Reproduce “MIONet: Learning multiple-input operators via tensor product” on OpenResearch

About this paper

Pengzhan Jin, Shuai Meng, Lu Lu

MIONet introduces a neural operator designed to learn mappings from multiple functional inputs, potentially residing in different Banach spaces, to an output function. This architecture, built on a new universal approximation theorem, consistently achieves superior accuracy over DeepONet baselines on various ODE and PDE problems, demonstrating effectiveness in handling complex system dependencies and integrating prior physical knowledge.

Key insights

• The first universal approximation theorem for operators with multiple functional inputs from product Banach spaces validates the capability of neural networks for such complex mappings.
• A low-rank tensor approximation strategy, central to MIONet's design, effectively manages parameter complexity while maintaining strong approximation power for high-order tensor interactions.
• Integrating prior knowledge, such as linearity of an input or periodicity of the output, directly into the network architecture (e.g., using linear layers or periodic features) significantly enhances model accuracy and interpretability.

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