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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2502.05621 |
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| _version_ | 1866918426829651968 |
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| author | Yazici, Enis |
| author_facet | Yazici, Enis |
| contents | We present a five-module pedagogical framework for teaching physics-informed machine learning (ML) through two progressively complex physical systems: a driven, damped nonlinear pendulum and a one-dimensional quantum anharmonic oscillator. Five model architectures are implemented and compared: a standard artificial neural network (ANN), a one-dimensional convolutional neural network (CNN), a long short-term memory (LSTM) network, and two physics-informed neural networks (PINNs) -- one per physical system. All models are implemented in PyTorch~2.9 and executed on an NVIDIA RTX~5090 GPU, making the framework directly applicable to modern deep learning laboratory courses. Quantitative benchmarks show that data-driven models achieve mean absolute errors of $1.3\times10^{-2}$~rad (pendulum ANN) and $4.4\times10^{-5}$~a.u.\ (quantum CNN), while the curriculum-trained pendulum PINN reaches an MAE of $3.1\times10^{-2}$~rad using only collocation points. A systematic CPU-vs-GPU benchmark reveals speedups ranging from $1.2\times$ (small ANN) to $24.6\times$ (LSTM), providing a concrete pedagogical demonstration of when GPU acceleration is -- and is not -- warranted. The framework is packaged as self-contained Jupyter notebooks designed for a graduate-level \emph{Deep Neural Networks for Physical Systems} course, with embedded reflection questions that guide students from data-driven thinking toward physics-constrained formulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05621 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Pedagogical Framework for Physics-Informed Machine Learning: From Classical Pendulum to Quantum Anharmonic Oscillator Using PyTorch on Modern GPU Hardware Yazici, Enis Quantum Physics We present a five-module pedagogical framework for teaching physics-informed machine learning (ML) through two progressively complex physical systems: a driven, damped nonlinear pendulum and a one-dimensional quantum anharmonic oscillator. Five model architectures are implemented and compared: a standard artificial neural network (ANN), a one-dimensional convolutional neural network (CNN), a long short-term memory (LSTM) network, and two physics-informed neural networks (PINNs) -- one per physical system. All models are implemented in PyTorch~2.9 and executed on an NVIDIA RTX~5090 GPU, making the framework directly applicable to modern deep learning laboratory courses. Quantitative benchmarks show that data-driven models achieve mean absolute errors of $1.3\times10^{-2}$~rad (pendulum ANN) and $4.4\times10^{-5}$~a.u.\ (quantum CNN), while the curriculum-trained pendulum PINN reaches an MAE of $3.1\times10^{-2}$~rad using only collocation points. A systematic CPU-vs-GPU benchmark reveals speedups ranging from $1.2\times$ (small ANN) to $24.6\times$ (LSTM), providing a concrete pedagogical demonstration of when GPU acceleration is -- and is not -- warranted. The framework is packaged as self-contained Jupyter notebooks designed for a graduate-level \emph{Deep Neural Networks for Physical Systems} course, with embedded reflection questions that guide students from data-driven thinking toward physics-constrained formulations. |
| title | A Pedagogical Framework for Physics-Informed Machine Learning: From Classical Pendulum to Quantum Anharmonic Oscillator Using PyTorch on Modern GPU Hardware |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2502.05621 |