Cut-DeepONet: Neural Operator for Discontinuities
A team of researchers has introduced Cut-DeepONet, a two-phase training framework designed to explicitly address discontinuities and sharp transitions in partial differential equations (PDEs). Traditional neural operators often find it challenging to handle these characteristics because of their continuous nature. This innovative method employs a lifting strategy to divide the domain into smooth subregions, treating discontinuities as boundaries in a higher-dimensional context, which aligns with the biases of neural networks. Furthermore, an auxiliary network forecasts the locations of discontinuities based on the input for previously unseen data. This technique simplifies the learning process and circumvents the need to directly approximate discontinuities within continuous function spaces.
Key facts
- Cut-DeepONet is a two-stage training framework for neural operators.
- It handles discontinuities and sharp transitions in PDEs.
- Existing neural operators struggle with discontinuities due to continuous representations.
- The method uses a lifting strategy to partition the domain into smooth subregions.
- Discontinuities are represented as boundaries in a higher-dimensional space.
- An additional network predicts input-dependent discontinuity locations.
- The approach reduces learning complexity.
- It avoids directly approximating discontinuities within continuous function spaces.
Entities
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