Is the end of Insight in Sight ?
Not on the map. Why?
Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 7 of its 28 references that are in the map. First posted on arXiv 7 May 2025.
Builds on
7 of 28 references.
References · 7
- 2017Attention Is All You Needcited by 60,361
- 2017Solving high-dimensional partial differential equations using deep learningcited by 556
- 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
- 2021Physics-informed neural networks with hard constraints for inverse designcited by 280
- 2016Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Reviewcited by 155
- 2020A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networkscited by 87
- 2025A note on the physical interpretation of neural PDE'scited by 7
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Citing papers per year: 2026: 1.
1 paper.