The paper introduces a variational, label‑free physics‑informed graph neural network (PI‑GNN) that models heterogeneous solid mechanics by embedding material heterogeneity into the discretization rather than the neural network’s trial field. The PI‑GNN operates on a conforming adaptive mesh graph, assigns constitutive behavior per element, and minimizes the discrete total potential energy without penalty terms or interface weights, yielding a discrete energy equivalent to the finite element Ritz functional. Across small‑strain elasticity and finite‑strain Neo‑Hookean hyperelasticity in 2D and 3D, the method achieves von Mises errors below 3.58 % over a wide stiffness‑contrast range, outperforming strong‑form PINNs and reducing displacement errors significantly.
By Aashay Rajan Yadav, Amiya Prakash Das, Ratna Kumar Annabattula
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.
By Hongyue Jiang, Jianjiang Zhan, Chenzhuo Zhang, Fan Wang
arXiv:2607. 13612v1 Announce Type: cross Abstract: Joint-Embedding Predictive Architectures (JEPAs) are the dominant design for latent world models, yet they are usually justified by empirical performance rather than a normative principle.
By Fabio Arnez, Alexandra Gomez-Villa
arXiv:2607. 07379v1 Announce Type: new Abstract: In agentic scientific machine learning (SciML), large language model (LLM) agents can discover surrogate models and select one by an automated score, typically an error metric.
By Diab W. Abueidda, Bilal Ahmed, Panos Pantidis, Mostafa E. Mobasher
GRALIS (Gradient‑Riesz Averaged Locally‑Integrated Shapley) merges coalition‑based and gradient‑based post‑hoc XAI techniques into a single estimator. It provides two certified guarantees: an exact closed‑form completeness deficit and a finite‑sample bound on the self‑normalized ratio. The method is grounded in a representation‑theoretic result that uniquely characterizes additive, linear, continuous attribution functionals, and it is experimentally illustrated on breast histology imaging.
By Raimondo Fanale
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.
By Matthias Knipper, Chenyi Ji, Malte Brand, Kevin Linka
arXiv:2606. 16028v1 Announce Type: new Abstract: Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models.
By Thomas Dittrich, Oliver Potocki, Philipp Grohs
arXiv:2606. 04834v1 Announce Type: new Abstract: Minimum Description Length (MDL) formalizes the principle of Occam's razor by optimizing the total description length: $L(\mathrm{model})+L(\mathrm{data} \ | \ \mathrm{model})$.
By Qian Li, Xinyu Mao, Shang-Hua Teng, Guangxu Yang
arXiv:2607. 13074v1 Announce Type: cross Abstract: This work studies the inverse problem of recovering the relative magnitudes of the tension, bending, and bearing loads acting on a crack from its stress-intensity-factor profile along the crack front, using the public SIFBench finite-element data.
By Giansalvo Cirrincione, Filippo Grassia
arXiv:2406. 13944v2 Announce Type: replace-cross Abstract: This paper establishes the generalization error of pooled min-$\ell_2$-norm interpolation in transfer learning, where data from diverse distributions are available.
By Yanke Song, Kenneth Gu, Sohom Bhattacharya, Pragya Sur
arXiv:2512. 08499v3 Announce Type: replace-cross Abstract: Development of reliable and physically interpretable probabilistic frameworks for industrial prognostics remain nascent, and existing literature is often insensitive as inputs move away from the training manifold.
By Waleed Razzaq, Yun-Bo Zhao