GON uses 2-jet features and an anchor-and-variance objective to fix gauge freedom in ordinal predictability scoring, enabling pretrained initialization to outperform scratch training on held-out dynamical systems.
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et al.Lagrangian Neural Networks
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A Set-Transformer architecture with self-attention encodes Pauli-string correlations, optimizes via commutation objective, and finds symmetries with near-deterministic success on physical models like Ising and Toric code.
FISolver trains a compact LLM on backward-generated (differential equation, first integral) pairs and uses guided reinforcement learning to outperform larger models and Mathematica on first-integral benchmarks at lower cost.
VHYDRO is a support-safe variational hybrid filter that jointly recovers continuous latent states, discrete contact modes, and sparse port-Hamiltonian laws per regime while preventing loss of feasible transitions.
HAAD detects deepfakes by modeling latent manifolds as potential energy surfaces and quantifying instability via Hamiltonian trajectory statistics such as action and energy dissipation.
piDMD learns a single parameter-affine Koopman surrogate ROM from training samples at multiple parameters to predict dynamics at unseen parameters with improved robustness over interpolation baselines.
MF-Net learns a shared field state and mechanical transition rule from trajectories to deliver competitive forecasting and recoverable relation matrices on Lorenz-96 and real systems.
NeuROK learns a data-driven latent kinematic parameterization on a large 4D dataset to generate realistic object deformations by simulating dynamics only in low-dimensional latent space via Lagrangian mechanics.
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.
ICDN is a neural network that models log-demand from log-prices so elasticities can be derived exactly by differentiation, showing better out-of-sample performance than log-log benchmarks on beer sales data.
Generative sequence models for physical tasks exhibit physical misgeneralization where local prediction errors propagate through physical measurements to distort aggregate distributions over quantities like distance or energy; a data deviation kernel explains and predicts the shifts and supports a内核
LaWM induces latent transitions from a learned discrete variational principle rather than an unconstrained neural predictor, yielding improved physical consistency on synthetic dynamics and robot benchmarks.
DiLaR-PINN learns dissipative effects in electromechanical systems via a skew-dissipative latent residual PINN that guarantees non-increasing energy and uses recurrent curriculum training for partial observations.
SLIDE is a deep learning estimator that truncates initial effects via complex eigenvalues of linearized equations to predict output sequences of damped multibody systems, reporting speedups up to several million times.
Geometric deep learning provides a unified mathematical framework based on grids, groups, graphs, geodesics, and gauges to explain and extend neural network architectures by incorporating physical regularities.
Embodied AI requires query-conditioned world models that select the simplest physical abstraction sufficient to answer intervention queries.
ELGIN is a graph-based physics-informed surrogate model that predicts carrier flow and polydisperse particle motion in dental aerosol scenarios, achieving lower tracking errors and 37x speedup versus full OpenFOAM CFD in a preliminary single-case test.
A quadratic Lagrangian incorporating dissipation models human mobility from population distributions and fits both synthetic and empirical data, showing comparable inertia and dissipation effects.
Physical admissibility is defined as a prediction-control interface using kinematic, dynamic, and composed-horizon conditions to reject invalid dynamics proposals, with AUC 0.957 on LeRobot PushT and 87-89% prevention of invalid actions in interventions.
The paper delivers a multi-axis taxonomy for world models that maps architectures, training families, reasoning strategies, and domains from early cognitive foundations through systems such as Dreamer, MuZero, and Sora while noting evaluation gaps.
L-Learning learns the system's energy function from data to deliver stable, accurate, and sample-efficient robot trajectory tracking with closed-loop stability guarantees.
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.
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Support-Safe Variational Hybrid Filtering for Contact-Mode and Sparse-Law Recovery
VHYDRO is a support-safe variational hybrid filter that jointly recovers continuous latent states, discrete contact modes, and sparse port-Hamiltonian laws per regime while preventing loss of feasible transitions.
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Can Predicted Dynamics Exist in the Physical World?
Physical admissibility is defined as a prediction-control interface using kinematic, dynamic, and composed-horizon conditions to reject invalid dynamics proposals, with AUC 0.957 on LeRobot PushT and 87-89% prevention of invalid actions in interventions.
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L-Learning : A Lyapunov-Based Approach Leveraging Lagrangian Mechanics for Efficient and Stable Robot Tracking
L-Learning learns the system's energy function from data to deliver stable, accurate, and sample-efficient robot trajectory tracking with closed-loop stability guarantees.