Ensemble learning for Physics Informed Neural Networks: a Gradient Boosting approach
Abstract: While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date, PINNs have not been successful in simulating multi-scale and singular perturbation problems. In this work, we present a new training paradigm referred to as "gradient boosting" (GB), which significantly enhances the performance of physics informed neural networks (PINNs). Rather than learning the solution of a given PDE using a single neural network directly, our algorithm employs a sequence of neural networks to achieve a superior outcome. This approach allows us to solve problems presenting great challenges for traditional PINNs. Our numerical experiments demonstrate the effectiveness of our algorithm through various benchmarks, including comparisons with finite element methods and PINNs. Furthermore, this work also unlocks the door to employing ensemble learning techniques in PINNs, providing opportunities for further improvement in solving PDEs.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: All the changed are marked as red. Please see the details in the response to the reviewer.
Assigned Action Editor: ~Vincent_Fortuin1
Submission Number: 1411
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