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Discovering Physics Laws of Dynamical Systems via Invariant Function Learning
- Researchers have developed a method called Disentanglement of Invariant Functions (DIF) to learn the underlying laws of dynamical systems governed by ordinary differential equations.
- The key challenge was to discover intrinsic dynamics across multiple environments while avoiding environment-specific mechanisms.
- The method addresses complex environments where changes extend beyond function coefficients to entirely different function forms.
- For example, it can detect the natural motion of an ideal pendulum like alpha^2 sin(theta_t) by observing pendulum dynamics in varied environments.
- The problem is formulated as an invariant function learning task grounded in causal analysis.
- A causal graph and an encoder-decoder hypernetwork are designed in the DIF method to disentangle invariant functions from environment-specific dynamics.
- The method ensures the independence between extracted invariant functions and environments through an information-based principle.
- Quantitative comparisons with meta-learning and invariant learning baselines on three ODE systems have shown the effectiveness and efficiency of the DIF method.
- Symbolic regression explanation results demonstrate the framework's ability to uncover intrinsic laws.
- The code for the method has been made available as part of the AIRS library on GitHub.
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