# Neural Network Emulation of the Classical Limit in Quantum Systems via Learned Observable Mappings

arXiv: https://arxiv.org/abs/2504.10781 · HTML: https://mlsanity.com/paper/2504.10781/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 14 references that are in the map.
- First posted on arXiv 15 Apr 2025.

## Built on by (most cited first, 1 of 1)

- [Deep Neural Network Emulation of the Quantum-Classical Transition via Learned Wigner Function Dynamics](https://mlsanity.com/paper/2504.16334/) (2025)

## Abstract (arXiv)

The classical limit of quantum mechanics, formally investigated through frameworks like strict deformation quantization, remains a profound area of inquiry in the philosophy of physics. This paper explores a computational approach employing a neural network to emulate the emergence of classical behavior from the quantum harmonic oscillator as Planck's constant hbar approaches zero. We develop and train a neural network architecture to learn the mapping from initial expectation values and hbar to the time evolution of the expectation value of position. By analyzing the network's predictions across different regimes of hbar, we aim to provide computational insights into the nature of the quantum-classical transition. This work demonstrates the potential of machine learning as a complementary tool for exploring foundational questions in quantum mechanics and its classical limit.