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DOE OSTI2026

ReMU: regional minimal updating for model-based derivative-free optimization

Derivative-free optimization (DFO) problems are optimization problems where derivative information is unavailable or extremely difficult to obtain. Model-based DFO solvers have been applied extensively in scientific computing. Powell's NEWUOA (2004) [Powell, The NEWUOA software for unconstrained optimization without derivatives, in Large-Scale Nonlinear Optimization, Nonconvex Optimization and its Applications Vol. 83, G. Di Pillo and M. Roma, eds., Springer, 2006, pp. 255–297] and Wild's POUNDerS (2014) [Wild, Solving derivative-free nonlinear least squares problems with POUNDERS, in Advances and Trends in Optimization with Engineering Applications, T. Terlaky, M.F. Anjos, and S. Ahmed, eds., SIAM, 2017, pp. 529–540] explore the numerical power of the minimal norm Hessian (MNH) model for DFO and contributed to the open discussion on building better models with fewer data to achieve faster numerical convergence. Another decade later, we propose the regional minimal updating (ReMU) models, and extend the previous models into a broader class, including the H 2 norm models [Xie and Yuan, Least H 2 norm updating of quadratic interpolation models for derivative-free trust-region algorithms, IMA J. Numer. Anal. 46 (2025), pp. 21–50]. This paper shows motivation behind ReMU models, computational details, theoretical and numerical results on particular extreme points and the barycentre of ReMU's weight coefficient region, and the associated KKT matrix error and distance. Novel metrics, such as the truncated Newton step error, are proposed to numerically understand the new models' properties. A new algorithmic strategy, based on iteratively adjusting the ReMU model type, is also proposed, and shows numerical advantages by combining and switching between the barycentric model and the classic least Frobenius norm model in an online fashion.

derivative-free trust-region methods↗

DOE OSTI2026

Improved Accuracy in Semi-Experimental Structure Determination by Resolving Problems Associated with Rotation of Principal Inertial Axes of Isotopologues: Structures of 1,3-Oxazole ( c -C 3 H 3 NO)

The rotational spectrum of the normal isotopologue of 1,3-oxazole (c-C 3 H 3 NO) was observed from 43 to 750 GHz. Over 3900 transitions for the ground vibrational state are measured, assigned, and least-squares fit to sextic centrifugally distorted-rotor Hamiltonians. The measured frequencies and resulting spectroscopic constants from this extended spectral range, combined with previous measurements of the nuclear quadrupole coupling constants, will facilitate astronomical searches for oxazole across the majority of the range of modern radiotelescopes. Spectra for a set of 30 oxazole isotopologues, which include multiple isotopic substitutions of each atom, are used to determine the first semi-experimental equilibrium ($r$$^{SE}_{e}$) structure and semi-experimental substitution structure ($r$$^{SE}_{e}$), each using CCSD(T) computed values for the vibration–rotation interaction and electron-mass corrections. The large number of isotopologues, including 21 isotopologues observed for the first time, and the redundant substitutions of each atom provide sufficient spectroscopic information to determine the $r$$^{SE}_{e}$ structure with the expected high level of accuracy and precision (0.0001 or 0.0002 Å in bond distances and 0.013 to 0.025° in bond angles). In the course of this study, we analyzed a known issue for some $r$$^{SE}_{e}$ structure determinations of near-oblate asymmetric tops in which inclusion of individual isotopologues degrades the structure determination. We demonstrate that this problem primarily arises from the difference in the values of the computed vibration–rotation interaction corrections as evaluated at the computed re geometry vs the $r$$^{SE}_{e}$ geometry of the “real” molecule. Our solution to this problem substantially improves the $r$$^{SE}_{e}$ structure of oxazole and likely can be generalized to many other molecules.

Chemical structure↗

DOE OSTI2022

The miniJPAS survey: White dwarf science with 56 optical filters

We analyze the white dwarf population in miniJPAS, the first square degree observed with 56 medium-band, 145 Å in width optical filters by the Javalambre Physics of the accelerating Universe Astrophysical Survey (J-PAS), to provide a data-based forecast for the white dwarf science with low-resolution ($R$ ~ 50) photo-spectra. We define the sample of the bluest point-like sources in miniJPAS with $r$ < 21.5 mag, a point-like probability larger than 0.5, ($u$ - $r$)< 0.80 mag, and ($g$ - $i$)< 0.25 mag. This sample comprises 33 sources with spectroscopic information: 11 white dwarfs and 22 quasi-stellar objects (QSOs). We estimate the effective temperature ($T$ eff ), the surface gravity, and the composition of the white dwarf population by a Bayesian fitting to the observed photo-spectra. The miniJPAS data are sensitive to the Balmer series and the presence of polluting metals. Our results, combined with those from the Javalambre Photometric Local Universe Survey (J-PLUS) which has a lower spectral resolution but has already observed thousands of white dwarfs, suggest that J-PAS photometry would permit – down to $r$ ~ 21.5 mag and at least for sources with 7000 < $T$ eff < 22 000 K – both the classification of the observed white dwarfs into H-dominated and He-dominated with 99% confidence and the detection of calcium absorption for equivalent widths larger than 15 Å. The effective temperature is estimated with a 2% uncertainty, which is close to the 1% from spectroscopy. A precise estimation of the surface gravity depends on the available parallax information. In addition, the white dwarf population at $T$ eff > 7000 K can be segregated from the bluest extragalactic QSOs, providing a clean sample based on optical photometry alone. The J-PAS low-resolution photo-spectra would produce precise effective temperatures and atmospheric compositions for white dwarfs, complementing the data from Gaia. J-PAS will also detect and characterize new white dwarfs beyond the Gaia magnitude limit, providing faint candidates for spectroscopic follow-up.

79 ASTRONOMY AND ASTROPHYSICS↗