|
| 1 | +--- |
| 2 | +title: Neural Operators for Fast Simulation of Strong Gravitational Lensing |
| 3 | +layout: gsoc_proposal |
| 4 | +project: DEEPLENSE |
| 5 | +project size: 350hr |
| 6 | +year: 2026 |
| 7 | +organization: |
| 8 | + - Alabama |
| 9 | + - MIT |
| 10 | +--- |
| 11 | + |
| 12 | +## Description |
| 13 | + |
| 14 | +Strong gravitational lensing is a powerful probe of dark matter substructure and cosmological structure formation. Current simulation pipelines (e.g., Lenstronomy-based ray tracing) require solving the lens equation repeatedly for different mass distributions and source configurations. While accurate, these simulations are computationally expensive and limit large-scale parameter sweeps, uncertainty quantification, and real-time inference. |
| 15 | +This project proposes the development of a Neural Operator framework to learn the functional mapping between mass distributions and lensed images. Unlike traditional neural networks that operate on finite-dimensional vectors, neural operators learn mappings between infinite-dimensional function spaces. This makes them particularly well-suited for approximating solutions of physical systems governed by partial differential equations. |
| 16 | +The goal is to train a neural operator that directly maps: |
| 17 | + * Lens mass distribution → Lensed image |
| 18 | + or |
| 19 | + * (Mass distribution, source light profile) → Observed lensed image |
| 20 | + |
| 21 | + |
| 22 | +Such a model would serve as a fast surrogate simulator capable of producing high-fidelity lensing outputs at a fraction of the computational cost of traditional ray-tracing solvers. |
| 23 | +This would represent the first exploration of neural operators within the ML4SCI DeepLense ecosystem. |
| 24 | + |
| 25 | + |
| 26 | +## Duration |
| 27 | + |
| 28 | +Total project length: 175/350 hours. |
| 29 | + |
| 30 | +## Difficulty level |
| 31 | + |
| 32 | +Advanced |
| 33 | + |
| 34 | +## Task ideas |
| 35 | +1. Literature Study |
| 36 | + 1. Study Fourier Neural Operators (FNO) |
| 37 | + 2. Study DeepONets |
| 38 | + 3. Review operator learning in physical systems |
| 39 | +2. Neural Operator Implementation |
| 40 | + 1. Implement Fourier Neural Operator for 2D fields |
| 41 | + 2. Compare with DeepONet-style architectures |
| 42 | + 3. Explore spectral vs spatial operator parameterizations |
| 43 | +3. Evaluation |
| 44 | + 1. Compare speed vs traditional solver |
| 45 | + 2. Measure pixel-wise reconstruction error |
| 46 | + 3. Evaluate preservation of physical invariants |
| 47 | + 4. Test generalization across: |
| 48 | + 1. Different mass profiles |
| 49 | + 2. Different redshifts |
| 50 | + 3. Different source morphologies |
| 51 | +4. Extensions (if time permits) |
| 52 | + 1. Conditional neural operators |
| 53 | + 2. Uncertainty-aware operator learning |
| 54 | + 3. Physics-informed operator constraints |
| 55 | + 4. Hybrid operator + diffusion refinement |
| 56 | + |
| 57 | + |
| 58 | + |
| 59 | + |
| 60 | +## Expected results |
| 61 | + * A neural operator capable of approximating the lensing simulation operator. |
| 62 | + * Significant speedup compared to ray-tracing pipelines. |
| 63 | + * Demonstration of generalization across varying astrophysical conditions. |
| 64 | + * A benchmark study comparing neural operators with CNN-based surrogate models. |
| 65 | + |
| 66 | + |
| 67 | + |
| 68 | +## Requirements |
| 69 | +Python, PyTorch, experience with machine learning and deep learning. |
| 70 | +Partial understanding of: |
| 71 | + * Representation learning |
| 72 | + * Spectral methods |
| 73 | + * Partial differential equations (basic familiarity) |
| 74 | + * Scientific machine learning concepts |
| 75 | +Familiarity with gravitational lensing is preferred but not mandatory. |
| 76 | + |
| 77 | + |
| 78 | + |
| 79 | +<!--- |
| 80 | +## Test |
| 81 | +Please use this [link](https://docs.google.com/document/d/1a-5JiHph3K59gV3-kEZWzKYTFMvDeYiJvoE0U2I4x0w/edit?usp=sharing) to access the test for this project. |
| 82 | +---> |
| 83 | + |
| 84 | +## Mentors |
| 85 | + * [Michael Toomey ](mailto:[email protected]) (Massachusetts Institute of Technology) |
| 86 | + * [Sergei Gleyzer ](mailto:[email protected]) (University of Alabama) |
| 87 | + * [Pranath Reddy ](mailto:[email protected]) (University of Florida) |
| 88 | + * [Ashutosh Ojha ](mailto:[email protected]) (Indian Institute of Technology (Indian School of Mines), Dhanbad) |
| 89 | + |
| 90 | + |
| 91 | +Please DO NOT contact mentors directly by email. Instead, please email [[email protected]](mailto:[email protected]) with Project Title and include **your CV ** and **test results **. The relevant mentors will then get in touch with you. |
| 92 | + |
| 93 | + |
| 94 | +## Links |
| 95 | + * [Paper 1](https://arxiv.org/abs/2010.08895) |
| 96 | + * [Paper 2](https://arxiv.org/abs/2108.08481) |
| 97 | + * [Paper 3](https://arxiv.org/abs/1910.03193) |
| 98 | + |
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