Tensegrity form-finding and physical property prediction are fundamental inverse problems in structural mechanics, which aim to determine equilibrium configurations and internal force distributions. These problems are challenging due to strong nonlinearity arising from the coupling between geometry and forces, the need to ensure structural stability, and the enforcement of constraints such as boundary conditions and symmetry.
arXiv:2607. 12888v1 Announce Type: new Abstract: Tensegrity form-finding and physical property prediction are fundamental inverse problems in structural mechanics, which aim to determine equilibrium configurations and internal force distributions.
arXiv:2603. 28707v3 Announce Type: replace-cross Abstract: We present a physics-based neural network framework for the discovery of constitutive models in fully coupled thermomechanics.
Extending the neural-operator element method from individually trained, fixed-geometry neural elements to a library of reusable, geometry-parameterized element types fails structurally: a field-predicting operator trained by value regression induces an energy whose assembled Hessian is indefinite, and Newton converges to spurious minima (247% error) even with 1%-accurate field predictions. We introduce convex neural energy elements: each element exports a scalar energy E(g,U), architecturally convex in its boundary degrees of freedom U and smoothly parameterized by its geometry g, realized as a hypernetwork-generated positive-semidefinite quadratic form (an input-convex correction is reserved for non-quadratic physics).
arXiv:2608. 02036v1 Announce Type: new Abstract: Extending the neural-operator element method from individually trained, fixed-geometry neural elements to a library of reusable, geometry-parameterized element types fails structurally: a field-predicting operator trained by value regression induces an energy whose assembled Hessian is indefinite, and Newton converges to spurious minima (247% error) even with 1%-accurate field predictions.
arXiv:2605. 24651v2 Announce Type: replace-cross Abstract: We propose a Weak-form Physics-Informed Neural Operator (WINO), a data-free framework that combines the efficiency of neural operators with the geometric flexibility of the $\varphi$-finite element method ($\varphi$-FEM).
arXiv:2606. 05199v1 Announce Type: cross Abstract: The identification of constitutive neural network models from heterogeneous full-field deformation data provides a robust alternative to traditional calibration methods based on homogeneous stress-strain experiments, particularly given the high dimensionality of trainable parameters.
arXiv:2508. 12448v2 Announce Type: replace-cross Abstract: In-context learning (ICL) lets large language models (LLMs) solve new tasks from prompts alone, across an ever-widening range of domains, yet the mechanisms underlying this ability remain poorly understood.
arXiv:2602. 03670v2 Announce Type: replace-cross Abstract: Equilibrium Propagation (EP) is a physics-inspired learning algorithm that uses stationary states of a dynamical system both for inference and learning.
arXiv:2606. 16624v1 Announce Type: new Abstract: Plate and shell structures are widely used in engineering, making rapid response prediction under varying geometries, materials, and loads highly desirable.
arXiv:2606. 16624v2 Announce Type: replace Abstract: Plate and shell structures are widely used in engineering fields.
arXiv:2606. 29874v1 Announce Type: cross Abstract: Data-driven material modeling techniques have gained significant attention due to their ability to capture complex constitutive behaviors beyond the limitations of classical material models.
arXiv:2602. 17750v2 Announce Type: replace-cross Abstract: A key problem of solid mechanics is the identification of the constitutive law of a material, that is, the relation between strain history and stress.