arXiv:2410.23667v2 Announce Type: replace
Abstract: Neural differential equations offer a powerful approach for learning dynamical systems from data. However, they do not inherently respect known con...
By Alistair White, Anna B\"uttner, Maximilian Gelbrecht, Valentin Duruisseaux, Niki Kilbertus, Frank Hellmann, Niklas Boers
arXiv:2603.13496v2 Announce Type: replace
Abstract: Constructing reduced-order models (ROMs) capable of efficiently predicting the evolution of parameter-dependent high-dimensional dynamical systems...
By Nicol\`o Botteghi, Silke Glas, Christoph Brune
The paper examines how boundary representation (B‑rep) encoders for CAD models fail to handle variations that do not change the underlying solid, such as different modeling operations or software export settings. By demonstrating that existing encoders collapse under these perturbations, the authors introduce the canonical region graph, a representation derived directly from the solid that is theoretically invariant to repartitioning and rigid motions. This new input format matches the best baseline on standard benchmarks and remains stable across all tested perturbations.
By Heinrich Jiang, Hager Yasser Mohamed, Alexander Hitt, Valeriia Lomakina, Henning Jiang, Jennifer Jang
Boundary representation (B‑rep) is the standard format for parametric 3D models in CAD systems, yet the same solid can be encoded by different B‑reps due to varying operations, kernel rebuilds, or export settings. Existing B‑rep encoders fail to handle these variations, collapsing on standard benchmarks and real‑world perturbations. The authors introduce the canonical region graph, an input representation derived directly from the solid, which offers theoretical invariance to repartitioning and rigid motions and performs as well as the best baseline while remaining stable across all tested perturbations.
arXiv:2606. 05247v1 Announce Type: new Abstract: Enforcing nonlinear inequality constraints in neural networks remains challenging, especially when the output is subject to many coupled constraints.
By Ziqian Wang, Chenxi Fang, Zhen Zhang
arXiv:2606. 11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation.
By Handi Zhang, Adrienne M. Propp, Brooks Kinch, Houman Owhadi, Nathaniel Trask