We consider the problem of discretization of neural operators between Hilbert spaces in a general framework including skip connections. We focus on bijec-tive neural operators through the lens of diffeomorphisms in infinite dimensions.

This research offers a fresh take on neural operators with a framework Representation equivalent Neural Operators (ReNO) designed to address these issues.

LMC can suffer from slow convergence - requiring a large number of steps of small step-size to obtain good quality samples.

Eq. (6) suggests that the SDE drift corresponding to the score may be broken down into 3 steps: 1. However, in practice this modification creates a "discontinuity" between the constrained and unconstrained components, leading to erroneous correlations between them in the generated samples. "learning rate" that is determined empirically such that the loss value reduces adequately close to zero Thus it needs to be tuned empirically. The correction in Eq. (16) is equivalent to imposing a Gaussian likelihood on Remark 2. The post-processing presented in this section is similar to [ In this section, we present the most relevant components for completeness and better reproducibility. B.2 Sampling The reverse SDE in Eq. (5) used for sampling may be rewritten in terms of denoiser D As stated in 4.1 of the main text, for this The energy-based metrics are already defined in Eq. (12) and Eq.