A reduced-order model represents woven weaver interactions via nodes and four stiffness elements (axial, uncrimping, shear, frictional slip), calibrated to 5% agreement on bending and shear data, then used to demonstrate emergent Poisson response, pullout, tearing, and anisotropy.
Mixed citations
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Mixed citation behavior. Most common role is background (69%).
29
Pith papers citing it
Background
69% of classified citations
citation-role summary
background 9
baseline 2
method 2
citation-polarity summary
representative citing papers
LiL-Q applies quasilinearization to nonlinear PDEs and solves each resulting linear problem by convex least-squares collocation on Linear-in-Learnables trial spaces, achieving fast convergence and high accuracy on multiple benchmarks.
A geometry-aligned bi-fidelity surrogate maps low- and high-fidelity wildfire solutions to a common domain for improved reduced-basis reconstruction, lower error near fronts, and practical uncertainty quantification.
QPCA-EnDCF is a deterministic ensemble data assimilation method that replaces stochastic observation perturbations with a spectrally regularized rank-κ update on whitened residuals, yielding better spread-skill and rank-histogram reliability than stochastic EnKF on Lorenz-96 in undersampled regimes.
A multilinear operator learned on PCA coefficients maps time-since-ignition inputs to smoke outputs, matching Monte Carlo accuracy with half the model calls and outperforming prior classifiers on holdout data.
A weighted FOSLS formulation for deep neural networks solves transmission problems robustly, with proofs that the loss aligns with the energy norm independently of material contrast and shows passive variance reduction.
Phase-field peridynamics degrades bond energies continuously via a bond phase-field parameter while using kinematic degradation to preserve nonlocal deformation gradient accuracy, with an analytically derived normalization constant for thermodynamic consistency.
Input-convex neural networks in elementary polynomials of signed singular values provably approximate any frame-indifferent isotropic polyconvex hyperelastic energy.
Self-attention mechanisms are used to build mesh-preserving neural surrogates that approximate PFEM dynamics for free-surface flows, delivering accurate transient predictions and improved scalability on 2D and 3D benchmarks.
A thermodynamics-constrained ML framework learns robust, consistent constitutive models for inelastic materials from macroscopic stress-strain data and generalizes to unseen paths.
NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.
A variational neural network using Kolosov-Muskhelishvili potentials solves 2D linear elasticity and fracture problems by minimizing total potential energy and embedding crack discontinuities into the ansatz, yielding higher accuracy and faster convergence than standard physics-informed networks.
EMSL groups material points into clusters, samples a reference strain per cluster once per increment, and computes a linearised stress estimate from the reference tangent and POD strain modes, yielding an affine reduced system that requires no iterations online and Pareto-dominates prior strain-cubc
The proximal Galerkin method reformulates phase-field fracture constraints into saddle-point problems to enforce physical bounds and irreversibility for static and dynamic cases.
Non-conformal immersed and union-based isogeometric methods with boundary-conformal quadrature reduce patch count and preprocessing for magnetostatics while union variants maintain accuracy on benchmarks.
A neural network with periodic activations parameterizes thin-shell mid-surfaces so that network weights can be optimized to minimize structural compliance subject to a volume limit.
A novel high-order stabilization-free virtual element method is developed for general second-order elliptic eigenvalue problems, with optimal a priori error estimates for eigenspaces and eigenvalues, validated on various polygonal meshes.
A decoupled kernel-only stabilization for finite-strain VEM hyperelasticity is introduced that scales deviatoric terms by shear modulus with geometry weights and volumetric terms independently by bulk modulus, with uniform stability proven under polygon regularity.
AMORE develops an adaptive multi-output DeepONet with custom losses, partition-of-unity trunk, and invertible/softmax mass-fraction maps to surrogate stiff kinetics on syngas (12 states) and GRI-Mech (24 states).
A robust containment query for collections of trimmed NURBS surfaces that computes generalized winding numbers directly via adaptive quadrature on solid angle boundary integrals without surface discretization.
KL-DNN uses low-rank SVD and nested Karhunen-Loeve expansions to enable scalable operator learning on large 3D GCS simulations, achieving 0.04% relative pressure error and two-order speedup over DeepONet.
Introduces a conservative, discretization- and PDE-agnostic redistribution limiting method for high-order approximations of conservation equations.
Systematic benchmark of PINN architectures on 1D stiff PNP system finds BRDR loss weighting competitive with NTK at lower wall-clock time.
Proposes an unbiased, second-order-free training framework for BSDE solvers of high-dimensional PDEs that corrects Euler-Maruyama discretization bias while preserving computational advantages.
citing papers explorer
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Exact Boundary Enforcement Along Implicit Geometries for Physics-Informed, Deep Learning Problems in Continuum Mechanics
PINNs for first-order plane-strain elastodynamics achieve higher accuracy with soft boundary enforcement over implicit geometries but require longer training than hard enforcement.