Summary of A Novel Data Generation Scheme For Surrogate Modelling with Deep Operator Networks, by Shivam Choubey et al.
A novel data generation scheme for surrogate modelling with deep operator networks
by Shivam Choubey, Birupaksha Pal, Manish Agrawal
First submitted to arxiv on: 24 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper proposes a novel method for generating training data for DeepONets, which is a type of neural network architecture used for surrogate modeling of physical systems. The traditional approach involves solving partial differential equations (PDEs) using techniques like Finite Element Method (FEM), but this can be computationally intensive. To alleviate this burden, the authors suggest a new framework that does not require PDE integration. Instead, they generate output fields randomly and use Gaussian Process Regression (GPR) to satisfy boundary conditions. The input source field is then calculated using finite difference techniques. This approach can be extended to other operator learning methods, making it widely applicable. The authors validate their method by developing surrogate models for various heat equation-based boundary value problems. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper finds a way to make neural networks easier to use for modeling physical systems. Right now, it takes a lot of computer power to generate the data needed to train these networks. The authors come up with a new way to do this that is much faster and more efficient. They do this by generating random output fields that meet certain conditions, rather than using complex math equations like PDEs. This makes it possible to use neural networks for many different types of problems, which could be really useful. |
Keywords
* Artificial intelligence * Neural network * Regression
