An n-dimensional hybrid system embeds into a continuous vector field in m > 2n dimensions, enabling latent Neural ODEs with consistency losses to recover hybrid flows from time series.
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et al.Lagrangian Neural Networks
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Trainable dissipative oscillator networks exhibit a trilemma in which damping governs memory horizon, gradient stability, and Lyapunov exponent, with learned substrates outperforming frozen ones only at short horizons before the advantage closes near eleven steps.
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.
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.
Hamiltonian Transformer with norm-preserving attention and phase embeddings outperforms baselines in RF fingerprinting on WiSig dataset, reaching 99.12% same-day accuracy and 61.64% at 150 transmitters.
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.
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.
LAPG combines conditional score-based diffusion with an action-derived guidance score to reduce phase drift and preserve physical invariants during temporal, parameter, and geometric extrapolation on free-fall, spring-mass, vortex, and airfoil 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.
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.
A geometry-conditioned FNO is trained on pseudospectral data to approximate the one-step operator for cubic NLS on 2D tori and reproduces distinct H²-norm growth on rational versus irrational aspect ratios.
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.
Embodied AI requires query-conditioned world models that select the simplest physical abstraction sufficient to answer intervention queries.
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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.