Continuous Fields
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Related Articles from SNS
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...
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.
Phong-Rodrigues Extrinsic Vector-Field Processing
arXiv:2601.10621v2 Announce Type: replace Abstract: We introduce a new extrinsic discretization of tangent vector fields on triangle meshes that is continuous, with bounded derivatives that are continuous almost everywhere, supporting pointwise evaluation and integration of differential operators. We achieve this by building a continuous normal field over the mesh via Phong interpolation and using minimal Rodrigues rotations to transport vertex-based tangent vectors into triangle interiors....
A Differentiable Framework for Full and Phaseless Data Inversion Using Neural Implicit Contrast-Source Representation
Announce Type: replace Abstract: In this study, we extend the contrast source inversion to a fully differentiable, unsupervised framework based on a neural implicit representation of the contrast source. Specifically, instead of a pixel-wise discrete representation, the contrast source is parameterized by a lightweight residual multilayer perceptron (ResMLP) as a continuous neural field conditioned on spatial coordinates and transmitter settings. This continuous parameterization provides a...
A Differentiable Framework for Full and Phaseless Data Inversion Using Neural Implicit Contrast-Source Representation
Announce Type: replace-cross Abstract: In this study, we extend the contrast source inversion to a fully differentiable, unsupervised framework based on a neural implicit representation of the contrast source. Specifically, instead of a pixel-wise discrete representation, the contrast source is parameterized by a lightweight residual multilayer perceptron (ResMLP) as a continuous neural field conditioned on spatial coordinates and transmitter settings. This continuous parameterization...
Uncertainty-Aware Graph Neural Reconstruction of Urban Temperature Fields from Sparse Sensors under Deployment Constraints
arXiv:2606.02038v1 Announce Type: new Abstract: Reconstructing spatially continuous daily temperature fields from sparse observations is important for urban climate monitoring and heat-risk analysis, but practical deployments are limited by sensor budgets and spacing constraints. This study proposes an uncertainty-aware graph neural network (GNN) framework for reconstructing daily maximum temperature fields from sparse sensors while supporting distance-constrained sensor placement and...
Uncertainty-Aware Graph Neural Reconstruction of Urban Temperature Fields from Sparse Sensors under Deployment Constraints
arXiv:2606.02038v1 Announce Type: cross Abstract: Reconstructing spatially continuous daily temperature fields from sparse observations is important for urban climate monitoring and heat-risk analysis, but practical deployments are limited by sensor budgets and spacing constraints. This study proposes an uncertainty-aware graph neural network (GNN) framework for reconstructing daily maximum temperature fields from sparse sensors while supporting distance-constrained sensor placement and...
Functional Attention: From Pairwise Affinities to Functional Correspondences
arXiv:2605.31559v1 Announce Type: new Abstract: Learning mappings between infinite-dimensional function spaces, or operator learning, is essential for many machine learning applications. Although transformer-based operators are popular, they often rely on token-wise attention. These methods treat continuous fields as discrete tokens and usually ignore the global functional structure.
Implicit Structural Modeling via Generative Diffusion Frameworks
Announce Type: new Abstract: Implicit structural modeling can support understanding subsurface spatial configurations, revealing patterns of geological evolution, and enabling quantitative simulation of geological processes, thereby offering substantial scientific and engineering value. Conventional approaches formulate it as an optimization problem or framework interpolation to fit a continuous scalar field, whereas machine learning methods typically adopt discriminative regression to...
A Unified Framework for Virtual Wave Transform: From Generalized Formulation to Excitation-Specific Projection
Announce Type: cross Abstract: We present a unified theoretical framework for the mapping between diffusive and wave-like dynamics, formulated as a spectral integral operator acting on temporal fields. By introducing an analytic continuation in the complex frequency plane, we establish an explicit correspondence between thermal diffusion and a virtual wave field governed by a hyperbolic equation. This mapping is shown to define a causal, compact Fredholm operator that acts as a nonstationary...