AXIOM-X

AXIOM-X is a high-performance symbolic physics discovery engine designed for the automatic identification of governing equations of dynamical systems from time-series data using advanced evolutionary search techniques. This innovative tool leverages the power of large-scale GPU acceleration to enhance performance and efficiency in discovering physical laws governing dynamic behaviors.

Key Features

• Population-scale evolution: Capable of evaluating up to 131,072 candidates simultaneously, enhancing the search for optimal equations.
• GPU-accelerated fitness evaluation through integration with PyTorch, ensuring rapid and efficient processing of candidate equations.
• Tournament selection mechanism that incorporates elite preservation, which helps to maintain the best-performing candidates throughout the evolutionary process.
• Adaptive mutation scheduling that optimizes the introduction of new genetic variations in the population.
• Robust checkpointing guarantees exact reproducibility of results, facilitating scientific rigor and verifiability.
• Deterministic seeding for both CPU and CUDA environments ensures consistent results across different computational settings.
• Automatic interruption recovery allows the system to resume operations seamlessly without losing progress.
• Real-time reporting of the best equations discovered during the evolution process.

Discovery Goals

AXIOM-X optimizes equations such as:

dx = a · mean(x) − b · x + c · tanh(d · mean(x))

This equation is refined by evolving parameters directly from time-series data while minimizing mean-squared error as the fitness criterion.

System Architecture

The framework operates on a:

• Batched tensor evolution pipeline
• GPU-based mean squared error evaluation
• Tournament genetic reproduction strategy
• Continuous population refresh through elitism
• Signal-safe autosave recovery mechanism
• Comprehensive preservation of the random number generator state across Python, NumPy, Torch, and CUDA.

Applications

AXIOM-X is applicable in various domains including:

• Symbolic regression, which involves inferring relationships from data.
• Dynamical system identification, enhancing understanding of system behaviors.
• Equation discovery, enabling researchers to derive mathematical expressions that represent observed phenomena.
• Evolutionary physics modeling, facilitating innovative approaches to physics research.

This comprehensive toolset empowers researchers and scientists to explore complex systems' behavior, uncover underlying physical laws, and contribute valuable insights to the field of physics modeling and analysis.