arXiv subjects

D Yang Eng

Publications and source records attributed to D Yang Eng.

3 recordsLinked to original sources

arXiv2026

Architecture Shapes Transfer Specificity in Implicit Neural Representations

Transfer in coordinate networks is often measured by warm-start gain, but whether that gain reflects source-specific structure or generic weight reuse is less clear. We study this question across three implicit neural representation (INR) families, SIREN, ReLU MLPs, and Fourier-feature MLPs, using controlled analytic tests, a 2D lid-driven-cavity Navier--Stokes benchmark, and 1D PDE reference-solution suites for heat, viscous Burgers, and focusing cubic NLS. The analytic tests use independent-seed random controls, while the PDE benchmarks use alternate same-family source controls and auxiliary ablations. Across settings, transfer magnitude and transfer specificity separate clearly. In a 10-seed controlled 1D geometric test, Fourier Features show the largest structured transfer ($33.1\times$), followed by SIREN ($23.0\times$) and ReLU ($10.7\times$), but ReLU is far more selective: random-control transfer is $0.41\times$ for ReLU versus $14.24\times$ for SIREN. On a controlled two-parameter 1D family, the ranking changes: ReLU gives the clearest structured-versus-control separation at default settings, whereas Fourier Features improve only after bandwidth retuning. In Navier--Stokes and the broader 1D PDE suite, no single architecture dominates every equation, yet the same pattern remains: SIREN often reuses weights broadly, whereas ReLU and, in some equations, Fourier Features are more source-selective. Static diagnostics remain weak, and the heuristic scaling law $A_{\text{transfer}} \propto 1/\Delta t^2$ is rejected in the implemented 1D audit. These results position transfer specificity as a useful diagnostic for coordinate networks and suggest that architecture selection in scientific machine learning should be evaluated under explicit control conditions, not by transfer magnitude alone.

cs.LG↗

arXiv2026

Sparse M\"untz--Sz\'asz Recovery for Boundary-Anchored Velocity Profiles: A Short-Record Roughness Diagnostic in Turbulence

We present a sparse convex-relaxation framework for estimating effective local scaling exponents from short boundary-anchored velocity-increment profiles ($N\approx40$). The detector solves an $\ell_1$-regularized regression in a mixed M\"untz--Sz\'asz/Jacobi dictionary and is interpreted throughout as a finite-scale, directional roughness diagnostic rather than a pointwise H\"older exponent. On isotropic datasets from the Johns Hopkins Turbulence Database, an internal subsampling benchmark against $N=200$ detector labels gives $F_1\approx0.93$ across nine unweighted reruns, and a balanced synthetic control gives balanced accuracy $0.928$ at $N=40$, indicating useful short-record self-consistency without constituting an external calibration. Across $Re_\lambda\approx433$--$1300$, the fixed-window sharp fraction remains of order $30$--$50\%$, but a scale-normalized control does not isolate a clean Reynolds-number trend. The recovered $\hat{\alpha}$ is only weakly associated with dissipation, whereas higher vorticity is consistently associated with smaller detected roughness exponents in conditioned samples. Directional controls on 60 high-vorticity centers further show a positive vorticity-aligned contrast $\Pi_\alpha$ (mean $0.093$, bootstrap 95\% CI $[0.028,0.158]$), stronger on the true vorticity axis than on fake axes, together with a statistically detectable low-order quadrupolar component in a joint Legendre fit. A seeded scale-transfer scan shows positive $\Pi_\alpha$ at both the smallest and largest tested radii, supporting finite-range persistence without a strong theorem-level nonlocal claim. The method is therefore best viewed as a finite-scale geometric diagnostic complementary to energetic observables, capable of resolving directional structure and low-order anisotropic organization in high-vorticity regions.

physics.flu-dyn↗

arXiv2026

Interpretable Analytic Calabi-Yau Metrics via Symbolic Distillation

The pointwise determinant ratio \[ R_\psi(z)\equiv \log\!\left(\frac{\det g_{\mathrm{RF}}(z;\psi)}{\det g_{\mathrm{FS}}(z)}\right) \] measures how the Ricci-flat metric on the Dwork quintic departs from the Fubini--Study baseline. We ask whether this scalar observable can be described compactly in terms of a small number of projective invariants, and whether the same scaffold remains usable across complex-structure moduli. Using Donaldson's $k=10$ balanced metric as an algebraic teacher and symbolic regression on sampled points, we find that, within the restricted moduli-only feature class studied here, two low-order symmetric features, the power sum $p_2=\sum_i |z_i|^4$ and the cubic elementary symmetric polynomial $\sigma_3=e_3$, already capture most of the teacher variation. A degree-3 polynomial in $(p_2,\sigma_3)$ achieves held-out test $R^2=0.946$, while adding the remaining low-order symmetric generators changes this by less than $10^{-3}$. Within the same two-feature space, symbolic regression identifies a five-term rational-polynomial expression that matches the $k=10$ teacher with $R^2=0.9994$. Refitting the same functional scaffold across $\psi\in[0,0.8]$ keeps the mean determinant-ratio proxy $\langle R_\psi\rangle$ within $0.01\%$ of the local teachers on the sampled point clouds and yields smoothly varying fitted coefficients over the studied range. The holomorphic Yukawa coupling $\kappa_{111}=5$ is reproduced as a normalization check only. Taken together, these results provide a compact symbolic description of one metric-derived scalar observable on the Dwork family, while remaining bounded by the finite-$k$ teacher used for distillation rather than establishing a closed-form Ricci-flat metric.

cs.LG↗