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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representative citing papers
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 general framework for parameter-free smooth nonconvex optimization via higher-order regularization yields algorithms with optimal complexity bounds without prior parameter knowledge.
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.
A nine-compartment nonlinear model with two viral strains and PCHIP-based time-varying parameters is calibrated to Italian COVID-19 third-wave data, achieving high R^2 fits and proving analytical stability properties.
citing papers explorer
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Laplace--Fisher Gate Identities for Optimal Matrix-Gated Blended Score Estimation
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.
-
Motion-Enabled Tomography via Gaussian Mixture Models
A parametric GMM model for motion-enabled tomography that decouples reconstruction into sub-problems and tests on 2D simulations of intersecting trajectories.
-
Bridging perturbation and variational approaches in brittle fracture
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.
-
When Descent Is Too Stable: Event-Triggered Hamiltonian Learning to Optimize
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: Automatic Differentiation for Efficient Laplace Inference Approximations
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 is Matrix-Valued Augmentation: Additive Hybrid Designs for Constrained Optimization
Matrix-valued optimism equals matrix-valued augmentation additively for symmetric parameters, enabling closed-form hybrid designs that improve finite-step feasibility in constrained optimization.
-
Direct From Darwin: Deriving Advanced Optimizers From Evolutionary First Principles
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 landing on the Stiefel manifold via Newton$\unicode{x2013}$Schulz iteration
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.
-
Trust-region filter algorithms utilizing Hessian information for gray-box optimization
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.
-
ModelPredictiveControl.jl: advanced process control made easy in Julia
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.
-
A Spectral Phase Diagram for Binary Few-Shot Classification: Intrinsic Dimensionality, Geometric Saturation, and Representational Diagnosis
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: a fast parametric Grad--Shafranov solver for fixed-boundary tokamak equilibria with flexible source profiles
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 General Recipe for Parameter-Free Nonconvex Optimization via Higher-Order Regularization
A general framework for parameter-free smooth nonconvex optimization via higher-order regularization yields algorithms with optimal complexity bounds without prior parameter knowledge.
-
Scalable parallel 3-D TEM inversion via rational approximation of the matrix exponential
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.
-
Technical results on the convergence of quasi-Newton methods for nonsmooth optimization
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 modified Riemannian Levenberg-Marquardt Algorithm for robust or constraint optimization on manifolds
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.
-
MaRDI Open Interfaces for Interoperable Nonlinear Optimization
The paper presents MaRDI Open Interfaces, a package providing unified interfaces and automated language interoperability for nonlinear optimization.
-
Learning Material-Aware Hamiltonian Risk Fields for Safe Navigation
A learned context-energy term in port-Hamiltonian policies creates selective risk navigation that activates evasive forces only when safer paths are available.
-
Does the total energy difference method for modelling core level photoemission fail for bigger molecules?
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
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.
-
What metric to optimize for suppressing instability in a Vlasov-Poisson system?
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.
-
An Efficient Stochastic Subgradient Method for the Global Placement Problem in Very Large-Scale Integration Circuits
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.
-
Numerical Eigenvalue Optimization by Shape-Variations for Maxwell's Eigenvalue Problem
Shape optimization of Maxwell eigenvalues via adjoint sensitivities on a reference domain, solved with a damped inverse BFGS method and mixed finite elements.
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A Nine-Compartment Nonlinear Epidemic Model with Spline-Based Identification of Time-Varying Transmission and Vaccination Dynamics: Application to the COVID-19 Third Wave in Italy
A nine-compartment nonlinear model with two viral strains and PCHIP-based time-varying parameters is calibrated to Italian COVID-19 third-wave data, achieving high R^2 fits and proving analytical stability properties.
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Noise and Configuration Recovery Impact on Quantum Selected Configuration Interaction
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.
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Sequential topology optimization: SIMP initialization for level-set boundary refinement
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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PISP: Projected-Space Inference of Stellar Parameters
PISP projects high-dimensional spectra into optimized subspaces using PCA or active subspaces plus L1 selection to raise accuracy and speed of stellar parameter inference over standard methods.
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Sustainability-Constrained Workload Orchestration for Sovereign AI Infrastructure: A Joint Compute-Network Optimization Framework
Introduces the Feasible Sovereign Operating Region (FSOR) as a construct for workloads sustainable under physical and regulatory limits, along with a joint compute-network optimization framework that enforces sustainability as hard constraints.
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Software package MaRDI Open Interfaces for improved interoperability in numerical optimization
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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Navigating LLM Valley: From AdamW to Memory-Efficient and Matrix-Based Optimizers
This survey organizes LLM optimizer literature into categories and argues the field is shifting toward rigorous, multi-factor comparisons of convergence, memory, stability, and complexity.
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An Introduction to Solving the Least-Squares Problem in Variational Data Assimilation
This is an introductory review of the linear algebraic subproblems and contemporary solvers in variational data assimilation for geophysical applications.
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SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
SciPy 1.0 documents a mature open-source library that has become the de facto standard for scientific algorithms in Python with broad adoption across research projects.
- Adaptive Reduced-Basis Trust-Region Methods for Defect Identification in Elastic Materials