NMIPS introduces a unified neuro-symbolic framework for solving PDE families with shared structures but varying parameters. It discovers interpretable analytical solutions via multifactorial optimization and affine transfer for efficiency. Experiments show up to 35.7% accuracy gains over baselines.
Key Points
- 1.Unified neuro-symbolic framework solves PDE families with shared structures and varying parameters
- 2.Discovers interpretable analytical solutions via multifactorial optimization and affine transfer
- 3.Demonstrates up to 35.7% accuracy gains over baselines in experiments
Impact Analysis
Scientists and engineers solving PDEs benefit from NMIPS's interpretable, efficient solutions for parameter-varying problems. It advances neuro-symbolic AI by combining neural approximation with symbolic discovery, potentially accelerating simulations in physics and engineering. Broader adoption could reduce reliance on black-box numerical solvers.
Technical Details
NMIPS uses multifactorial optimization to search for analytical solutions within PDE families and applies affine transfer to adapt across parameter variations efficiently. The neuro-symbolic design integrates neural networks for initial approximations with symbolic methods for exact, interpretable expressions.