arXiv:2505.21573v3 Announce Type: replace Abstract: Learning PDE dynamics from limited data with unknown physics is challenging. Existing neural PDE solvers either require large datasets or rely on known physics (e.g., PDE residuals or handcrafted stencils), leading to limited applicability. To address these challenges, we propose Spectral-Inspired Neural Operator (SINO), which can model complex systems from just 2-5 trajectories, without requiring explicit PDE terms. Specifically, SINO automatically captures both local and global spatial derivatives from frequency indices, enabling a compact
This development addresses a critical limitation in AI's ability to model complex physical systems with sparse data, a bottleneck for many scientific and engineering applications.
Improved data efficiency in learning PDE dynamics can accelerate scientific discovery, optimize industrial processes, and enable more robust AI simulations across various fields.
Machine learning models can now effectively learn complex physical laws from significantly less data and without explicit prior knowledge of underlying physics, broadening AI's applicability in scientific computing.
- · Scientific computing researchers
- · Engineering design & simulation sectors
- · AI model developers
- · Drug discovery & materials science
- · Traditional physics-based simulation methods requiring extensive initial data
- · Sectors heavily reliant on large, labeled datasets for physical modeling
Reduced computational resources and time needed for high-fidelity physical simulations.
Faster iteration cycles in R&D, leading to more rapid innovation in areas like fluid dynamics or climate modeling.
Democratization of sophisticated simulation capabilities to researchers and engineers with limited data access or computational infrastructure.
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Read at arXiv cs.LG