arXiv:2606. 06046v1 Announce Type: cross Abstract: We investigate the approximation of solution operators for partial differential equations (PDEs) using sparse high-dimensional techniques.
arXiv:2608. 13504v1 Announce Type: new Abstract: We develop the Sparse Orthogonal Regression Technique (SORT), a sparse spectral framework for learning orthonormal-basis expansions from noisy and irregularly sampled data.
arXiv:2507.07292v2 Announce Type: replace Abstract: We develop a new and general encode-approximate-reconstruct operator learning model that leverages learned neural representations of bases for inpu...
arXiv:2608.30070v1 Announce Type: new Abstract: Sparse representations are often expected to make models smaller and also reduce inference cost. For Fourier Neural Operators (FNOs), these objectives...
arXiv:2510. 10350v3 Announce Type: replace-cross Abstract: Operator learning provides a data-driven approach to approximating solution operators of partial differential equations, but its effectiveness depends strongly on how input and output functions are represented.
arXiv:2601. 20496v2 Announce Type: replace-cross Abstract: Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications.
arXiv:2609.36527v1 Announce Type: new Abstract: Recovering complete physical fields from sparse observations is challenging because the measurements may not uniquely determine the underlying state. D...
arXiv:2606. 03936v1 Announce Type: new Abstract: Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters.
arXiv:2601. 00672v2 Announce Type: replace-cross Abstract: In this paper, we study the finite element operator network (FEONet), an operator-learning method for parametric problems, originally introduced in J.
Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters. Sparse sensor measurements of the field are often available too, offering pointwise accuracy without spectral distortion but covering only a small fraction of the domain.
arXiv:2606. 10975v1 Announce Type: new Abstract: Finding convenient spaces in which certain hypotheses regarding an assumed sparse structure of natural signals hold true has become a desirable result in recent research, its implications being reflected in areas such as data compression, noise reduction and feature extraction.
arXiv:2606. 12182v1 Announce Type: new Abstract: Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering.
Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering. While early approaches relied on empirical data and heuristics, modern data-driven methods offer greater flexibility and fewer assumptions.