Ensemble and Mixture-of-Experts DeepONets For Operator Learning
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913736761016320 |
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| author | Sharma, Ramansh Shankar, Varun |
| author_facet | Sharma, Ramansh Shankar, Varun |
| contents | We present a novel deep operator network (DeepONet) architecture for operator learning, the ensemble DeepONet, that allows for enriching the trunk network of a single DeepONet with multiple distinct trunk networks. This trunk enrichment allows for greater expressivity and generalization capabilities over a range of operator learning problems. We also present a spatial mixture-of-experts (MoE) DeepONet trunk network architecture that utilizes a partition-of-unity (PoU) approximation to promote spatial locality and model sparsity in the operator learning problem. We first prove that both the ensemble and PoU-MoE DeepONets are universal approximators. We then demonstrate that ensemble DeepONets containing a trunk ensemble of a standard trunk, the PoU-MoE trunk, and/or a proper orthogonal decomposition (POD) trunk can achieve 2-4x lower relative $\ell_2$ errors than standard DeepONets and POD-DeepONets on both standard and challenging new operator learning problems involving partial differential equations (PDEs) in two and three dimensions. Our new PoU-MoE formulation provides a natural way to incorporate spatial locality and model sparsity into any neural network architecture, while our new ensemble DeepONet provides a powerful and general framework for incorporating basis enrichment in scientific machine learning architectures for operator learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11907 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ensemble and Mixture-of-Experts DeepONets For Operator Learning Sharma, Ramansh Shankar, Varun Machine Learning We present a novel deep operator network (DeepONet) architecture for operator learning, the ensemble DeepONet, that allows for enriching the trunk network of a single DeepONet with multiple distinct trunk networks. This trunk enrichment allows for greater expressivity and generalization capabilities over a range of operator learning problems. We also present a spatial mixture-of-experts (MoE) DeepONet trunk network architecture that utilizes a partition-of-unity (PoU) approximation to promote spatial locality and model sparsity in the operator learning problem. We first prove that both the ensemble and PoU-MoE DeepONets are universal approximators. We then demonstrate that ensemble DeepONets containing a trunk ensemble of a standard trunk, the PoU-MoE trunk, and/or a proper orthogonal decomposition (POD) trunk can achieve 2-4x lower relative $\ell_2$ errors than standard DeepONets and POD-DeepONets on both standard and challenging new operator learning problems involving partial differential equations (PDEs) in two and three dimensions. Our new PoU-MoE formulation provides a natural way to incorporate spatial locality and model sparsity into any neural network architecture, while our new ensemble DeepONet provides a powerful and general framework for incorporating basis enrichment in scientific machine learning architectures for operator learning. |
| title | Ensemble and Mixture-of-Experts DeepONets For Operator Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2405.11907 |