arXiv:2605. 18250v2 Announce Type: replace-cross Abstract: Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport.
arXiv:2605. 18250v3 Announce Type: replace-cross Abstract: Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport.
arXiv:2606. 08258v1 Announce Type: cross Abstract: Understanding and comparing structures in scalar fields is a central challenge in scientific visualization, with applications ranging from feature analysis to temporal and structural comparison.
arXiv:2404. 02692v3 Announce Type: replace-cross Abstract: The explosion of data available in life sciences is fueling an increasing demand for expressive models and computational methods.
Continuous-time generative frameworks construct probability paths between base and target domains by optimizing time-dependent velocity fields. While theoretical targets favor straight trajectories, empirical networks develop complex path deformations.
arXiv:2607. 21421v1 Announce Type: new Abstract: Generative models can support decision-making under uncertainty by producing ensembles of plausible future system trajectories, but statistical plausibility does not ensure structural feasibility.
arXiv:2608. 08689v1 Announce Type: new Abstract: The state evolution of a complex system arises jointly from object laws, relational propagation, domain conservation, and unmodeled error.
arXiv:2608. 07161v1 Announce Type: cross Abstract: Simulating complex fluid flows requires capturing full equilibrium distributions rather than just mean trajectories, yet high-fidelity solvers remain computationally prohibitive.
Generative AI emulators are increasingly used in scientific domains where we already have strong theory, benchmarks, and physical intuition. This raises a central evaluation and interpretability question: when a foundation-style model can reproduce known continuum dynamics, what internal mechanism supports that behavior, is the internal behaviour consistent with known physics, and how does it relate to where the emulator succeeds or fails?
arXiv:2511. 10841v3 Announce Type: replace-cross Abstract: Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge.
arXiv:2607. 12616v1 Announce Type: new Abstract: Continuous-time generative frameworks construct probability paths between base and target domains by optimizing time-dependent velocity fields.
arXiv:2602. 23035v2 Announce Type: replace Abstract: Cardiac blood flow patterns contain rich information about disease severity and clinical interventions, yet current imaging and computational methods fail to capture underlying relational structures of coherent flow features.
arXiv:2606. 00937v1 Announce Type: new Abstract: Neural operators provide fast surrogate models for PDE simulations, but standard architectures often treat geometry and discretization as secondary to field data.