Single-operator learning can be used to solve PDE-related problems by using neural operators to approximate the target PDE operator. However, when the distribution of the input functions is changed or a new operator is given, a trained neural operator may not approximate the given new problems directly. Multi-operator learning uses a single neural network structure to approximate different operators simultaneously. In this work, we will discuss to use of multi-operator learning models to handle new problems. Specifically, we show that we need to include an operator encoding structure in the network to enable operator identification and extrapolation. We propose to use symbolic encoding to encode the PDEs, and the trained symbols corresponding to the operations and variables can represent the new PDE format. Our generalization tests show that a multi-operator learning framework can leverage information from different operators to enable generalization, which shows the importance of learning different operators simultaneously using a single neural network.
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