Branched Latent Neural Maps.

Area of Science:

• Computational Science and Engineering
• Biophysics
• Machine Learning

Background:

• Complex physical processes, such as cardiac electrophysiology, require accurate yet computationally efficient models.
• Traditional models often face challenges with high dimensionality and long simulation times.
• Reduced-order models are crucial for applications like digital twinning and real-time simulations.

Purpose of the Study:

• Introduce Branched Latent Neural Maps (BLNMs) as a novel method for learning finite-dimensional input-output maps.
• Demonstrate the capability of BLNMs in encoding complex physical processes, specifically cardiac electrophysiology.
• Provide a computationally efficient tool for reduced-order modeling and digital twinning.

Main Methods:

• BLNMs utilize a compact, feedforward, partially-connected neural network architecture.
• Latent outputs are leveraged to enhance learned dynamics and mitigate the curse of dimensionality.
• The method was tested on biophysically detailed electrophysiology simulations of a pediatric cardiac model.

Main Results:

• BLNMs achieved excellent in-distribution generalization with small datasets and short training times on a single CPU.
• An optimal BLNM was trained in under 3 hours, requiring minimal layers and neurons.
• The model demonstrated high accuracy with a mean square error on the order of $$ on an independent test set.
• Online simulations were 5000x faster than traditional methods, enabling real-time performance.

Conclusions:

• BLNMs offer a reliable and efficient computational tool for creating reduced-order models.
• The developed method significantly accelerates simulations and facilitates inverse problem-solving.
• BLNMs hold promise for advancing digital twinning applications in engineering and medicine.