GMLS-Nets: A Machine Learning Framework for Unstructured Data
summary
Framework generalizes convolutional networks to scattered point data by parameterizing a GMLS estimator that encodes local least-squares reconstructions into learned maps. It outputs stencil coefficients from small dense solves, with TensorFlow/PyTorch code and Compadre GPU acceleration available. Tested on 200 CFD runs to regress drag from velocity fields, on particle simulations where short MD bursts recover the homogenized heat equation, and on learned descretizations that permit a CFL number 10 and deliver an order-of-magnitude improvement over standard schemes.
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chapters (13)
- 0:00Introduction
- 0:30Scientific Machine Learning
- 2:43Operator Regression
- 5:13Convolutional Networks
- 7:29Generalized MLS
- 10:04GMLS Methodology
- 12:37Forward Modeling Applications
- 15:27GMLS Net Architecture
- 18:02Validation and Results
- 21:11Data-Driven Modeling
- 22:58Data-Driven Discretization
- 25:03Summary and Future Work
- 27:03Q&A Session
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