New technique finds globally optimal symbolic equations.
problem Finding globally optimal mathematical expressions.
method Formulated a mixed integer non-linear program (MINLP).
result Guaranteed global optimality in symbolic regression.
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169,181 papers · 148 categories
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48 results for “Galileo's pendulum”
GALILEO creates better mixture models for categorical data.
problem Generating high-quality mixture models for categorical data.
method Entropy-based density metric and annealing of components.
result GALILEO consistently finds high-quality clusters with the optimal number of components.
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.
This paper studies the topology of the constant energy surfaces of the double spherical 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.
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.
In the first of these two lectures, I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable q. The two main steps are to reinterpret three-dimensional Chern-Simons gauge theory in four dimensional terms and then to apply electric-magnetic duality. The var…
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.
Approach uses neural networks to learn and extrapolate equations from data.
problem Learning concise equations from data for extrapolation and control.
method Shallow neural network approach to identify functional relations.
result Can extrapolate to unseen domains and learn true underlying equations.
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.
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.
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.
Posing Kepler's problem of motion around a fixed "sun" requires the geometric mechanician to choose a metric and a Laplacian. The metric provides the kinetic energy. The fundamental solution to the Laplacian (with delta source at the "sun") provides the potential energy. Posing Kepler's three laws (with input from Gali…
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.
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…
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 …
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.
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…
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.
Two FFT-based detectors improve GPS multipath detection.
problem Improving GPS positioning accuracy by detecting multipath errors.
method Developed two FFT-based detectors for binary hypothesis tests.
result Detectors can exclude multipath contaminated satellites from navigation solutions.
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…
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 …
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.
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.
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.
This anniversary paper is an occasion to recall some of the events that shaped institutional econophysics. But in these thoughts about the evolution of econophysics in the last 15 years we also express some concerns. Our main worry concerns the relinquishment of the simplicity requirement. Ever since the groundbreaking…
Approximate 3D elastic curves with exact constraints
problem Designing and approximating 3D elastic curves
method Numerically stable method for recovering 11 parameters
result Fast and stable approximation of arbitrary curves
Paper extends variational problem to spheres using control methods.
problem Extending classical variational problem to spheres.
method Variational and optimal control approaches.
result Established relation between Hamiltonian and Euler-Lagrange equations.
Integrates multiple feedback channels into policy learning for reinforcement learning.
problem Combining multiple types of feedback into policy gradient algorithms.
method Lagrangian relaxation to satisfy constraints using gradient descent while maximizing rewards.
result Constraints are respected and can accelerate learning in reinforcement learning tasks.
PID control architectures are widely used in industrial applications. Despite their low number of open parameters, tuning multiple, coupled PID controllers can become tedious in practice. In this paper, we extend PILCO, a model-based policy search framework, to automatically tune multivariate PID controllers purely bas…
Energies of knot diagramsmath-ph
We introduce and begin the study of new knot energies defined on knot diagrams. Physically, they model the internal energy of thin metallic solid tori squeezed between two parallel planes. Thus the knots considered can perform the second and third Reidemeister moves, but not the first one. The energy functionals consid…
Alpha Zero adapts to continuous action spaces for real-world tasks.
problem Real-world reinforcement learning domains often have continuous action spaces.
method Interleaves tree search and deep learning, extending Alpha Zero for continuous action spaces.
result Preliminary experiments on the Pendulum task show feasibility of the approach.
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.
Optimizes reinforcement learning controllers for reliability.
problem Lack of robustness in reinforcement learning controllers due to deterministic reward.
method Introduces a reliability-based optimization framework using a model-based approach.
result Stable controllers learned in static and dynamic environments on classical tasks.
The paper tackles control policy learning for unknown systems using convex optimization.
problem Learning control policies for unknown linear dynamical systems to maximize a quadratic reward function.
method Sequential convex programming to optimize expected reward over posterior system parameter distribution.
result The method achieves reliable local convergence and robust stability, demonstrated with strong performance and robustness in simulations and real-world applications.