Cox process representation and inference for stochastic reaction-diffusion processes.

Area of Science:

• Computational modeling
• Statistical physics
• Machine learning

Background:

• Complex behaviors often emerge from stochastic interactions in spatially distributed systems.
• Stochastic reaction-diffusion processes are crucial for modeling these behaviors across various scientific disciplines.
• Simulating and calibrating these processes to observational data presents significant computational challenges.

Purpose of the Study:

• To address the inverse problem of learning stochastic reaction-diffusion processes directly from data.
• To develop an efficient and flexible algorithm for parameter inference and model selection.
• To bridge the gap between complex stochastic systems and practical computational modeling.

Main Methods:

• Leveraging statistical physics and machine learning principles.
• Establishing a connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes.
• Developing a novel algorithm for parameter inference and model selection.

Main Results:

• Demonstrated excellent accuracy in parameter inference and model selection.
• Validated the approach on both numerical simulations and real-world data.
• Successfully applied the method to systems biology and epidemiology case studies.

Conclusions:

• The study provides a practical and efficient solution for learning stochastic reaction-diffusion models from data.
• The findings offer new insights into the analysis of spatio-temporal stochastic systems.
• This work overcomes a long-standing challenge in computational modeling of complex systems.