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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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1122 · Sep 202319922001200920172026
10 results for hyperelasticity

A hybrid model combines diffusion and neural operator methods for stress prediction in hyperelastic materials.

problem Challenges in predicting stress fields in hyperelastic materials with complex microstructures.
method A hybrid surrogate framework combining a conditional denoising diffusion probabilistic model (cDDPM) and a modified DeepONet.
result The hybrid model consistently outperforms traditional methods by one to two orders of magnitude.

Hyperelastic bodies in Riemannian manifolds can levitate due to curvature-induced forces.

problem Hyperelastic bodies in Riemannian manifolds can levitate due to curvature-induced forces.
method Numerical simulations of static solutions to a particular class of problems in hyperelastic mechanics.
result Hyperelastic bodies in Riemannian manifolds can levitate due to curvature-induced forces.

This work ensures stability in POD basis interpolation for pMOR in hyperelasticity.

problem Stability of POD basis interpolation on Grassmann manifolds for pMOR in hyperelasticity.
method Stability conditions derived from Grassmannian Exponential map and principal angles.
result Explicit stability conditions for practical pMOR applications and non-monotonic error behavior.

Study on materials with disclinations, limiting their size.

problem Limiting the size of disclinations in materials with symmetries.
method Defining material-uniform hyperelastic bodies with disclinations, rigorously analyzing their properties.
result The size of disclinations is limited by the symmetries of the constitutive relation.

Bayesian-guided method selects optimal design from large candidate pool.

problem Optimizing complex structures with high-fidelity evaluations.
method Bayesian active learning with surrogate modeling.
result Optimal design identified with minimal oracle evaluations.

In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger stretch tensor in a Gaussian process. We then consider an improvement on this a…

2019-12-23abs ↗pdf ↗

Local laGPR speeds up multiscale mechanics simulations without neural networks.

problem High computational costs in multiscale mechanics simulations.
method Local approximate Gaussian process regression (laGPR) combined with FE schemes.
result laGPR offers better accuracy than neural networks for stress predictions.

Neural operators correct PDE residuals to improve BIP solutions.

problem Reducing error in infinite-dimensional Bayesian inverse problems with neural operators.
method Error correction using PDE residuals to improve neural operator approximation.
result Trained neural operators with error correction achieve a quadratic reduction in approximation error.

Geometrically reformulates Cosserat solid mechanics using differential geometry.

problem Formalizing Cosserat solid mechanics in modern differential geometry.
method Formulation as a principal fibre bundle, using Cartan's magic formula, and integrating infinitesimal strains.
result Reveals strain as a Lie algebra-valued one-form and finite strain through integration.