Will Neural Operators Replace Numerical Solvers?
Submitted to Proceedings of the Indian National Science Academy
- Compares FNO with conventional numerical solvers for repeated PDE simulations, evaluating solver time, training and preparation cost, inference speed, memory usage, predictive accuracy, and cumulative computational cost across Burgers and periodic heat equations.
- Shows that neural operators can deliver substantially faster individual predictions, but their overall advantage depends on simulation workload, training investment, accuracy requirements, and break-even thresholds, with benefits emerging at approximately 2.98×10³ simulations for baseline Burgers and 2.75×10⁴ for the heat equation.
