arXiv:2608. 14743v1 Announce Type: new Abstract: The identification and reconstruction of the boundaries separating basins of attraction in multistable, multidimensional dynamical systems presents a fundamental challenge in computational dynamics.
arXiv:2608. 12624v1 Announce Type: new Abstract: Structure-preserving machine learning embeds physical structure directly into model architectures, yet uncertainty quantification (UQ) for such hard-constrained models remains limited because standard UQ methods may violate the encoded admissibility conditions, require architectural modifications, or impose substantial computational costs.
arXiv:2606. 16073v1 Announce Type: new Abstract: Sampling from complex, unnormalized probability densities is a fundamental challenge in Bayesian inference and probabilistic modeling.
arXiv:2606. 09949v1 Announce Type: cross Abstract: Data-driven PDE surrogates are trained with data produced by numerical PDE solvers.
arXiv:2606. 23838v1 Announce Type: new Abstract: When two or more parameters or labels produce similar data, they are degenerate, or hard to distinguish.
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.
arXiv:2512. 18454v3 Announce Type: replace Abstract: Predictive machine learning models generally excel on in-distribution data, but their performance degrades on out-of-distribution (OOD) inputs.
arXiv:2606. 27029v2 Announce Type: replace Abstract: Hamiltonian Neural Networks (HNNs) integrate physical priors into neural models by learning a system's Hamiltonian, improving generalization and sample efficiency.
arXiv:2606. 14737v1 Announce Type: cross Abstract: Molecular dynamics (MD) simulations generate trajectories in a high-dimensional configuration space whose analysis critically depends on molecular descriptors, typically handcrafted observables or learned kinetic embeddings.
arXiv:2606. 05581v1 Announce Type: cross Abstract: Intrinsic methods fill the default toolbox for geometry processing on meshes.
arXiv:2605. 08832v3 Announce Type: replace Abstract: Neural surrogate models for computational fluid dynamics (CFD) are typically trained as forward operators that map explicit problem specifications, such as geometry and boundary conditions, to solution fields.
arXiv:2604. 24662v2 Announce Type: replace-cross Abstract: Identifying the dynamical state variables of a system from high-dimensional observations is a central problem across physical sciences.
arXiv:2606. 27029v1 Announce Type: new Abstract: Hamiltonian Neural Networks (HNNs) integrate physical priors into neural models by learning a system's Hamiltonian, improving generalization and sample efficiency.