Aug 2026· Proceedings of the 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.2· pp. 10453-10464· 0 citations· 20 references
TL;DR
This work reinterpret OOD generalization under covariate shift as a problem of preserving geodesic relationships on the data manifold, and proposes Geometry Support Anchoring (GSA), a geometry-aware learning framework that anchors predictions using geodesic distances to data-dependent reference representations.
Abstract
Machine learning methods have recently shown promise in predicting composite material properties more efficiently than traditional finite element simulations. However, in real-world applications of composite materials, variations in filler characteristics or processing conditions can cause a significant mismatch between the training and test distributions, leading to degradation in model performance. Existing approaches to domain adaptation typically aim to learn feature representations that are invariant across distribution shifts or minimize worst case risk across predefined environments, which are not suitable for composite materials where the distribution shifts are feature driven and localized. In this work, we argue that such shifts are more naturally characterized by the geometry of the data manifold rather than Euclidean distances in the ambient feature space. We reinterpret OOD generalization under covariate shift as a problem of preserving geodesic relationships on the data manifold. Building on this perspective, we propose Geometry Support Anchoring (GSA), a geometry-aware learning framework that anchors predictions using geodesic distances to data-dependent reference representations. For our approach, we have developed a multimodal conditional Joint Embedding Predictive Architecture (JEPA) that learns invariant, material-relevant representations by predicting latent targets using context from complementary modalities. By enforcing consistency in intrinsic geometry rather than raw features, our approach preserves physically meaningful variation while improving robustness to regime shifts. Experiments on both public and in-house composite material datasets with realistic distribution shifts demonstrate that our method consistently improves robustness and OOD generalization compared to state-of-the-art tabular learning and domain adaptation methods.
Machine learning is rapidly reshaping constitutive modeling, offers new ways to learn material behavior directly from experimental data, and challenges long-established modeling paradigms. But with a growing number of machine-learning-based approaches available, how do they compare in practice? In this paper, we use the classic experimental data of Treloar to benchmark popular frameworks for hyperelasticity: (Generalized-Invariant) Constitutive Artificial Neural Networks, Physics-Augmented Neural Networks, (Adaptive) Material Fingerprinting, and Efficient Unsupervised Constitutive Law Identification&Discovery. We compare their fitting performance, computational cost, hyperparameter sensitivity, and ease of implementation. Furthermore, we discuss the trade-offs between predictive accuracy and model complexity. The latter is assessed by quantifying both the number of material parameters in the discovered models and the computational time required to evaluate the constitutive model and its derivatives. The results show that all methods can reproduce the benchmark data remarkably well. Rather than identifying a single winner, we highlight the strengths and limitations of each approach and provide practical guidance for their use. The source code for all six methods, including the training and comparison scripts, as well as all results and data used in this study, is publicly available via https://doi.org/10.5281/zenodo.21915635.
H. Holthusen, Moritz Flaschel, Denisa Martonova et al.· 0 citations
This work proposes Projected Energy Matching, a scalable framework that resolves structural and computational bottlenecks in energy matching, and introduces Helmholtz Distillation, a structural relaxation that leverages a Hutchinson trace estimator to explicitly absorb rotational noise into an auxiliary residual network.
Daniel Barco, M. Balcerak, Suprosanna Shit et al.· 0 citations
This work builds ORDER, a multimodal framework linking microstructures and descriptors with preserved property trends, aiding prediction, retrieval, and microstructure generation and consistently outperforms alignment-oriented and property-aware baselines across property prediction, cross-modal retrieval, and microstructure generation tasks.
Xinyao Li, Hangwei Qian, Jingjing Li et al.· Nature Communications· 0 citations
Large pretrained models have reshaped artificial intelligence, yet their Euclidean design assumptions often limit their ability to model hierarchy, curvature, symmetry, and heterogeneous relations in real-world data. The Geometric Space, Architecture and Learning Objective for Large Pre-Trained Models (GALOP) workshop is an accepted half-day KDD 2026 workshop that examines how geometric principles can make large pretrained models more expressive, robust, interpretable, and efficient. The workshop is organized around three complementary themes: (1) Geometric Space, which studies non-Euclidean representation spaces such as hyperbolic, spherical, and mixed-curvature manifolds; (2) Geometric Architecture, which designs model architectures that respect data symmetries, manifold structure, and relational geometry; and (3) Geometric Learning Objective, which develops objectives and optimization methods that preserve distances, angles, curvature, and topology during training. Through two invited talks and four contributed talks, the workshop brings together researchers from machine learning, data mining, and related fields to advance geometrically-informed foundation models for language, vision, graphs, knowledge discovery, and scientific discovery.
Menglin Yang, Jiahong Liu, Lucas Vinh Tran et al.· Proceedings of the 32nd ACM...· 0 citations
Spectral methods are widely used to construct representations from the geometry of data, but they often rely on a fixed kernel, graph Laplacian, or manually selected feature scaling. We propose Physics-Informed Eigenfunction Features with Learnable Scaling (PIEFS), a supervised neural representation-learning framework with a spectral inductive bias, based on a modified Dirichlet energy. In PIEFS, scalar coordinate maps are trained under empirical Gram orthogonality, a supervised linear readout, and a Dirichlet penalty in which the input gradient is transformed by a learnable metric $A(x)=\Lambda(x)U(x)$. The diagonal factor $\Lambda(x)$ controls anisotropic scaling, while the orthogonal factor $U(x)$ is parameterized by a structured product of Givens rotations. This construction yields task-adaptive Dirichlet-regularized coordinates rather than eigenfunctions of a fixed supervision-independent operator. Experiments on synthetic, tabular, and image-based benchmarks study the effect of identity, diagonal, and rotation-scaling metrics, and compare the resulting coordinates with classical baselines and NeuralEF. The results support PIEFS as a compact supervised spectral representation method and identify optimization stability, validation on explicit operator eigenproblems, and richer metric parameterizations as the main directions for future work.
V. Nazarenko, T. Lidzhiev, A. Tarakanov· 0 citations