# LSTM Variants for Chaotic Dynamical Systems: An Empirical Study on the Lorenz Attractor

arXiv: https://arxiv.org/abs/2606.22662 · HTML: https://mlsanity.com/paper/2606.22662/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 9 references that are in the map.
- First posted on arXiv 21 Jun 2026.

## Builds on (most cited first, 4 of 4)

- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [Common Task Framework For a Critical Evaluation of Scientific Machine Learning Algorithms](https://mlsanity.com/paper/2510.23166/) (2025)

## Abstract (arXiv)

Forecasting chaotic dynamical systems such as the Lorenz attractor is notoriously difficult: small numerical errors are amplified exponentially over long autoregressive rollouts. We study seven recurrent and convolutional architectures for the AI-DEEDS 2026 Chaotic Systems Challenge: a vanilla LSTM, an LSTM with additive attention, a Bidirectional LSTM (BiLSTM), a BiLSTM trained with the Huber loss, a Temporal Convolutional Network (TCN), a CNN front-end followed by an LSTM, and a CNN front-end followed by a BiLSTM. All models share the same pre-processing, sequence length, and rollout procedure, isolating the contribution of each design choice. The challenge scores predictions on a 0-100 scale where higher is better. We obtain leaderboard scores between 45.72 and 58.81, with the BiLSTM trained with Huber loss being the strongest configuration. Two findings stand out: (i) adding additive attention to the unidirectional baseline degraded performance by over ten points, and (ii) prepending a CNN front-end to either an LSTM or a BiLSTM did not help and slightly hurt the score. Per-pair RMSE measurements confirm that the BiLSTM family generalizes better in the harder pairs (6-7), while the LSTM + Attention model collapses there (RMSE up to 8.94 on pair 6). We discuss why bidirectional context and a robust loss help in chaotic regimes while attention and CNN front-ends fail in this setting.