Acceleration of PDE-Based Biological Simulation Through the Development of Neural Network Metamodels

Area of Science:

• Computational Biology
• Mathematical Modeling
• Machine Learning

Background:

• Partial differential equation (PDE) models are crucial for hypothesis testing and inferring regulatory interactions in biological systems.
• Optimizing PDE models against observed data requires extensive simulations, leading to high computational complexity and long compute times.
• Current brute-force simulation approaches are often infeasible for complex, high-dimensional parameter spaces.

Purpose of the Study:

• To review the capabilities of machine learning methods in accelerating parametric screening of biophysical informed-PDE systems.
• To discuss the benefits and limitations of extending PDE acceleration methods using neural network metamodels.
• To demonstrate the potential of neural network metamodels for optimizing complex spatiotemporal biological problems.

Main Methods:

• Review of existing literature on machine learning applications for PDE model acceleration.
• Discussion of neural network metamodels as a strategy to enhance PDE model calibration, optimization, and sensitivity analysis.
• Quantitative and qualitative demonstration using an example simulation.

Main Results:

• Neural network metamodels offer an efficient approach to accelerate PDE model calibration and optimization.
• These methods can accurately and rapidly approximate complex PDE model behaviors.
• The acceleration achieved by neural network metamodels addresses the computational bottleneck of traditional PDE-based approaches.

Conclusions:

• Neural network metamodels show significant potential for accelerating scientific research and discovery in biology.
• These approaches are expected to be broadly applied to systems described by complex PDE systems.
• The use of machine learning can overcome computational limitations, enabling faster inference and hypothesis testing.