Derivative-enhanced Deep Operator Network
This work addresses the challenge of accurate and efficient surrogate modeling for parametric PDEs, which is incremental as it builds on existing neural operators like DeepONet and FNO.
The authors tackled the problem of improving surrogate models for parametric PDEs by proposing a derivative-enhanced deep operator network (DE-DeepONet), which leverages derivative information to enhance prediction accuracy and reduce training data requirements, with numerical experiments validating its effectiveness.
The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a derivative-enhanced deep operator network (DE-DeepONet), which leverages derivative information to enhance the solution prediction accuracy and provides a more accurate approximation of solution-to-parameter derivatives, especially when training data are limited. DE-DeepONet explicitly incorporates linear dimension reduction of high dimensional parameter input into DeepONet to reduce training cost and adds derivative loss in the loss function to reduce the number of required parameter-solution pairs. We further demonstrate that the use of derivative loss can be extended to enhance other neural operators, such as the Fourier neural operator (FNO). Numerical experiments validate the effectiveness of our approach.