In astronomical surveys, such as the Zwicky Transient Facility, supernovae (SNe) are relatively uncommon objects compared to other classes of variable events. Along with this scarcity, the processing of multi-band light-curves is a challenging task due to the highly irregular cadence, long time gaps, missing-values, few observations, etc. These issues are particularly detrimental to the analysis of transient events: SN-like light-curves. We offer three main contributions: 1) Based on temporal modulation and attention mechanisms, we propose a Deep attention model (TimeModAttn) to classify multi-band light-curves of different SN types, avoiding photometric or hand-crafted feature computations, missing-value assumptions, and explicit imputation/interpolation methods. 2) We propose a model for the synthetic generation of SN multi-band light-curves based on the Supernova Parametric Model, allowing us to increase the number of samples and the diversity of cadence. Thus, the TimeModAttn model is first pre-trained using synthetic light-curves. Then, a fine-tuning process is performed. The TimeModAttn model outperformed other Deep Learning models, based on Recurrent Neural Networks, in two scenarios: late-classification and early-classification. Also, the TimeModAttn model outperformed a Balanced Random Forest (BRF) classifier (trained with real data), increasing the balanced-$F_1$score from $\approx.525$ to $\approx.596$. When training the BRF with synthetic data, this model achieved similar performance to the TimeModAttn model proposed while still maintaining extra advantages. 3) We conducted interpretability experiments. High attention scores were obtained for observations earlier than and close to the SN brightness peaks. This also correlated with an early highly variability of the learned temporal modulation.

We have derived theoretical maximum likelihood estimators of trends for standard dynamics and implemented them. We have reframed the problem of trend detection into a classification problem amenable to machine learning methods. We have shown that RNN are in a way a generalization of simple moving average techniques and motivated this by theory. In a simple case, we have shown that this generalization transforms the trend estimation problem into simply locating the state vector into convex polytopes cells. Finally, we have showed empirically that GRU or LSTM cells are on average the best building block to use compared to a broad range of estimators in order to detect trends in time series. Putting the emphasis on learning stylized data and then transferring to real data rather than building complex structures fitted to data is also an important takeaway of this paper. Ongoing preliminary research seems to validate our approach for financial applications. This might pave the way to building efficient market estimators protected against over-fitting.