This paper studies the topology of the constant energy surfaces of the double spherical pendulum.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
Trend · papers per month
48 results for “double pendulum”
Study evaluates manifold alignment methods for noisy double pendulum dynamics.
problem Aligning manifolds of double pendulum dynamics under noise.
method Compared four manifold alignment methods: semi-supervised feature-level global and local.
result Local alignment methods were more robust to noise and faster.
Discover conservation laws from trajectories using a neural network.
problem Finding invariants and conservation laws from large-scale data without prior knowledge.
method ConservNet, a neural network trained with noise-variance loss to discover hidden invariants in grouped multi-dimensional observables.
result Successfully discovers underlying invariants from simulated and real-world systems.
Technical Report: Adaptive Control for Linearizable Systems Using On-Policy Reinforcement Learningcs.LG
Paper proposes adaptive control for unknown systems using reinforcement learning.
problem Adaptive control for unknown, linearizable systems.
method On-policy reinforcement learning for discrete-time, stochastic systems.
result Stability and tracking errors concentrate near zero with high probability.
Estimates system parameters from a single observation using kernel-based score.
problem Estimating parameters of a dynamical system from a high-dimensional signal.
method Kernel-based score to compare temporal dependencies between signal and model.
result Accuracy and efficiency demonstrated on chaotic systems.
Paper solves pendulum swing-up problem using RL.
problem Solving the classic pendulum swing-up problem.
method Deep Deterministic Policy Gradient algorithm applied to continuous action domain.
result Optimal pendulum achieved with increasing average return and decreasing loss.
In this paper we show that there are applications that transform the movement of a pendulum into movements in . This can be done using Euler top system of differential equations. On the constant level surfaces, Euler top system reduces to the equation of a pendulum. Those properties are also considered in…
Paper optimizes energy-based controller for swinging up a pendulum using entropy search.
problem Finding optimal parameters for energy-based controllers is hard.
method Bayesian optimization (Entropy Search) applied to energy-based controller design.
result Optimal controller improves performance of a swinging pendulum.
SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systemscs.LG
SympNets identify Hamiltonian systems from data using linear, activation, and gradient modules.
problem Identifying Hamiltonian systems from data.
method Composition of linear, activation, and gradient modules; universal approximation theorems.
result SympNets can approximate arbitrary symplectic maps and generalize well to various Hamiltonian systems.
Expert augmentation improves hybrid model generalization.
problem Limited generalization of hybrid models outside training distribution.
method Introducing expert augmentation to improve hybrid model performance.
result Expert augmentation improves generalization of hybrid models.
Method learns latent dynamics of complex systems from noisy data.
problem Challenging to construct ROMs from noisy high-dimensional data.
method Recurrent stochastic variational deep kernel learning (SVDKL).
result Framework accurately predicts system evolution in low-dimensional latent spaces.
Study of sub-Riemannian problem on specific Lie groups, revealing symmetries and bounds.
problem Sub-Riemannian problem on solvable, non-nilpotent Lie groups.
method Qualitative phase-space analysis of Hamiltonian system, focusing on vertical component.
result Explicit upper bound for cut time in terms of pendulum period.
Physics-enhanced NNs improve predictive accuracy in small data scenarios.
problem Predicting physical systems dynamics with limited data.
method Integrating physical principles (Hamiltonian/Lagrangian) and regularization term based on energy level into neural networks.
result Significant gains in predictive accuracy for small data cases.
Random features enhance control of complex systems.
problem Flexible nonlinear models for control-affine systems.
method Random features approximations for control-affine structure.
result Methods formalized and shown to relate to ADP and AD kernels.
New method discovers discrepancies between simplified models and experimental data.
problem Model discrepancies in nonlinear systems lead to significant deviations from true behavior.
method Sparse Identification of Nonlinear Dynamics (SINDy) algorithm to discover sparse model terms.
result Improvement in performance with a discrepancy model in simulations.
This paper classifies Legendre singularities of sub-Riemannian geodesics on surfaces.
problem Classifying singularities of sub-Riemannian geodesics.
method Complete local classification using Legendre fibrations.
result Legendre singularities are completely classified for sub-Riemannian geodesics.
LNNs learn Lagrangians without canonical coordinates, conserving energy and relativity.
problem Neural networks struggle to learn physical symmetries like conservation laws.
method Lagrangian Neural Networks (LNNs) parameterize arbitrary Lagrangians using neural networks.
result LNNs conserve energy and relativity in complex systems.
SINDy-PI robustly identifies implicit dynamics from noisy data.
problem Accurately modeling nonlinear dynamics from noisy data.
method Parallel, implicit SINDy algorithm with multiple optimization algorithms and model selection.
result Significantly more noise robust than previous SINDy approaches.
The paper connects geometric structures to mechanical systems and introduces new numerical methods.
problem Analyzing and simulating systems with constraints.
method Introduces Dirac integrators based on generalized geometry.
result Dirac integrators can conserve constraints and provide new insights.
Method learns to map dynamics of different systems.
problem Mapping dynamics of different systems.
method Learned latent dynamical system for mapping.
result Learned correspondences enable imagined motions and bisimulation.
Study on elastic curves with variable stiffness, derived from bending energy.
problem Modeling elastic wires with varying thickness.
method Derive Euler-Lagrange equations for curves with variable bending stiffness.
result Characterizations of elastic curves with variable stiffness.
CW-EDMD improves prediction accuracy by learning local Koopman models for different state-space regions.
problem Inefficient global Koopman operator approximation for distinct local dynamics.
method Cluster-Weighted EDMD (CW-EDMD) learns a soft phase-space partition and per-cluster EDMD operators using EM objective.
result CW-EDMD significantly reduces prediction errors across various systems and configurations.
Reinforcement learning is a powerful paradigm for learning optimal policies from experimental data. However, to find optimal policies, most reinforcement learning algorithms explore all possible actions, which may be harmful for real-world systems. As a consequence, learning algorithms are rarely applied on safety-crit…
Spiral Minimal Productsmath.DG
Paper constructs new minimal submanifolds in spheres by spinning given ones.
problem Creating new minimal submanifolds in spheres from given ones.
method Spin given minimal submanifolds by a curve in a balanced way.
result Generates spiral minimal products forming a two-dimensional family.
In this study we introduce a new technique for symbolic regression that guarantees global optimality. This is achieved by formulating a mixed integer non-linear program (MINLP) whose solution is a symbolic mathematical expression of minimum complexity that explains the observations. We demonstrate our approach by redis…
We present a self-contained proof of the Gauss-Bonnet theorem for two-dimensional surfaces embedded in using just classical vector calculus. The exposition should be accessible to advanced undergraduate and non-expert graduate students. It may be viewed as an illustration and exercise in multivariate calculus and…
StreaMRAK improves KRR for streaming data.
problem Streaming data with memory constraints.
method Divides problem into levels of resolution, sub-sampling.
result Efficiently integrates new samples, reduces memory and complexity.
We propose directed time series regression, a new approach to estimating parameters of time-series models for use in certainty equivalent model predictive control. The approach combines merits of least squares regression and empirical optimization. Through a computational study involving a stochastic version of a well …
We study the determination of the second-order normal form for perturbed Hamiltonians , relative to the periodic flow of the unperturbed Hamiltonian . The formalism presented here is global, and can be easily implemented in any CAS. We illustrate it by means of two examples: the H…
Bayesian method improves forecasting of nonseparable Hamiltonian systems with noise.
problem Forecasting nonseparable Hamiltonian systems with multiplicative noise.
method Bayesian approach using deep learning and reduced-order modeling.
result Bayesian method yields up to 724 times improvement in forecasting accuracy.
New model predicts stochastic dynamics with hidden variables.
problem Predicting state transitions in stochastic dynamical systems.
method Hierarchical Bayesian linear regression with local features and variational EM algorithm.
result Parsimonious model structures and fast, accurate predictions.
Comparison of UQ methods in deep learning for a simple physical system.
problem Uncertainty quantification in deep learning for physical systems.
method Bayesian Neural Networks (BNN), Concrete Dropout (CD), Deep Ensembles (DE), and Analytic Error Propagation.
result Pitfalls in using UQ methods, especially Bayesian Neural Networks and Concrete Dropout.
New AI learns like neurons, generalizing from sparse rewards.
problem Designing AI that learns without explicit instructions and applies that learning to sparse reward scenarios.
method Combining neuroscience principles with computational efficiency, creating the Neurons-in-a-Box architecture.
result The architecture can learn efficiently and generalize across various tasks, including challenging environments.
Proposes learning latent reward model for planning from rewards.
problem Planning in high-dimensional state spaces with limited reward information.
method Directly learns a latent dynamics model from rewards, planning in latent state-space.
result Successfully learns accurate latent reward prediction model, achieving strong performance and high sample efficiency.
Almost toric manifolds form a class of singular Lagrangian fibered symplectic manifolds that is a natural generalization of toric manifolds. Notable examples include the K3 surface, the phase space of the spherical pendulum and rational balls useful for symplectic surgeries. The main result of the paper is a complete c…
Enhanced model predicts chaotic systems with improved long-term accuracy.
problem Learning chaotic systems and long-term predictions from incomplete data.
method Path-dependent Neural Jump ODE (PD-NJ-ODE) model for online prediction.
result The model matches true chaotic system dynamics closely and improves long-term predictions.
We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for the case of (co)adjoint orbits, the usual Liouville integrability by means of ana…
Study of rotation angles in a rotating disc model.
problem Understanding geometric phase in rotating systems.
method Analyzes a simple kinematic model of rotating discs.
result Explicit form of geometric phase found using Baumkuchen lemma.
Safe learning for optimal control with known and unknown dynamics.
problem Safe learning of control strategies for systems with unknown dynamics.
method Reachability analysis and Gaussian Process regression for updating disturbances.
result Algorithm learns optimal control policies without violating safety constraints.
This paper detects Markov violations in RL with noise, improving policy development.
problem Partial observability and sensor/actuator noise invalidate Markovian assumptions in RL.
method Combines PCMCI causal discovery with Markov Violation score (MVS).
result Even substantial noise doesn't always disrupt multi-step dependencies.
We briefly review the notion of second order constrained (continuous) system (SOCS) and then propose a discrete time counterpart of it, which we naturally call discrete second order constrained system (DSOCS). To illustrate and test numerically our model, we construct certain integrators that simulate the evolution of …
A Klein surface is a surface with a dianalytic structure. A double of a Klein surface is a Klein surface such that there is a degree two morphism (of Klein surfaces) . There are many doubles of a given Klein surface and among them the so-called natural doubles which are: the complex double, the …
Symbolic regression constructs simple equations for complex systems.
problem Creating accurate yet simple models for dynamic systems.
method Employing symbolic regression with two genetic programming algorithms.
result Analytic models outperform neural networks and local regression.
Generative ODE model learns unknown variables in medical systems.
problem Estimating unknown variables in complex medical systems.
method Variational autoencoder incorporating known ODE functions.
result Modeling known-unknowns improves system parameter discovery and extrapolation.
We study the motion of a particle in the hyperbolic plane (embedded in Minkowski space), under the action of a potential that depends only on one variable. This problem is the analogous to the spherical pendulum in a unidirectional force field. However, for the discussion of the hyperbolic plane one has to distinguish …
Neural SVEs model complex systems with memory, outperforming traditional methods.
problem Modeling systems with memory effects and irregular behavior.
method Introducing neural stochastic Volterra equations as a physics-inspired architecture.
result Neural SVEs outperform neural SDEs and DeepONets in various applications.
We define a general notion of abstract double Lie algebroid. We show (1) that the double Lie algebroid of a double Lie groupoid is a double Lie algebroid in this sense; (2) that the double cotangent constructed from Lie algebroid structures on a vector bundle A and its dual A* is a double Lie algebroid if and only if (…
Controller seeks informative system observations to predict nonlinear dynamics.
problem Predicting nonlinear dynamics with uncertain parameters.
method Expected free energy minimization for balancing goal state and informative observations.
result Controller improves performance in uncertain parameter scenarios.