Position: Optimization in SciML Should Employ the Function Space Geometry
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866907917448380416 |
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| author | Müller, Johannes Zeinhofer, Marius |
| author_facet | Müller, Johannes Zeinhofer, Marius |
| contents | Scientific machine learning (SciML) is a relatively new field that aims to solve problems from different fields of natural sciences using machine learning tools. It is well-documented that the optimizers commonly used in other areas of machine learning perform poorly on many SciML problems. We provide an infinite-dimensional view on optimization problems encountered in scientific machine learning and advocate for the paradigm first optimize, then discretize for their solution. This amounts to first choosing an appropriate infinite-dimensional algorithm which is then discretized in a second step. To illustrate this point, we show that recently proposed state-of-the-art algorithms for SciML applications can be derived within this framework. As the infinite-dimensional viewpoint is presently underdeveloped in scientific machine learning, we formalize it here and advocate for its use in SciML in the development of efficient optimization algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Position: Optimization in SciML Should Employ the Function Space Geometry Müller, Johannes Zeinhofer, Marius Optimization and Control Scientific machine learning (SciML) is a relatively new field that aims to solve problems from different fields of natural sciences using machine learning tools. It is well-documented that the optimizers commonly used in other areas of machine learning perform poorly on many SciML problems. We provide an infinite-dimensional view on optimization problems encountered in scientific machine learning and advocate for the paradigm first optimize, then discretize for their solution. This amounts to first choosing an appropriate infinite-dimensional algorithm which is then discretized in a second step. To illustrate this point, we show that recently proposed state-of-the-art algorithms for SciML applications can be derived within this framework. As the infinite-dimensional viewpoint is presently underdeveloped in scientific machine learning, we formalize it here and advocate for its use in SciML in the development of efficient optimization algorithms. |
| title | Position: Optimization in SciML Should Employ the Function Space Geometry |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2402.07318 |