Composite Bayesian Optimization In Function Spaces Using NEON -- Neural Epistemic Operator Networks
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909044162166784 |
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| author | Guilhoto, Leonardo Ferreira Perdikaris, Paris |
| author_facet | Guilhoto, Leonardo Ferreira Perdikaris, Paris |
| contents | Operator learning is a rising field of scientific computing where inputs or outputs of a machine learning model are functions defined in infinite-dimensional spaces. In this paper, we introduce NEON (Neural Epistemic Operator Networks), an architecture for generating predictions with uncertainty using a single operator network backbone, which presents orders of magnitude less trainable parameters than deep ensembles of comparable performance. We showcase the utility of this method for sequential decision-making by examining the problem of composite Bayesian Optimization (BO), where we aim to optimize a function $f=g\circ h$, where $h:X\to C(\mathcal{Y},\mathbb{R}^{d_s})$ is an unknown map which outputs elements of a function space, and $g: C(\mathcal{Y},\mathbb{R}^{d_s})\to \mathbb{R}$ is a known and cheap-to-compute functional. By comparing our approach to other state-of-the-art methods on toy and real world scenarios, we demonstrate that NEON achieves state-of-the-art performance while requiring orders of magnitude less trainable parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03099 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Composite Bayesian Optimization In Function Spaces Using NEON -- Neural Epistemic Operator Networks Guilhoto, Leonardo Ferreira Perdikaris, Paris Machine Learning Artificial Intelligence Computational Engineering, Finance, and Science Information Theory 68T37 J.2; I.2.6 Operator learning is a rising field of scientific computing where inputs or outputs of a machine learning model are functions defined in infinite-dimensional spaces. In this paper, we introduce NEON (Neural Epistemic Operator Networks), an architecture for generating predictions with uncertainty using a single operator network backbone, which presents orders of magnitude less trainable parameters than deep ensembles of comparable performance. We showcase the utility of this method for sequential decision-making by examining the problem of composite Bayesian Optimization (BO), where we aim to optimize a function $f=g\circ h$, where $h:X\to C(\mathcal{Y},\mathbb{R}^{d_s})$ is an unknown map which outputs elements of a function space, and $g: C(\mathcal{Y},\mathbb{R}^{d_s})\to \mathbb{R}$ is a known and cheap-to-compute functional. By comparing our approach to other state-of-the-art methods on toy and real world scenarios, we demonstrate that NEON achieves state-of-the-art performance while requiring orders of magnitude less trainable parameters. |
| title | Composite Bayesian Optimization In Function Spaces Using NEON -- Neural Epistemic Operator Networks |
| topic | Machine Learning Artificial Intelligence Computational Engineering, Finance, and Science Information Theory 68T37 J.2; I.2.6 |
| url | https://arxiv.org/abs/2404.03099 |