Numerous developments show the promising potential of deep learning in obtaining numerical solutions to partial differential equations beyond the reach of current numerical solvers. However, data-driven neural operators tend to suffer from the issue that the data needed to train a network depends on classical numerical solvers such as finite difference or finite element, among others. We propose a different approach to generating synthetic functional training data that does not require solving a PDE numerically. The proposed `backwards' approach to generating training data only requires derivative computations, in contrast to standard `forward' approaches, which require a numerical PDE solver, enabling us to generate many data points quickly and efficiently. Open research directions and limitations are discussed.
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