Can Kans (re)discover predictive models for Direct-Drive Laser Fusion?

TL;DR

This paper explores the use of Kolmogorov-Arnold Networks (KANs) as a novel data-driven approach for predictive modeling in high-complexity, data-scarce laser fusion physics, demonstrating potential advantages over traditional physics-informed learning methods.

Contribution

It introduces KANs as an alternative to PIL for physics modeling, showing their effectiveness in high-energy laser fusion applications with limited data.

Findings

KANs achieve high prediction accuracy and interpretability.

KANs outperform baseline MLP models in generalization.

KANs show promise in data-starved physics domains.

Abstract

The domain of laser fusion presents a unique and challenging predictive modeling application landscape for machine learning methods due to high problem complexity and limited training data. Data-driven approaches utilizing prescribed functional forms, inductive biases and physics-informed learning (PIL) schemes have been successful in the past for achieving desired generalization ability and model interpretation that aligns with physics expectations. In complex multi-physics application domains, however, it is not always obvious how architectural biases or discriminative penalties can be formulated. In this work, focusing on nuclear fusion energy using high powered lasers, we present the use of Kolmogorov-Arnold Networks (KANs) as an alternative to PIL for developing a new type of data-driven predictive model which is able to achieve high prediction accuracy and physics interpretability. A KAN based model, a MLP with PIL, and a baseline MLP model are compared in generalization ability and interpretation with a domain expert-derived symbolic regression model. Through empirical studies in this high physics complexity domain, we show that KANs can potentially provide benefits when developing predictive models for data-starved physics applications.