Before revision:  As in the case of ODE discovery, the weak form replaces pointwise approximation of derivatives with local integrations against test functions and achieves effective machine-precision recovery of weights from noise-free data (i.e. below the tolerance of the simulation scheme) as well as natural robustness to noise without the use of noise filtering .
After revision:  As in the case of ODE discovery, the weak form enables effective machine-precision recovery of weights from noise-free data (i.e. below the tolerance of the simulation scheme) as well as natural robustness to noise without the use of noise filtering .