Summary of Learning Chaotic Systems and Long-term Predictions with Neural Jump Odes, by Florian Krach and Josef Teichmann
Learning Chaotic Systems and Long-Term Predictions with Neural Jump ODEs
by Florian Krach, Josef Teichmann
First submitted to arxiv on: 26 Jul 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Dynamical Systems (math.DS); Probability (math.PR)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The Path-dependent Neural Jump ODE (PD-NJ-ODE) is a novel approach for predicting generic stochastic processes with irregular observations. The model converges theoretically to the L2-optimal predictor, allowing training solely based on realizations of the underlying process without requiring knowledge of its law. In deterministic cases, the conditional expectation matches the system’s dynamics, enabling learning of ODE/PDE systems from diverse initial conditions. We demonstrate the method’s potential by applying it to a chaotic double pendulum system, where enhancements improve performance and enable long-term predictions for general stochastic datasets. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The PD-NJ-ODE is a new way to predict unpredictable things that happen in random order. It can learn about these processes just from seeing them happen, without knowing what’s causing them. This model is useful because it can be used to understand how things change over time, like the motion of a double pendulum. By making some changes to this model, we were able to make predictions that are very close to the real thing. |
