our case, we use the interim distribution that is derived from Monte Carlo method as a representation of the prior physical knowledge.
• This is equivalent to draw more data points to cover the more important areas in the feature space for a better Bayesian inference.
• We draw the training samples from the interim distribution with a certain probability “\(\alpha\)” and from a uniform distribution with a probability “\(1-\alpha\)”.
• Eventually, the training dataset is consists of samples from interim distribution and a general distribution without any prior knowledge.
• Therefore, the prior knowledge can be effective utilized in a more controlled way.

• In addition to tweak the data, we also employ a more recent machine learning method dubbed as normalizing flow, instead of using traditional Bayesian approaches, in our high-dimensional GW data analysis.

• Although we recognize a similar idea that applies normalizing flow technique to characterize the distribution exits in the previous works [Green & Gair (2020), 2106.12594], our method still differs from the recent study in GW study:
  1. Improved data preparetion
     (sampling all 15 dims instead of extrinsic only)
  2. Prior sampling to construct the training dataset with domain knowledge using SMOTETomek technique.
     (Relatively a better performance than [Green & Gair (2020)])
  3. Effectively and efficiently perform Bayesian inference on ultra-high dimension gravitational-wave data.
     (8s for 50,000 posterior samples)

• This implies that roughly 10% physical prior knowledge incorporated is enough for accurate Bayesian inference of the high-dimensional gravitational-wave data.

• The results from our approach are indistinguishable, both qualitatively and quantitatively, with the ground truth.

• Our method may show a highly scalable performance.
  (In working)

• Marginalized one- (1-σ) and two- dimensional posterior distributions for the benchmarking event (GW150914) over the complete 15 physical parameters, with our approach (orange) and the ground truth (blue).
• The JS divergences are showed on the top