arXiv:2607. 04123v1 Announce Type: new Abstract: Inverse design of mechanical metamaterials seeks a periodic unit cell whose homogenized elastic properties meet a prescribed target, but current learning-based methods are data-hungry, mostly interpolative, and provide no guarantee that the generated design satisfies the specification.
arXiv:2607. 14475v1 Announce Type: cross Abstract: Disordered metamaterials feature microstructures with inherent randomness and irregularity, enabling them to achieve broader property coverage and superior performance unavailable in their regular counterparts.
arXiv:2608. 08322v1 Announce Type: cross Abstract: Physics-informed neural networks applied to the level-set formulation of interface advection commonly augment the residual and initial-condition losses with an eikonal regulariser, penalising the deviation of $\|\nabla\phi\|$ from unity.
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.
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:2605. 23967v2 Announce Type: replace-cross Abstract: In biological systems, sensing is not performed by the brain alone: the body deforms, vibrates, and filters external stimuli before they are transduced into neural signals.
arXiv:2606. 09266v1 Announce Type: cross Abstract: Acoustic metamaterial (AMM) inverse design is particularly challenging for broadband target responses due to acoustic dispersion: a structure that matches the desired response at one frequency may deviate at others, and modifying geometry to improve one sub-band often perturbs neighboring sub-bands.
arXiv:2608. 08608v1 Announce Type: cross Abstract: Fourier neural operators (FNOs) provide efficient nonlocal spectral learning, but varying geometries and independently chosen discretizations remain difficult to accommodate.
arXiv:2607. 24777v1 Announce Type: new Abstract: Architected metamaterials derive their functions from structure, creating vast opportunities to program physical responses through topology design.
arXiv:2606. 10909v1 Announce Type: cross Abstract: Reconstructing local stress fields in heterogeneous microstructures under non-linear, history-dependent loading remains a major computational bottleneck in multi-scale simulations.
arXiv:2608. 05437v1 Announce Type: cross Abstract: Supervised training of finite-element (FE) surrogate models requires reference solutions, and each reference solution is obtained by solving the system that the surrogate is intended to replace.
arXiv:2608. 15187v1 Announce Type: new Abstract: Scientific machine learning for partial differential equations commonly targets solution fields, as in physics-informed neural networks, or solution maps, as in neural operators.
arXiv:2607. 09967v1 Announce Type: cross Abstract: Many neural networks operations have a multiplicative nature rather than additive: halving or doubling a norm are analogous relatively but require unequal optimization distances when taking linear steps.