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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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.
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.
citing papers explorer
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Learning Transferable Predictability Representations
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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Learning First Integrals via Backward-Generated Data and Guided Reinforcement Learning
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.
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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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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.
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Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems
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.
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Mechanical Field Networks: Structured Neural Dynamics for Multivariate Systems
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.
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NeuROK: Generative 4D Neural Object Kinematics
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.
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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.
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Integrable Elasticity via Neural Demand Potentials
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.
-
Mechanisms of Misgeneralization in Physical Sequence Modeling
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
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LaWM: Least Action World Models for Long-Horizon Physical Consistency from Visual Observations
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.
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Dissipative Latent Residual Physics-Informed Neural Networks for Modeling and Identification of Electromechanical Systems
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.
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SLIDE: A machine-learning based method for forced dynamic response estimation of multibody systems
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.
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Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
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.
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Physically Viable World Models: A Case for Query-Conditioned Embodied AI
Embodied AI requires query-conditioned world models that select the simplest physical abstraction sufficient to answer intervention queries.
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Physics-Informed Graph Neural Network Surrogates for Turbulent Nanoparticle Dispersion in Dental Clinical Environments
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.
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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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World Models: A Comprehensive Survey of Architectures, Methodologies, Reasoning Paradigms, and Applications
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.
- Physically Native World Models: A Hamiltonian Perspective on Generative World Modeling
- Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physics