Scalable physical source-to-field inference with hypernetworks
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908812182552576 |
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| author | James, Berian Pollok, Stefan Peis, Ignacio Baker, Elizabeth Louise Frellsen, Jes Bjørk, Rasmus |
| author_facet | James, Berian Pollok, Stefan Peis, Ignacio Baker, Elizabeth Louise Frellsen, Jes Bjørk, Rasmus |
| contents | We present a generative model that amortises computation for the field and potential around e.g.~gravitational or electromagnetic sources. Exact numerical calculation has either computational complexity $\mathcal{O}(M\times{}N)$ in the number of sources $M$ and evaluation points $N$, or requires a fixed evaluation grid to exploit fast Fourier transforms. Using an architecture where a hypernetwork produces an implicit representation of the field or potential around a source collection, our model instead performs as $\mathcal{O}(M + N)$, achieves relative error of $\sim\!4\%-6\%$, and allows evaluation at arbitrary locations for arbitrary numbers of sources, greatly increasing the speed of e.g.~physics simulations. We compare with existing models and develop two-dimensional examples, including cases where sources overlap or have more complex geometries, to demonstrate its application. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05981 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scalable physical source-to-field inference with hypernetworks James, Berian Pollok, Stefan Peis, Ignacio Baker, Elizabeth Louise Frellsen, Jes Bjørk, Rasmus Machine Learning Computational Engineering, Finance, and Science Computational Physics We present a generative model that amortises computation for the field and potential around e.g.~gravitational or electromagnetic sources. Exact numerical calculation has either computational complexity $\mathcal{O}(M\times{}N)$ in the number of sources $M$ and evaluation points $N$, or requires a fixed evaluation grid to exploit fast Fourier transforms. Using an architecture where a hypernetwork produces an implicit representation of the field or potential around a source collection, our model instead performs as $\mathcal{O}(M + N)$, achieves relative error of $\sim\!4\%-6\%$, and allows evaluation at arbitrary locations for arbitrary numbers of sources, greatly increasing the speed of e.g.~physics simulations. We compare with existing models and develop two-dimensional examples, including cases where sources overlap or have more complex geometries, to demonstrate its application. |
| title | Scalable physical source-to-field inference with hypernetworks |
| topic | Machine Learning Computational Engineering, Finance, and Science Computational Physics |
| url | https://arxiv.org/abs/2405.05981 |