Even if a time series is constructed up of numbers only, finding abstract fixed-dim vector representation would be interesting for classification/clustering purposes. As we can learn & find abstract representations/embeddings of text/images, can we do something similar on Time series? Finding such ways would result in better clustering & related tasks instead of traditional ways using some statistical measures like Pearson correlation etc. All thoughts are welcome.
Maybe the framework of Neural Processes could be interesting here? It defines a family of functions parameterized by a neural network. The parameters could serve as your embeddings, eventually after projecting into a lower dimension. See the paper Attentive Neural Processes and the preceding papers cited therein.