Neural Hamilton: Can A.I. Understand Hamiltonian Mechanics?
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Abstract (arXiv)
We propose a novel framework based on neural network that reformulates classical mechanics as an operator learning problem. A machine directly maps a potential function to its corresponding trajectory in phase space without solving the Hamilton equations. Most notably, while conventional methods tend to accumulate errors over time through iterative time integration, our approach prevents error propagation. Two newly developed neural network architectures, namely VaRONet and MambONet, are introduced to adapt the Variational LSTM sequence-to-sequence model and leverage the Mamba model for efficient temporal dynamics processing. We tested our approach with various 1D physics problems: harmonic oscillation, double-well potentials, Morse potential, and other potential models outside the training data. Compared to traditional numerical methods based on the fourth-order Runge-Kutta (RK4) algorithm, our model demonstrates improved computational efficiency and accuracy. Code is available at: https://github.com/Axect/Neural_Hamilton
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 20 of its 48 references that are in the map. First posted on arXiv 28 Oct 2024.
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References · 20
- 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,616
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
- 2019Hamiltonian Neural Networkscited by 702
- 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 321
- 2023Neural Operators for Accelerating Scientific Simulations and Designcited by 218
- 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 183
- 2019Symplectic Recurrent Neural Networkscited by 148
- 2023Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performancecited by 143
- 2017Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activationscited by 104
- 2020AI Poincar'e: Machine Learning Conservation Laws from Trajectoriescited by 77
- 2022Generic bounds on the approximation error for physics-informed (and) operator learningcited by 65
8 more
- 2020DeepGreen: Deep Learning of Green's Functions for Nonlinear Boundary Value Problemscited by 61
- 2022Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separatelycited by 46
- 2021Data-driven discovery of Green's functions with human-understandable deep learningcited by 43
- 2023On the training and generalization of deep operator networkscited by 31
- 2022Learning Neural Hamiltonian Dynamics: A Methodological Overviewcited by 8
- 2023Scattering with Neural Operatorscited by 7
- 2024HyperbolicLR: Epoch insensitive learning rate schedulercited by 3
- 2023Unsupervised sequence-to-sequence learning for automatic signal quality assessment in multi-channel electrical impedance-based hemodynamic monitoringcited by 2
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