Oscillatory state-space models boost physics-informed neural PDE solvers
New method solves 100D PDEs with less memory and higher accuracy
Solving time-dependent partial differential equations (PDEs) is critical in computational science and engineering. Physics-informed neural networks (PINNs) learn solutions directly from governing equations, but capturing temporal dynamics remains difficult. Existing sequence-model-based PINNs use general-purpose models that lack structured dynamical priors and suffer from memory scaling issues at high resolutions or dimensionalities.
Abhishek Chandra and Taniya Kapoor's new approach incorporates oscillatory state-space dynamics to represent the modal structure of PDE solutions. It combines a linear-oscillator temporal evolution with a PDE-aware spectral basis, enabling closed-form spatial differentiation and consistent boundary enforcement. Evaluated on forward, inverse, and up to 100-dimensional PDE problems, the method outperforms recent sequence-model-based PINNs in accuracy while significantly reducing memory usage. This work paves the way for more efficient, physics-aligned neural PDE solvers suitable for large-scale simulations.
- Uses linear-oscillator temporal evolution and a PDE-aware spectral basis for structured temporal dynamics
- Achieves higher accuracy and lower memory usage than existing sequence-model-based PINN approaches
- Validated on complex PDE problems including forward, inverse, and up to 100 spatial dimensions
Why It Matters
Enables faster, more memory-efficient simulations of complex physical systems for engineering and scientific computing.