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A Unified Framework for Structured Flow Modeling: From Continuous Fields to Data-Driven Representations

arXiv:2605.18250v2 Announce Type: replace Abstract: Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of domains, including physical, engineered, and data-driven systems. This work provides a unified perspective on such systems by connecting continuous formulations based on the Helmholtz-Hodge decomposition with discrete and data-driven representations.

arXiv Physics 8d ago

A Unified Framework for Structured Flow Modeling: From Continuous Fields to Data-Driven Representations

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. These features arise across a wide range of domains, including physical, engineered, and data-driven systems. This work provides a unified perspective on such systems by connecting continuous formulations based on the Helmholtz-Hodge decomposition with discrete and data-driven...

arXiv CS 8d ago

Diffusion Bridge or Flow Matching? A Unifying Framework and Comparative Analysis

arXiv:2509.24531v2 Announce Type: replace Abstract: Diffusion Bridge and Flow Matching have both demonstrated compelling empirical performance in transformation between arbitrary distributions. However, there remains confusion about which approach is generally preferable, and the substantial discrepancies in their modeling assumptions and practical implementations have hindered a unified theoretical account of their relative merits. We have, for the first time, provided a unified theoretical...

arXiv CS 1d ago

MatMind: A Structure-Activity Knowledge-Driven Generative Foundation Model for Materials Science

Announce Type: cross Abstract: Progress in AI-driven crystal materials science has so far been carried by narrow architectures purpose-built for individual tasks -- graph neural networks for property prediction, diffusion and flow-matching models for crystal generation -- each excelling within its niche yet unable to act as a shared backbone across the full spectrum of materials problems. Generative large language models offer a fundamentally different paradigm, in which structural...

arXiv CS 1d ago

Deep learning four decades of human migration

Abstract Human migration is a fundamental driver of global demographic change, shaping population structure, labour markets and social policy across countries1,2,3. Although long-term migration patterns are often linked to economic development4, they can shift rapidly in response to shocks such as conflict, environmental crises and political change5. Despite its importance, migration remains difficult to measure consistently: existing data are sparse, concentrated in high-income settings and...

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Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networks

arXiv:2508.11911v2 Announce Type: replace Abstract: We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learning within a single, end-to-end neural architecture. The encoder-decoder is built from Henon neural networks (HenonNets) and may be augmented with linear SGS-reflector layers. This yields an exact symplectic map between full and latent phase spaces.

arXiv CS 9d ago

Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networks

arXiv:2508.11911v2 Announce Type: replace-cross Abstract: We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learning within a single, end-to-end neural architecture. The encoder-decoder is built from Henon neural networks (HenonNets) and may be augmented with linear SGS-reflector layers. This yields an exact symplectic map between full and latent phase spaces.

arXiv Physics 9d ago

Self-Consistent Generative Paths via Admissible Random Variational Transport

arXiv:2606.08953v1 Announce Type: new Abstract: Modern generative models often define an entire probability path from a simple prior to the data law, rather than only an endpoint map. Diffusion models follow stochastic denoising paths, flow matching learns transport fields, consistency and distillation methods compress paths into one or a few steps, adversarial models match terminal distributions, and VAEs generate through latent kernels. Existing unifying views mainly describe how such...

arXiv CS 1d ago

AMix-1: A Pathway to Test-Time Scalable Protein Foundation Model

arXiv:2507.08920v4 Announce Type: replace-cross Abstract: We introduce AMix-1, a powerful protein foundation model built on Bayesian Flow Networks and empowered by a systematic training methodology, encompassing pretraining scaling laws, emergent capability analysis, in-context learning mechanism, and test-time scaling algorithm. To guarantee robust scalability, we establish a predictive scaling law and reveal the progressive emergence of structural understanding via loss perspective,...

arXiv CS 1d ago

QuadLink: Autoregressive Quad-Dominant Mesh Generation via Point-Relation Learning

arXiv:2605.16813v2 Announce Type: replace Abstract: The generation of production-ready quad-dominant meshes is a cornerstone of modern 3D content creation. Generating anisotropic quad-dominant meshes from point clouds is challenging, as existing methods are typically limited to producing either pure triangular meshes or pure quadrilateral meshes with isotropic densities. In this paper, we present QuadLink, a unified framework consisting of three stages for quad-dominant mesh generation by...

arXiv CS 7d ago