Is the end of Insight in Sight ?

TL;DR

This paper investigates the tension between deep learning's predictive power and the interpretability of models, using a physics-informed neural network trained on gas dynamics to question the necessity of explainability.

Contribution

It provides a case study showing that neural networks can perform well without reflecting underlying physical principles, challenging the universality of interpretability in AI.

Findings

Neural network weights appeared as Gaussian random matrices.

The trained model lacked explicit physical insight despite accurate predictions.

Deep learning may follow different cognitive paths from traditional simulation.

Abstract

The rise of deep learning challenges the longstanding scientific ideal of insight - the human capacity to understand phenomena by uncovering underlying mechanisms. In many modern applications, accurate predictions no longer require interpretable models, prompting debate about whether explainability is a realistic or even meaningful goal. From our perspective in physics, we examine this tension through a concrete case study: a physics-informed neural network (PINN) trained on a rarefied gas dynamics problem governed by the Boltzmann equation. Despite the system's clear structure and well-understood governing laws, the trained network's weights resemble Gaussian-distributed random matrices, with no evident trace of the physical principles involved. This suggests that deep learning and traditional simulation may follow distinct cognitive paths to the same outcome - one grounded in mechanistic insight, the other in statistical interpolation. Our findings raise critical questions about the limits of explainable AI and whether interpretability can - or should-remain a universal standard in artificial reasoning.