EOMR slashes prediction error by orders of magnitude on chaotic dynamics
New regression method beats neural nets and transformers using just 8 parameters
Illia Horenko (University of Lugano) extends his Entropy-Optimal Manifold Clustering (EOMC) into a new regression framework, Entropy-Optimal Manifold Regression (EOMR), for joint simultaneous identification of relevant feature subsets and subspaces. The method is designed for nonstationary and nonlinear regression problems, where traditional static feature selection fails. Crucially, EOMR maintains linearly-scaling iteration and memory complexities, making it practical for large-scale scientific datasets.
In head-to-head benchmarks against the state of the art—including gradient-boosted random forests, deep neural networks, and the transformer-based TabPFN v0.3—EOMR delivers orders of magnitude lower root mean squared prediction error on two notoriously difficult chaotic systems: the Lorenz-96 model in strongly and very-strongly chaotic regimes (F=8 and F=12), and the Hasegawa-Wakatani model for tokamak edge plasma. For the tokamak case, EOMR distills a remarkably simple, causal, weakly-stationary autoregressive process with just 8 parameters to describe leading EOF dynamics, demonstrating interpretability without sacrificing skill.
- EOMR jointly learns feature subsets and subspaces with linearly-scaling iteration and memory complexity
- Outperforms deep neural networks, gradient-boosted forests, and TabPFN v0.3 by orders of magnitude in RMSE on Lorenz-96 and Hasegawa-Wakatani benchmarks
- Distills an interpretable 8-parameter autoregressive model for tokamak plasma dynamics, replacing black-box AI
Why It Matters
Scientific ML gets an interpretable, low-complexity alternative to deep learning that beats it on chaotic physical systems.