B-Spline
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Related Articles from SNS
Ionization energies for Rydberg $^4 \mathrm{He}$ ($1snp\,^{1,3}P$) states using the correlated B-spline basis function method
Announce Type: new Abstract: We extend the correlated B-spline basis function (C-BSBF) method to high-precision calculations of the ionization energies of helium Rydberg $n^{1,3}P$ states ($n=24$--$35$). Using a unified basis set, we evaluate nonrelativistic energies, relativistic corrections of order $m\alpha^4$ (including finite-mass recoil), QED contributions of order $m\alpha^5$, and partial $m\alpha^6$ terms (singlet-triplet mixing, one- and two-loop radiative corrections). The...
Ionization energies for Rydberg $^4 \mathrm{He}$ ($1snp\,^{1,3}P$) states using the correlated B-spline basis function method
arXiv:2606.04768v2 Announce Type: replace Abstract: We extend the correlated B-spline basis function (C-BSBF) method to high-precision calculations of the ionization energies of helium Rydberg $n^{1,3}P$ states ($n=24$--$35$). Using a unified basis set, we evaluate nonrelativistic energies, relativistic corrections of order $m\alpha^4$ (including finite-mass recoil), QED contributions of order $m\alpha^5$, and partial $m\alpha^6$ terms (singlet-triplet mixing, one- and two-loop radiative...
A Physics-Informed B-Spline Framework for Continuous Approximation of Flow Data
new Abstract: Continuous approximations of flow data are useful for downstream analysis, differentiation, and visualization, but purely data-driven reconstructions do not, in general, preserve the governing physics. This limitation becomes particularly important when input data are physically inconsistent, whether due to low-fidelity discretizations or unmodeled discrepancies. In such cases, reconstructed fields may exhibit inaccurate PDE residuals, violated balance laws, or unreliable...
Composite B-Spline Current Deposition and Interpolation Operators for Thin-Wire Finite-Difference Time-Domain Simulations
arXiv:2605.21450v3 Announce Type: replace Abstract: Holland-Simpson thin-wire finite-difference time-domain (FDTD) simulations of obliquely oriented closed-loop antennas exhibit persistent low-frequency parasitic currents because the current-deposition operator fails to conserve charge. This deposition operator, together with an interpolation operator that samples the tangential electric field along the wire, can be realized as regularizations of distributions: the wire current is deposited...
B-Spline for Self-Consistent Field Theory with a Z-Dependent Pauli Potential for Atomic Binding Energies
arXiv:2606.07273v1 Announce Type: new Abstract: Polymer self-consistent field theory (SCFT) has recently been established as a promising alternative framework to Kohn-Sham density functional theory (KS-DFT) for modeling quantum many-body systems. It uses real-valued propagators instead of orbitals, simplifying the self-consistent numerical solution.
Constructing $C^1$ limit surfaces from unstructured splines via averaging and refinement
arXiv:2606.07149v1 Announce Type: new Abstract: In this paper we present a construction for unstructured splines over quadrilateral meshes by iterative averaging and refinement. We represent the spline as a multi-patch B-spline, where the degrees of freedom are those B-spline coefficients on the quadrilateral patches that are not associated with interior edges and vertices of the mesh, i.e., their corresponding Greville points lie inside the patches. In every averaging step, we replace the...
Ultrafast machine learning on FPGAs via Kolmogorov-Arnold Networks
Ultrafast machine learning on FPGAs via Kolmogorov-Arnold Networks This post is a high-level explainer for my Master’s thesis, which involves designing hardware architectures for ultrafast inference and online learning using the Kolmogorov-Arnold Network (KAN) architecture. I’ll assume familiarity with standard machine learning concepts, as well as some understanding of hardware and digital circuits; read my previous post here for the latter. Please read the two papers below for more...
Nonlinear Factor Decomposition via Kolmogorov-Arnold Networks: A Spectral Approach to Asset Return Analysis
arXiv:2603.28257v2 Announce Type: replace-cross Abstract: KAN-PCA is an autoencoder that uses a KAN as encoder and a linear map as decoder. It generalizes classical PCA by replacing linear projections with learned B-spline functions on each edge. The motivation is to capture more variance than classical PCA, which becomes inefficient during market crises when the linear assumption breaks down and correlations between assets change dramatically.
Single-Line Drawing Generation via Semantics-Driven Optimization
arXiv:2606.01910v1 Announce Type: new Abstract: Line drawings are a highly expressive art form that requires the artist to abstract and distill the essence of their subject. We present the first semantics-driven method for automatically generating single-line drawings in vector format, guided either by a text prompt describing the concept or an input image depicting it. Our approach leverages score distillation sampling to optimize the parameters of a uniform rational B-spline (URBS) curve,...
Basis construction for polynomial spline spaces over arbitrary T-meshes
arXiv:2508.12950v3 Announce Type: replace Abstract : This paper presents the first method for constructing bases for polynomial spline spaces over an arbitrary T-meshes (PT-splines for short). We construct spline basis functions for an arbitrary T-mesh by first converting the T-mesh into a diagonalizable one via edge extension, ensuring a stable dimension of the spline space.