Neural ordinary differential equations (NODEs) mark a significant advance in geometric deep learning, the pursuit of incorporating non-Euclidean structures in machine learning using geometrical principles. NODEs describe the dynamics of information propagating through recurrent neural networks in the limit of infinite depth using ordinary differential equations. These models offer several beneficial properties, e.g. bijectivity, scalability and universality, and have been used successfully primarily to construct continuous normalizing flows (CNFs) to model probability densities in different geometries. An important aspect of geometric deep learning is the ability to accommodate the symmetries of the data, or equivalently, the space where the NODE is defined, by constructing models that are manifestly equivariant under the action of the symmetry Lie groups. However, the dynamical systems in NODE models are constrained by the fixed dimensionality of their state vectors, hindering the efficient exploration of diverse data representations. For example, a powerful architectural element in feed-forward machine learning models is the encoder-decoder that extracts a lower-dimensional latent representation from which the original data can be efficiently reconstructed. The dimensional bottleneck is used to extract features from information-dense representations and is, e.g., employed in ubiquitous models such as autoencoders and sequence-to-sequence prediction. The inability to efficiently enforce similar architectural constraints in NODEs is a significant limitation. To remedy the limitations in the current framework, we have proposed PolyNODEs, an extension of NODEs from manifolds to M-polyfolds, which are generalisations of manifolds modelled on Banach spaces rather than Euclidean spaces. The number of local coordinates in M-polyfold theory can vary smoothly through the introduction of scale structures, or sc-structures. In the previous project supported by NAISS (2025/22-454), we experimentally validated the PolyNODE models on simple (but non-trivial) M-polyfolds and showed that PolyNODEs are viable machine learning models that incorporate geometrical structures beyond classical manifold theory. The project resulted in the publication https://arxiv.org/abs/2602.15128 The goal of the current project is to continue the development of PolyNODEs to create a comprehensive geometric framework for equivariant NODEs on M-polyfolds. This will involve theoretical developments and accompanying experimental validation. In particular, we plan to conduct numerical experiments probing the ability of the PolyNODEs (and possible generalisations) to incorporate topological and geometrical structures beyond the stratifications considered in previous work. This would greatly expand the utility of the models in geometric deep learning and probe the theoretical capabilities of PolyNODEs.