MAGIC: Microlensing Analysis Guided by Intelligent Computation

This repo contains the code for the paper

MAGIC: Microlensing Analysis Guided by Intelligent Computation (arXiv)

and the short paper

Parameter Estimation in Realistic Binary Microlensing Light Curves with Neural Controlled Differential Equation

at ICML 2022 Workshop on Machine Learning for Astrophysics.

Abstract

The modeling of binary microlensing light curves via the standard sampling-based method can be challenging, because of the time-consuming light curve computation and the pathological likelihood landscape in the high-dimensional parameter space. In this work, we present MAGIC, which is a machine learning framework to efficiently and accurately infer the microlensing parameters of binary events with realistic data quality. In MAGIC, binary microlensing parameters are divided into two groups and inferred separately with different neural networks. The key feature of MAGIC is the introduction of neural controlled differential equation, which provides the capability to handle light curves with irregular sampling and large data gaps. Based on simulated light curves, we show that MAGIC can achieve fractional uncertainties of a few percent on the binary mass ratio and separation. We also test MAGIC on a real microlensing event. MAGIC is able to locate the degenerate solutions even when large data gaps are introduced. As irregular samplings are common in astronomical surveys, our method also has implications to other studies that involve time series.

Checkpoints

Checkpoints of pretrained models can be downloaded at Google Drive or Tsinghua Cloud.

This includes locator with $k=1/3, 0.75, 1, 1.25, 1.5, 1.75, 2$ and estimator with latent dim $32$, $n_G=12$ and diagonal covariance used in the paper.

Experiments

Experiments and tests in the paper can be reproduced with the Jupyter notebooks in the test folder (see this readme file). This folder, along with the simulate folder also contains additional tests not shown in the paper, which might be useful references for other uses.

As an example, the ground truth v.s. prediction plots of binary microlensing parameters are as follows (taken from the paper):

Training

Run the scripts train_locator.py and train_cde_mdn.py to train locator and estimator from scratch. More settings can be specified with additional flags (see the script contents).

Before training the models, you might want to simulate some light curves if you haven't got any. Use the script simulate/simulate.py for the simulation. Note that this step is better done on a CPU cluster.

Model

As described in the paper, MAGIC consists of a locator and an estimator.

The locator is a one-dimensional U-Net, which can be found in model/locator.py.

The estimator is composed of a neural controlled differential equation for feature extraction and a mixture density network for posterior modelling. See model/cde_mdn.py.

In case you'd like to customize the models for your own works, you should also have a look at the other files in the model folder.

Citation

If you find our work useful, please give us credit by citing our paper:

@article{zhao2022magic,
  title={MAGIC: Microlensing Analysis Guided by Intelligent Computation},
  author={Zhao, Haimeng and Zhu, Wei},
  journal={The Astronomical Journal},
  volume={164},
  number={5},
  pages={192},
  year={2022},
  publisher={IOP Publishing}
}