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Hamiltonian Generative Networks
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The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful properties, like time reversibility and smooth interpolation in time. These properties are important for many machine learning problems - from sequence prediction to reinforcement learning and density modelling - but are not typically provided out of the box by standard tools such as recurrent neural networks. In this paper, we introduce the Hamiltonian Generative Network (HGN), the first approach capable of consistently learning Hamiltonian dynamics from high-dimensional observations (such as images) without restrictive domain assumptions. Once trained, we can use HGN to sample new trajectories, perform rollouts both forward and backward in time and even speed up or slow down the learned dynamics. We demonstrate how a simple modification of the network architecture turns HGN into a powerful normalising flow model, called Neural Hamiltonian Flow (NHF), that uses Hamiltonian dynamics to model expressive densities. We hope that our work serves as a first practical demonstration of the value that the Hamiltonian formalism can bring to deep learning.
Forward citations
Cited by 5 Pith papers
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Quantum Port-Hamiltonian Neural Networks: Learning Conservative and Dissipative Dynamics via Measurement-Induced Nonlinearity
Q-pHNNs learn classical conservative and dissipative dynamics by mapping the port-Hamiltonian J matrix to unitary gates and the R matrix to mid-circuit measurement nonlinearity, enforcing structure by construction.
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IRIS: A Real-World Benchmark for Inverse Recovery and Identification of Physical Dynamic Systems from Monocular Video
IRIS releases 220 real 4K videos of eight dynamical systems with ground-truth parameters plus a protocol that measures parameter recovery, equation selection, and multi-body failure modes of unsupervised video-to-phys...
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Learning Stochastic Hamiltonian Systems via Stochastic Generating Function Neural Network
SGFNN learns a stochastic generating function via an autoencoder from paired state observations, yielding symplectic and more accurate long-term predictions for stochastic Hamiltonian systems than sFML.
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Learning long range dependencies through time reversal symmetry breaking
RHEL computes backpropagation-equivalent gradients for Hamiltonian recurrent networks using finite differences of time-reversed, nudged trajectories, and matches BPTT accuracy on sequence tasks up to 50k steps.
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KITINet: Kinetics Theory Inspired Network Architectures with PDE Simulation Approaches
KITINet modifies residual connections during training with a DSMC-style collision simulation, but at test time it is identical to the baseline residual network and reports small accuracy gains without error bars.
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