mPOD-DeepONet: POD-DeepONet for Multiple Outputs

Chieh-An Chou, Lu-Hung Chen

Keywords: DeepONet, POD-DeepONet, Multiphysics PDEs, Multivariate Functional PCA (mFPCA)

Abstract: Many scientific systems require predicting multiple coupled fields simultaneously, yet naïve strategies for extending DeepONet to multi-output settings—such as adding output channels or training separate trunks—yield inconsistent and often poor performance across problems. We propose two POD-based alternatives: cPOD-DeepONet, which performs POD independently per output field and predicts coefficients channel-wise, and mPOD-DeepONet, which leverages multivariate functional PCA to produce a shared basis across all fields so that the branch network predicts a single compact latent vector, significantly reducing model size. Additionally, we explore mKPCA-DeepONet, a kernel PCA extension that captures non-linear cross-channel correlations while maintaining the same compact architecture as mPOD-DeepONet. Extensive evaluations on four multiphysics benchmarks show that all POD-based architectures dramatically improve over naïve DeepONet extensions and deliver consistently robust results, outperforming FNO on half of the benchmarks while remaining competitive on the others—all with substantially faster inference. Between the two linear variants, mPOD-DeepONet achieves comparable accuracy to cPOD-DeepONet with a notably smaller model footprint. Both models remain robust across a wide range of basis sizes, simplifying practical deployment.

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Submission Number: 69