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Figure 4
Case study: first-pass fit of the integrated spectrum from a plant sample. Both methods start from random parameter and amplitude initialization (within reasonable ranges) with no manual adjustments and use the same target element list. Top: NLopt result (finite-difference gradients with a traditional nonlinear optimizer) stalls far from the data (R2 = −0.050). Bottom: MapsTorch (automatic differentiation with Adam optimizer) reaches a substantially better first-pass fit (R2 = 0.872). Spectra are shown as log10(counts+1) versus energy (keV).

Journal logoJOURNAL OF
SYNCHROTRON
RADIATION
ISSN: 1600-5775
Volume 33| Part 1| January 2026| Pages 235-245
https://doi.org/10.1107/S160057752501032X
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