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Related Articles from SNS
Modified augmented Lagrangian preconditioning for mixed-dimensional beam-solid coupling
Announce Type: new Abstract: This paper presents modified augmented Lagrangian block preconditioners for the mixed-dimensional coupling of three-dimensional solid bodies with embedded one-dimensional torsion-free Kirchhoff-Love beams using Lagrange multipliers for constraint enforcement. The finite element discretization of this mixed formulation leads to an indefinite saddle-point system. An augmented Lagrangian formulation is employed to regularize the linear system while maintaining exact...
Minimal surfaces: A Lagrangian derivation of first and second variations
Differential Geometry [Submitted on 4 Jun 2026] Title:Minimal surfaces: A Lagrangian derivation of first and second variations View PDFAbstract:This article develops a rigorous Lagrangian formulation of variational calculus for minimal surfaces, using extensively the concept of pullback covariant derivative. It is shown, in particular, using a geometric argument that all tangential variations vanish.
Augmented Lagrangian Predictive Coding
arXiv:2605.31022v1 Announce Type: new Abstract: Predictive coding (PC) is a local-learning alternative to backpropagation (BP), training deep networks via local energy-minimization dynamics rather than a global backward pass. We introduce Augmented Lagrangian Predictive Coding (PC-ALM), which maintains PC's inference budget but aligns each weight update toward BP by accumulating per-layer constraint errors into a layer-local Lagrange multiplier. In linear PC networks, PC-ALM converges to an...
Stochastic Multiscale Reconstruction of Lagrangian Turbulence via Guided Diffusion Models
arXiv:2606.05783v1 Announce Type: new Abstract: Lagrangian turbulence is characterized by intermittent, fat-tailed fluctuations and nontrivial correlations across temporal scales, making a quantitative description of its full multiscale probability distribution a longstanding challenge. A particularly important question is whether unresolved fine-scale fluctuations can be inferred from coarse-grained trajectory information. Here, we address this problem by sampling the conditional...
Beyond Stokes drift -- Lagrangian transport in evolving gravity waves
arXiv:2604.24069v3 Announce Type: replace Abstract: Finite-amplitude gravity waves at the air-water interface induce net fluid and particle transport, known as Stokes drift. While this mechanism is well understood for steady waves, transport under unsteady, evolving conditions remains poorly characterized. Here, we investigate Lagrangian transport in freely decaying waves using high-resolution two-phase simulations and a perturbative analytical model.
Lagrangian Perturbation Diffusion Steering: Latent Reinforcement Learning for Generative Policies
Announce Type: new Abstract: Behavior cloning with high-capacity generative policies achieves strong imitation performance, but is often limited by demonstration coverage and distribution shift. Direct reinforcement learning fine-tuning can improve performance, but updating large action decoders is frequently unstable and sample inefficient. We propose Lagrangian Perturbation Diffusion Steering (LP-DS), a lightweight adaptation method that improves a frozen generative policy by learning a...
Lagrangian Extensions of Newtonian Gravity constrained by Solar System tests
Announce Type: cross Abstract: We explore an extension to Newtonian gravity through a generalised Lagrangian function with the introduction of a second dynamical scalar field. Building on previous research into gravity with variable gravitational coupling, the work derives the complete field equations and applies a weak-field approximation. This leads to an effective post-Newtonian gravitational potential that includes key aspects of relativistic theories.
OnlyDense: Reduced-Order Modeling for Lagrangian simulation
arXiv:2606.09065v1 Announce Type: new Abstract: In science and engineering, Lagrangian simulation methods such as Smooth Particle Hydrodynamics (SPH) or Material Point Method (MPM) are often employed to study the behavior of dynamic systems. However, these methods can be prohibitively computationally expensive, particularly when simulating multi-scale spatial or temporal phenomena, e.g., void growth and coalescence within macro-scale geometries, structural failure of spacecraft components...
Lagrangian-Eulerian learning of flow field and trajectories with TrajectoryFlowNet
Announce Type: replace Abstract: Predicting particle transport in complex flows is traditionally achieved by solving the Navier-Stokes equations. While various numerical and experimental methods exist, they typically require deep physical insights and incur high computational costs. Machine learning offers an alternative by learning predictive patterns directly from data, avoiding explicit physical modeling.
Scaling Decision-Focused Learning to Large Problems with Lagrangian Decomposition
arXiv:2606.08797v1 Announce Type: new Abstract: Decision-focused learning has shown great promise for addressing predict-then-optimize problems, particularly in the presence of under-specified models. However, its practical deployment is often hindered by high computational costs and limited scalability, as it requires solving a constrained optimization problem for each training instance at every iteration. To address these challenges, we propose a novel framework that incorporates...