Automata Learning for Neural Event ODEs: An Interpretable Model of Piecewise Dynamics
Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
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Keywords: Automata Learning, Neural ODEs, Domain Informed Machine Learning, Interpretable AI, Hybrid Systems, Piecewise ODEs, Active Learning, Event Detection Problem, Initial Value Problem, Discontinuous Dynamics
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TL;DR: This paper presents a hybrid method combining automata learning and Neural Event ODEs for efficient and interpretable learning of black-box piecewise ODEs.
Abstract: Discrete events within a continuous system cause discontinuities in its derivatives.
Given event specifications and state update functions,
ODE solvers can integrate until an event, apply the update function, and restart the integration process to obtain a piecewise solution for the system.
However, in many real-world scenarios,
the event specifications are not readily available or vary across different black-box implementations.
We present a method to learn the dynamics of a black-box ODE implementation that uses abstract automata learning and Neural Event ODEs.
Without prior knowledge of the system, the method extracts the event specifications and state update functions, and generates a high-coverage training dataset
through abstract automata learning.
Additionally, our approach introduces a significantly more efficient training process for Neural Event ODEs that slices training trajectories into temporally consecutive pairs within continuous dynamics.
Both contributions ensure well-posed initial values for each ODE slice.
A~proof-of-concept implementation captures event specifications in an interpretable automaton and uses the trajectories from automata learning to efficiently train a simple feed-forward neural network by solving well-posed, single-step IVPs.
During inference, the implementation detects the events and solves the IVP piecewise.
Preliminary empirical results show significant improvements in training time and computational resource requirements while retaining all advantages of a piecewise solution.
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Submission Number: 3584
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