The Laplace-Fisher Gate Identity supplies the variance-optimal matrix gate for blended score estimation under Ornstein-Uhlenbeck diffusion and yields improved normalized posterior-density surrogates from MCMC pilot samples in Bayesian inverse problems.
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Numerical Optimization
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A parametric GMM model for motion-enabled tomography that decouples reconstruction into sub-problems and tests on 2D simulations of intersecting trajectories.
A variational reduced-order model bridges perturbation and variational fracture approaches to simulate coplanar 3D crack propagation in heterogeneous brittle solids, uncovering size-dependent weakening-to-toughening crossovers driven by depinning instabilities.
SHAPE lifts gradient descent to an augmented phase space with a learned Hamiltonian vector field and event-triggered port updates to balance descent, exploitation, and exploration, improving best-so-far performance over fixed-policy methods in nonconvex tasks.
ADELIA is the first AD-enabled INLA system that computes exact hyperparameter gradients via a structure-exploiting multi-GPU backward pass, delivering 4.2-7.9x per-gradient speedups and 5-8x better energy efficiency than finite differences on models with up to 1.9 million latent variables.
Matrix-valued optimism equals matrix-valued augmentation additively for symmetric parameters, enabling closed-form hybrid designs that improve finite-step feasibility in constrained optimization.
SGD, approximations of Newton's method, natural gradient descent, and Adam are proven compatible with evolutionary dynamics when augmented with DLS noise, turning them into valid in silico simulations of asexual Darwinian evolution.
A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
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.
The paper presents ModelPredictiveControl.jl, an open-source Julia toolkit for model predictive control including nonlinear, economic, and successive linearization variants, illustrated with CSTR and inverted pendulum simulations and benchmarked against MATLAB.
Defines saturation index S(K) = erank(Σ̂_W^(K))/K that identifies when linear discriminant stabilizes in binary few-shot classification, with empirical phase diagram and stopping-rule AUC of 0.752 on 17 tasks.
VEQ introduces a compact parametric Grad-Shafranov solver using MXH harmonics and Chebyshev coefficients that maps six input routes to a single variational residual operator and achieves millisecond solves with 10^-3 shape errors on G-EQDSK test cases.
A Gauss-Newton-based parallel 3-D TEM inversion method employs rational near-best approximations of the matrix exponential to make time-dependent computations independent of the number of observation times.
Sufficient conditions on eigenvalue vanishing in quasi-Newton updates, observed numerically, are shown to imply convergence to criticality for piecewise differentiable nonsmooth functions, along with the method's ability to explore piecewise structure.
A robust Riemannian Levenberg-Marquardt algorithm is formulated in block-wise form, with convergence results carried over from prior work and demonstrated via an open-source Manopt.jl implementation on tasks including geodesic regression and Procrustes analysis.
The paper presents MaRDI Open Interfaces, a package providing unified interfaces and automated language interoperability for nonlinear optimization.
A learned context-energy term in port-Hamiltonian policies creates selective risk navigation that activates evasive forces only when safer paths are available.
New gas-phase measurements of C 1s binding energies in anthrone agree with ΔSCF calculations, and a benchmark of 44 core levels in molecules with 10-40 atoms yields a mean absolute error of 0.19 eV.
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.
Comparison of objective functions for stabilizing the Vlasov-Poisson system shows that time-integrated metrics produce more convex optimization landscapes favorable to gradient-based methods.
A ReLU-penalty formulation for VLSI global placement is solved via stochastic subgradient descent, with the first claimed convergence proof for ReLU-type nonsmooth nonconvex problems.
Shape optimization of Maxwell eigenvalues via adjoint sensitivities on a reference domain, solved with a damped inverse BFGS method and mixed finite elements.
Noise in LUCJ sampling for QSCI on N2 expands the configuration space beyond the ideal ansatz and, when paired with recovery, produces more accurate CI energies than noiseless sampling.
A sequential topology optimization approach uses SIMP results to initialize level-set refinement via signed distance function transfer on 3D meshes, achieving comparable compliance with up to 4.6x speedup on benchmarks.
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