arXiv subjects

Ridham Patel

Publications and source records attributed to Ridham Patel.

4 recordsLinked to original sources

arXiv2026

The Symbol of the Surrogate: Measuring Numerical Provenance in Neural PDE Solvers

Neural PDE surrogates are trained on numerical solver outputs that contain both physical evolution and solver-specific discretization errors. Because surrogates are also evaluated against held-out trajectories from the same solver, standard benchmarks cannot distinguish fidelity to the exact evolution from imitation of the numerical scheme. We introduce an empirical Fourier-symbol diagnostic that probes a trained surrogate's linearized one-step operator with individual Fourier modes and compares it with both exact-evolution and training-scheme references. To address architectural spectral bias, we train identical networks on schemes with orthogonal dissipative and dispersive signatures and compare their learned operators. In linear advection, the learned surrogates reproduce the training schemes' amplitude and phase errors, with the twin-scheme difference reaching more than 99.8\% of the analytically predicted full-imitation ceiling. The same behavior occurs for a non-local Fourier neural operator and at the operator level for nonlinear Burgers dynamics. These results show that agreement with solver-generated test data does not by itself establish fidelity to the exact evolution. Fourier-symbol measurements provide a direct diagnostic of numerical provenance.

cs.LG↗

arXiv2026

Exact SO(3)-Equivariant Isotropic Kernels for Rotation-Robust Neural Dynamics

Neural surrogates for vector-valued partial differential equations can fit training data yet change their predictions when the same physical state is expressed in a rotated coordinate frame. We study this failure on three-dimensional Navier--Stokes dynamics observed at irregularly placed points. We introduce the Invariant-Conditioned Isotropic Kernel Neural Operator (IKNO), a compact graph model that builds local interactions from scalar quantities unchanged by rotation and vector directions that rotate with the data. Consequently, rotating the positions and velocities rotates the predicted velocity change in exactly the same way. On a held-out test set fixed after model design, training unconstrained graph models on randomly rotated examples reduces but does not eliminate their coordinate dependence. In contrast, IKNO is consistent to numerical precision, matches the forecasting accuracy of a general rotation-aware Tensor Field Network with $5.6$ times fewer parameters, and outperforms a parameter-matched graph simulator. These results show that a compact, PDE-specialized model can remove coordinate dependence without sacrificing forecasting accuracy.

cs.LG↗

arXiv2026

Measuring Effective Data Resolution in Guided Diffusion Posteriors

Guided diffusion samplers are increasingly used to reconstruct physical fields from sparse observations, but standard diagnostics do not say how much of the reconstruction was actually determined by the data. We introduce effective data resolution for black-box generative posteriors: a comparison between the resolution warranted by the inverse problem, $\mathrm{dof}_{\mathrm{ref}}$, and the resolution realised by the sampler, $\mathrm{dof}_{\mathrm{samp}}$. A perturbation estimator measures $\mathrm{dof}_{\mathrm{samp}}$ and the spatial map $R(x,x)$ from sampler queries alone. We validate the estimator against exact references and use it to study guided diffusion. The resulting measurements show that guidance weight can strongly alter apparent information transfer, that mean, spread and resolution are not jointly corrected by one weight even with an exact prior and score, and that resolution fidelity does not follow reliably from the apparent principledness of a guidance rule.

cs.LG↗

arXiv2026

Towards Robust Classroom Attendance: A Comprehensive Evaluation of Face Detection and Recognition Models

Manual attendance methods, such as paper or register-based systems, take a lot of time, can lead to errors, and are easy to falsify. Face recognition is more reliable, but it frequently struggles in classrooms because lighting and other conditions can vary. Face recognition datasets are designed for regulated environments and do not capture the actual challenges found in classrooms. To address this, a new face detection and recognition dataset, the Visage Face dataset, comprising 16,234 face samples, is proposed for the task of face detection and recognition. The photos are taken from different angles and under varying lighting conditions, with students showing a range of expressions, and some faces partly covered to reflect real-life situations. A YOLO-based system is used to detect faces and tested seven advanced face recognition models with thirteen configurations: LVFace, QCFace, FaceLiVTv2, TopoFR, EdgeFace, TransFace, and GhostFaceNets. Of these, FaceLiVTv2-M performed best, with 99.75% Top-1/Top-5 accuracy and an inference time of 6.459 ms. These results show that the Visage Face Dataset is a realistic and challenging benchmark for face recognition in classroom attendance.

cs.CV↗