Physics-informed neural networks for aggregation kinetics

TL;DR

This paper presents a physics-informed neural network approach that models aggregation kinetics efficiently, accurately capturing cluster distributions and handling multiple kernels simultaneously, advancing computational methods for Smoluchowski equations.

Contribution

The novel framework models aggregation kinetics with a single neural network capable of handling multiple kernels and improves accuracy and efficiency over traditional methods.

Findings

Accurately predicts density distributions of clusters.

Handles four different kernels with one network.

Enhances computational efficiency for long-term simulations.

Abstract

We introduce a novel physics-informed approach for accurately modeling aggregation kinetics which provides a comprehensive solution in a single run by outputting all model parameters simultaneously, a clear advancement over traditional single-output networks that require multiple executions. This method effectively captures the density distributions of both large and small clusters, showcasing a notable improvement in predicting small particles, which have historically posed challenges in computational models. This approach yields significant advancements in computational efficiency and accuracy for solving the Smoluchowski equations by minimizing the interval over which the physics-informed loss function operates, allowing for efficient computation over extended time-frames with minimal increase in computational cost. Due to the the independence of predefined shapes for bias or weight outputs, it removes the dependency on prior assumptions about output structures. Furthermore, our physics-informed framework exhibits high compatibility with the generalized Brownian kernel, maintaining robust accuracy for this previously unaddressed kernel type. The framework's notable novelty also lies in addressing four different kernels with one neural network architecture. Therefore with high computational efficiency, combined with low error margins it indicates significant potential for long-term predictions and integration into broader computational systems.