DurstewitzLab<p>Can time series (TS) <a href="https://mathstodon.xyz/tags/FoundationModels" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FoundationModels</span></a> (FM) like Chronos zero-shot generalize to unseen <a href="https://mathstodon.xyz/tags/DynamicalSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>DynamicalSystems</span></a> (DS)? <a href="https://mathstodon.xyz/tags/AI" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>AI</span></a></p><p>No, they cannot!</p><p>But *DynaMix* can, the first TS/DS foundation model based on principles of DS reconstruction, capturing the long-term evolution of out-of-domain DS: <a href="https://arxiv.org/pdf/2505.13192v1" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/pdf/2505.13192v1</span><span class="invisible"></span></a></p><p>Unlike TS foundation models, DynaMix exhibits <a href="https://mathstodon.xyz/tags/ZeroShotLearning" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ZeroShotLearning</span></a> of long-term stats of unseen DS, incl. attractor geometry & power spectrum, w/o *any* re-training, just from a context signal. <br>It does so with only 0.1% of the parameters of Chronos & 10x faster inference times than the closest competitor.</p><p>It often even outperforms TS FMs on forecasting diverse empirical time series, like weather, traffic, or medical data, typically used to train TS FMs. <br>This is surprising, cos DynaMix’ training corpus consists *solely* of simulated limit cycles & chaotic systems, no empirical data at all!</p><p>And no, it’s neither based on Transformers nor Mamba – it’s a new type of mixture-of-experts architecture based on the recently introduced AL-RNN (<a href="https://proceedings.neurips.cc/paper_files/paper/2024/file/40cf27290cc2bd98a428b567ba25075c-Paper-Conference.pdf" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">proceedings.neurips.cc/paper_f</span><span class="invisible">iles/paper/2024/file/40cf27290cc2bd98a428b567ba25075c-Paper-Conference.pdf</span></a>), specifically trained for DS reconstruction.</p><p>Remarkably, DynaMix not only generalizes zero-shot to novel DS, but it can even generalize to new initial conditions and regions of state space not covered by the in-context information.</p><p>We dive a bit into the reasons why current time series FMs not trained for DS reconstruction fail, and conclude that a DS perspective on time series forecasting & models may help to advance the <a href="https://mathstodon.xyz/tags/TimeSeriesAnalysis" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>TimeSeriesAnalysis</span></a> field.</p>