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Recently, the work of Kusch et al. (J Comput Phys 470:111587, 2022) showed that performing a low-rank approximation can be very effective in reducing the high memory requirement and computational cost of such problems. In this work, we propose a rank adaptive approach that changes the rank during the inverse power iteration. This allows us to progressively increase the rank (i.e. changing the fidelity of the model) as we get closer to convergence, thereby further reducing computational cost. We then exploit this multi-fidelity approach to optimize a simplified nuclear reactor. In this case the system is parameterized and the values of the parameters that give criticality are sought.<\/jats:p>","DOI":"10.1007\/s10915-025-02907-z","type":"journal-article","created":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T20:23:34Z","timestamp":1748636614000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Multi-fidelity Adaptive Dynamical Low-Rank Based Optimization Algorithm for Fission Criticality Problems"],"prefix":"10.1007","volume":"104","author":[{"given":"Carmela","family":"Scalone","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lukas","family":"Einkemmer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonas","family":"Kusch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ryan G.","family":"McClarren","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,30]]},"reference":[{"issue":"12","key":"2907_CR1","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1002\/nme.4533","volume":"95","author":"AG Buchan","year":"2013","unstructured":"Buchan, A.G., Pain, C.C., Fang, F., Navon, I.M.: A POD reduced-order model for eigenvalue problems with application to reactor physics. 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