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Lagrangian Neural Networks
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Lagrangian Neural Networks
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Accurate models of the world are built upon notions of its underlying symmetries. In physics, these symmetries correspond to conservation laws, such as for energy and momentum. Yet even though neural network models see increasing use in the physical sciences, they struggle to learn these symmetries. In this paper, we propose Lagrangian Neural Networks (LNNs), which can parameterize arbitrary Lagrangians using neural networks. In contrast to models that learn Hamiltonians, LNNs do not require canonical coordinates, and thus perform well in situations where canonical momenta are unknown or difficult to compute. Unlike previous approaches, our method does not restrict the functional form of learned energies and will produce energy-conserving models for a variety of tasks. We test our approach on a double pendulum and a relativistic particle, demonstrating energy conservation where a baseline approach incurs dissipation and modeling relativity without canonical coordinates where a Hamiltonian approach fails. Finally, we show how this model can be applied to graphs and continuous systems using a Lagrangian Graph Network, and demonstrate it on the 1D wave equation.
Forward citations
Cited by 54 Pith papers
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Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach
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CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts
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Physically Viable World Models: A Case for Query-Conditioned Embodied AI
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Physics-Informed Graph Neural Network Surrogates for Turbulent Nanoparticle Dispersion in Dental Clinical Environments
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Physically Native World Models: A Hamiltonian Perspective on Generative World Modeling
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Physically Native World Models: A Hamiltonian Perspective on Generative World Modeling
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Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physics
Mesh Field Theory proves mesh-based continuum physics reduces to port-Hamiltonian dynamics with topology fixing interconnections and metrics entering only via constitutive relations, enabling MeshFT-Net for stable, da...
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Optimal transport by a Lagrangian dynamics of population distribution
A quadratic Lagrangian incorporating dissipation models human mobility from population distributions and fits both synthetic and empirical data, showing comparable inertia and dissipation effects.
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Geometry-Conditioned Fourier Neural Operators for Cubic Nonlinear Schrodinger Dynamics on Periodic Domains
A Fourier neural operator conditioned on the torus aspect-ratio parameter learns NLS dynamics and reproduces stronger H²-norm growth on rational tori than on irrational tori.
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Can Predicted Dynamics Exist in the Physical World?
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World Models: A Comprehensive Survey of Architectures, Methodologies, Reasoning Paradigms, and Applications
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L-Learning : A Lyapunov-Based Approach Leveraging Lagrangian Mechanics for Efficient and Stable Robot Tracking
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A comparative study of accuracy and rollout stability of temporal surrogate models
Comparative experiments on three chaotic systems find that architectures using integrator-like updates exhibit lower bias, reduced perturbation amplification, and more stable long-horizon rollouts than other common de...
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