Fast and accurate predictions for complex physical dynamics are a significant
challenge across various applications. Real-time prediction on
resource-constrained hardware is even more crucial in real-world problems. The
deep operator network (DeepONet) has recently been proposed as a framework for
learning nonlinear mappings between function spaces. However, the DeepONet
requires many parameters and has a high computational cost when learning
operators, particularly those with complex (discontinuous or non-smooth) target
functions. This study proposes HyperDeepONet, which uses the expressive power
of the hypernetwork to enable the learning of a complex operator with a smaller
set of parameters. The DeepONet and its variant models can be thought of as a
method of injecting the input function information into the target function.
From this perspective, these models can be viewed as a particular case of
HyperDeepONet. We analyze the complexity of DeepONet and conclude that
HyperDeepONet needs relatively lower complexity to obtain the desired accuracy
for operator learning. HyperDeepONet successfully learned various operators
with fewer computational resources compared to other benchmarks.

提出了一种使用超网络的方法，即 HyperDeepONet，通过较少的参数来学习复杂操作符，并成功地在较少的计算资源下学习各种操作符，并具有实时预测的能力。