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Fast and accurate predictions for complex physical dynamics are a significantchallenge across various applications. Real-time prediction onresource-constrained hardware is even more crucial in real-world problems. Thedeep operator network (DeepONet) has recently been proposed as a framework forlearning nonlinear mappings between function spaces. However, the DeepONetrequires many parameters and has a high computational cost when learningoperators, particularly those with complex (discontinuous or non-smooth) targetfunctions. This study proposes HyperDeepONet, which uses the expressive powerof the hypernetwork to enable the learning of a complex operator with a smallerset of parameters. The DeepONet and its variant models can be thought of as amethod of injecting the input function information into the target function.From this perspective, these models can be viewed as a particular case ofHyperDeepONet. We analyze the complexity of DeepONet and conclude thatHyperDeepONet needs relatively lower complexity to obtain the desired accuracyfor operator learning. HyperDeepONet successfully learned various operatorswith fewer computational resources compared to other benchmarks.

HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork