Rafael Moschopoulos

Noam Koren, Rafael Moschopoulos, Kira Radinsky et al. · princeton

Partial differential equations (PDEs) govern complex systems, yet neural operators often struggle to efficiently capture the long-range, nonlocal interactions inherent in their solution maps. We introduce Spectral Filtering Operator (SFO), a neural operator that parameterizes integral kernels using the Universal Spectral Basis (USB), a fixed, global orthonormal basis derived from the eigenmodes of the Hilbert matrix in spectral filtering theory. Motivated by our theoretical finding that the discrete Green's functions of shift-invariant PDE discretizations exhibit spatial Linear Dynamical System (LDS) structure, we prove that these kernels admit compact approximations in the USB. By learning only the spectral coefficients of rapidly decaying eigenvalues, SFO achieves a highly efficient representation. Across six benchmarks, including reaction-diffusion, fluid dynamics, and 3D electromagnetics, SFO achieves state-of-the-art accuracy, reducing error by up to 40% relative to strong baselines while using substantially fewer parameters.

Erich Liang, Roma Bhattacharjee, Sreemanti Dey et al. · princeton

Accurately tracking camera intrinsics is crucial for achieving 3D understanding from 2D video. However, most 3D algorithms assume that camera intrinsics stay constant throughout a video, which is often not true for many real-world in-the-wild videos. A major obstacle in this field is a lack of dynamic camera intrinsics benchmarks--existing benchmarks typically offer limited diversity in scene content and intrinsics variation, and none provide per-frame intrinsic changes for consecutive video frames. In this paper, we present Intrinsics in Flux (InFlux), a real-world benchmark that provides per-frame ground truth intrinsics annotations for videos with dynamic intrinsics. Compared to prior benchmarks, InFlux captures a wider range of intrinsic variations and scene diversity, featuring 143K+ annotated frames from 386 high-resolution indoor and outdoor videos with dynamic camera intrinsics. To ensure accurate per-frame intrinsics, we build a comprehensive lookup table of calibration experiments and extend the Kalibr toolbox to improve its accuracy and robustness. Using our benchmark, we evaluate existing baseline methods for predicting camera intrinsics and find that most struggle to achieve accurate predictions on videos with dynamic intrinsics. For the dataset, code, videos, and submission, please visit https://influx.cs.princeton.edu/.