Wasserstein Lagrangian Mechanics formalizes second-order dynamics in Wasserstein space and provides an algorithm to learn them from observed marginals without specifying the Lagrangian, outperforming gradient flows on various dynamics.
Symplectic ODE-Net: Learning Hamiltonian Dy- namics with Control
10 Pith papers cite this work. Polarity classification is still indexing.
10
Pith papers citing it
abstract
In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learning framework which can infer the dynamics of a physical system, given by an ordinary differential equation (ODE), from observed state trajectories. To achieve better generalization with fewer training samples, SymODEN incorporates appropriate inductive bias by designing the associated computation graph in a physics-informed manner. In particular, we enforce Hamiltonian dynamics with control to learn the underlying dynamics in a transparent way, which can then be leveraged to draw insight about relevant physical aspects of the system, such as mass and potential energy. In addition, we propose a parametrization which can enforce this Hamiltonian formalism even when the generalized coordinate data is embedded in a high-dimensional space or we can only access velocity data instead of generalized momentum. This framework, by offering interpretable, physically-consistent models for physical systems, opens up new possibilities for synthesizing model-based control strategies.
citation-role summary
background 3
citation-polarity summary
roles
background 2polarities
background 2representative citing papers
HAAD detects deepfakes by modeling latent manifolds as potential energy surfaces and quantifying instability via Hamiltonian trajectory statistics such as action and energy dissipation.
Universal Differential Equations unify scientific models with machine learning by embedding flexible approximators into differential equations, enabling applications from biological mechanism discovery to high-dimensional optimization.
Neural ODEs constrained by the gradient of a jointly learned maximal Lyapunov function universally approximate locally exponentially stable dynamics within a region of attraction exactly given by the Lyapunov 1-sublevel set.
NEXUS introduces a graph-based neural energy-field model that derives forces from scalar energy and dissipation terms to achieve physically consistent contact-rich 3D dynamics.
NHODE framework learns partially observed dynamical systems by combining Hamiltonian neural networks with neural ODEs, enforcing energy conservation and improving long-horizon stability over data-driven baselines on mass-spring and three-body problems.
Lifting non-conservative, actuated, and contact-constrained robot dynamics into an exactly symplectic phase-space map yields state-of-the-art out-of-distribution autoregressive rollout error at low parameter and FLOP cost.
The paper identifies four missing interfaces (data autolabelling, embodiment retargeting, physics-grounded world models, and video-based reward inference) as the central bottleneck beyond VLA scaling for robot intelligence.
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 designs when model capacity is matched.
citing papers explorer
-
A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshots
Wasserstein Lagrangian Mechanics formalizes second-order dynamics in Wasserstein space and provides an algorithm to learn them from observed marginals without specifying the Lagrangian, outperforming gradient flows on various dynamics.
-
Detecting Deepfakes via Hamiltonian Dynamics
HAAD detects deepfakes by modeling latent manifolds as potential energy surfaces and quantifying instability via Hamiltonian trajectory statistics such as action and energy dissipation.
-
Universal Differential Equations for Scientific Machine Learning
Universal Differential Equations unify scientific models with machine learning by embedding flexible approximators into differential equations, enabling applications from biological mechanism discovery to high-dimensional optimization.
-
Locally Stable Neural ODEs with Characterized Region of Attraction
Neural ODEs constrained by the gradient of a jointly learned maximal Lyapunov function universally approximate locally exponentially stable dynamics within a region of attraction exactly given by the Lyapunov 1-sublevel set.
-
NEXUS: Neural Energy Fields for Physically Consistent Contact-Rich 3D Object Dynamics
NEXUS introduces a graph-based neural energy-field model that derives forces from scalar energy and dissipation terms to achieve physically consistent contact-rich 3D dynamics.
-
Learning partially observed systems with neural Hamiltonian ordinary differential equations
NHODE framework learns partially observed dynamical systems by combining Hamiltonian neural networks with neural ODEs, enforcing energy conservation and improving long-horizon stability over data-driven baselines on mass-spring and three-body problems.
-
CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts
Lifting non-conservative, actuated, and contact-constrained robot dynamics into an exactly symplectic phase-space map yields state-of-the-art out-of-distribution autoregressive rollout error at low parameter and FLOP cost.
-
Robots Need More than VLA and World Models
The paper identifies four missing interfaces (data autolabelling, embodiment retargeting, physics-grounded world models, and video-based reward inference) as the central bottleneck beyond VLA scaling for robot intelligence.
-
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 designs when model capacity is matched.
- Symplectic Neural Networks for Learning Non-Separable Hamiltonians