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In low-dimensional parameter spaces, classical interpolation schemes yield algebraic convergence rates based on Sobolev regularity in the parameter variable. In higher-dimensional parameter spaces, we replace classical interpolation by extreme learning machine (ELM) surrogates and obtain error bounds under explicit approximation and stability assumptions. The proposed framework is applied to inverse problems in quantitative photoacoustic tomography, where we derive potential and parameter reconstruction error estimates and demonstrate substantial computational savings compared to standard approaches, without sacrificing accuracy.
| Subjects: | Numerical Analysis (math.NA); Machine Learning (cs.LG) |
| Cite as: | arXiv:2602.14757 [math.NA] |
| (or arXiv:2602.14757v2 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2602.14757 arXiv-issued DOI via DataCite |
From: Karl Larsson [view email]
[v1]
Mon, 16 Feb 2026 14:01:50 UTC (1,932 KB)
[v2]
Fri, 17 Apr 2026 05:22:28 UTC (2,377 KB)
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