An adaptive solution to the chemical master equation using quantized tensor trains with sliding windows

Area of Science:

• Computational biology
• Biophysical chemistry
• Applied mathematics

Background:

• Solving the chemical master equation for large biological systems requires efficient state space representation.
• Finite State Projection (FSP) with Quantized Tensor Train (QTT) offers storage savings and accuracy.
• Previous adaptive FSP-QTT algorithms could lead to unnecessarily large state spaces, impacting performance.

Purpose of the Study:

• To develop an improved adaptive FSP-QTT algorithm for chemical master equation problems.
• To enhance computational efficiency and accuracy by reducing the state space.
• To address limitations of previous adaptive FSP-QTT methods.

Main Methods:

• Implementation of a novel sliding window mechanism for dynamic state space adjustment.
• Integration of stochastic simulation algorithm trajectories to guide window updates.
• Comparison of the new algorithm against the original adaptive FSP-QTT approach through numerical experiments.

Main Results:

• The sliding window approach dynamically reduces the hyper-rectangular state space to include only the most probable states.
• The improved algorithm demonstrates significant reductions in state space compared to the previous method.
• Numerical experiments show potential improvements in execution time and stepping scheme.

Conclusions:

• The novel sliding window adaptive FSP-QTT algorithm offers a more efficient approach to solving chemical master equations.
• This method effectively manages large state spaces in biological modeling.
• Further validation through diverse numerical experiments confirms the algorithm's advantages.