Four Hessian-informed trust-region filter variants using low- and high-fidelity surrogates reduce iterations and black-box evaluations by up to an order of magnitude on 25 benchmarks and five engineering cases while lowering tuning sensitivity.
Conn, Nicholas I
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DSGNAR optimization framework for PINNs reaches relative L2 errors of 3e-16 in double precision and improves prior results by 5-8 orders of magnitude on Burgers' and high-dimensional Poisson problems while remaining faster.
A general framework for parameter-free smooth nonconvex optimization via higher-order regularization yields algorithms with optimal complexity bounds without prior parameter knowledge.
A WLaSDI-based framework creates noise-robust latent surrogates for PDE-constrained optimization, deriving direct and adjoint gradients to achieve up to five orders of magnitude speedup on radiative transfer, Vlasov-Poisson, and Burgers benchmarks.
Fully implicit resolvent discretization of noisy accelerated gradient dynamics produces a Lyapunov mean-square recursion whose contraction factor improves and stationary error scales as O(1/α), vanishing for large α under accurate inner solves.
This paper isolates admissibility conditions for trust-region radius updates that guarantee first-order stationarity and O(ε^{-2}) complexity, verifies them across five mechanism classes, and extends prior frameworks with new convergence results under linear Hessian growth.
A trust-region funnel algorithm for gray-box optimization achieves global convergence to first-order critical points and performs comparably or better than the classical trust-region filter method.
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Systematic benchmarks on NACA0012, RAE2822, and ONERA M6 cases show derivative-free optimizers competitive with adjoint-based methods and stronger in higher dimensions.
MaRDI Open Interfaces supplies common interfaces for nonlinear optimization solvers, shown via an application to physics-informed neural network training on the viscous Burgers' equation.
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