SSL framework identifies non-linear systems without labeled data.
problem System identification in non-linear environments without labeled data.
method Dynamics contrastive learning framework.
result SSL can identify non-linear dynamics in latent space.
Study absolute equivalence for Pfaffian systems, applying to control systems.
problem Absolute equivalence of Pfaffian systems with specific independence conditions.
method Structural results for Pfaffian systems of corank 3, applied to control systems.
result Dynamic feedback linearization of control systems with 2 inputs.
Paper connects dynamics of mechanical systems to Reeb dynamics.
problem Understanding dynamics in mechanical systems with Poisson structures.
method Using Jacobi bundle metrics and linear Poisson structures.
result Extends classical results on Reeb dynamics to mechanical systems.
Many interesting geometric structures can be described as regular infinitesimal flag structures, which occur as the underlying structures of parabolic geometries. Among these structures we have for instance conformal structures, contact structures, certain types of generic distributions and partially integrable almost …
Learning to control linear systems is statistically hard, especially for underactuated systems.
problem Statistical difficulty of learning to control linear systems, especially underactuated ones.
method Utilized minimax lower bounds and structural assumptions to prove learning complexity can be exponential.
result Learning complexity can be at most exponential with the controllability index of the system.
Introduces linear K-systems for Hamiltonian Floer theory.
problem Constructing Floer cohomology for Hamiltonian systems on compact manifolds.
method Geometric realization of linear K-systems via pseudo-holomorphic curves and inductive construction of Kuranishi structures.
result Construction of Floer cohomology and isomorphism with singular cohomology.
A new Dirac algebroid approach for nonholonomic systems.
problem Nonholonomic constraints in mechanical systems.
method Developed a Dirac algebroid to generate phase equations for systems with linear nonholonomic constraints.
result Unified approach to describe systems with different potentials.
dynoNet learns dynamical systems using linear operators.
problem Learning complex dynamical systems.
method dynoNet uses linear dynamical operators for sequence modeling and system identification.
result dynoNet effectively identifies systems on benchmarks.
Efficiently designs distributed controllers for sparse systems with sub-linear sample complexity.
problem Designing robust distributed controllers for unknown-but-sparse linear systems.
method Combining distributed controller synthesis and structured linear inverse problems for system identification.
result Near-optimal distributed controllers can be learned with sub-linear sample complexity and near-linear time complexity.
BP fails to find sparsest solution for structured matrices.
problem Finding sparsest solution to linear equations with structured matrices.
method Introduced class of structured matrices for BP failure.
result Determines columns corresponding to unrecoverable non-zero entries.
New algorithms solve dense linear systems with low-rank structure efficiently.
problem Solving dense linear systems with specific singular value conditions.
method Randomized algorithms using matrix sketching and low-rank update formulas.
result Achieves nearly-linear time complexity for solving such systems.
Weak correlations explain linear dynamics in deep learning models.
problem Understanding the linear structure in gradient-based learning algorithms.
method Characterization of weak correlations between derivatives and parameters.
result Weak correlations are the underlying principle for linearization in deep learning models.
The paper studies quadratic Poisson structures on Lie algebras, finding a 10-parametric family.
problem Compatibility of quadratic Poisson structures with linear structures on Lie algebras.
method Developed general theory and studied families of functions in involution.
result Found a 10-parametric family of quadratic Poisson structures on $\gl(3)^*$ .
Simplifies NL models by approximating them as LPV systems and identifying NL subterms.
problem Complex NL models are hard to interpret and impractical.
method Linear approximation around operating points, sparse estimation in RKHS, LPV model reduction.
result Identifies NL subterms and their input spaces in sparse additive NL models.
We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results for systoles of local systems.
Proves energy estimates for tensorial wave equations, decoupling components for stability proof.
problem Proving stability of ( 1 + 3 ) (1+3) ( 1 + 3 ) -Minkowski space-time with various non-linearities. method Decouples energy estimates for tensorial wave equations, exploiting tensorial structure and Lie derivatives.
result Decoupled energy estimates for tensorial solutions, allowing new stability proofs.
Improved electricity price forecasting model combining linear and non-linear structures.
problem Day-ahead electricity price forecasting in energy systems.
method Recurrent neural networks with embedded linear structures.
result Approximately 11% higher accuracy than state-of-the-art models.
The paper tackles joint learning of linear systems, improving accuracy with pooled data.
problem Estimating transition matrices of multiple related linear systems more accurately.
method Developed novel techniques to bound estimation errors and establish high probability bounds for singular values.
result Significant gains in accuracy achieved by pooling data across systems.
Method solves ∂ ˉ \bar\partial ∂ ˉ -harmonic forms on Kodaira-Thurston manifold.
problem Finding ∂ ˉ \bar\partial ∂ ˉ -harmonic forms on Kodaira-Thurston manifold. method Weil-Brezin transform, linear ODE systems, fundamental problem solving.
result Dimension of almost complex ∂ ˉ \bar\partial ∂ ˉ -Hodge numbers can be arbitrarily large. New algorithm optimizes linear system estimation from single trajectory.
problem Estimating LTI systems from a single trajectory.
method SGD with Reverse Experience Replay ( S G D − R E R \mathsf{SGD}-\mathsf{RER} SGD − RER ) result Optimal guarantees for parameter and prediction errors.
New systems of linear PDEs discovered in 3D contact manifolds.
problem Investigating linear PDEs of s l 3 \mathfrak{sl}_3 sl 3 -type. method Complete local classification using extrinsic geometry.
result 7 new systems of second-order linear PDEs with 8-dimensional solution spaces.
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling them. While there are many methods for modeling nonlinear dynamical systems, exist…
New proof of generalized Chow-Rashevskii theorem for non-linear systems.
problem Generalized Chow-Rashevskii Theorem for non-linear systems.
method Independent proof structure allowing generalizations to orbits of compositions of flows.
result Proof structure applicable to applications in Control Theory and controllability criteria.
A novel method uses GPLFMs for joint input-state estimation in linear structural systems.
problem Combined state and input estimation of linear structural systems.
method Gaussian process latent force models (GPLFMs) combined with Kalman filters.
result GPLFMs outperform conventional Kalman filters in state and input estimation.
Policy gradient converges to globally optimal policy in nearly linear-quadratic systems.
problem Finding optimal policies in nonlinear control systems with partial information.
method Policy gradient algorithm designed for nearly linear-quadratic regulators with small Lipschitz nonlinear components.
result Policy gradient algorithm converges to globally optimal policy with linear rate.
We prove that under certain linear reciprocal transformation, an evolutionary PDE of hydrodynamic type that admits a bihamiltonian structure is transformed to a system of the same type which is still bihamiltonian.
SKOLR uses linear RNNs to approximate Koopman operators for time-series forecasting.
problem Nonlinear dynamical system analysis and time-series forecasting with infinite-dimensional Koopman operators.
method Established a connection between Koopman operator approximation and linear RNNs, integrating learnable spectral decomposition and MLP.
result SKOLR delivers exceptional performance in various forecasting benchmarks and dynamical systems.
The study sets limits on how well systems can be controlled adaptively.
problem Learning to control unknown linear Gaussian systems with quadratic costs.
method Combining ideas from experiment design, estimation theory, and perturbation bounds of information matrices.
result Regret lower bounds of the order of T \sqrt{T} T in the time horizon T T T accurately capture control-theoretic parameters. New algorithms predict causal links better than traditional methods in time series data.
problem Learning causal structure from time series data with challenges in real-world Earth sciences.
method Combination of established ideas for linear methods to identify causal links in non-linear systems, with a focus on large regression coefficients.
result Large regression coefficients can predict causal links better than small p-values in practice.
A fast method estimates correlations in hybrid systems using observable market data.
problem Estimating instantaneous correlations in hybrid systems from observable data.
method Empirical correlations between observable market quantities are used to estimate state variables' correlations. Linear systems are involved, and the matrix is converted to positive semidefinite if necessary.
result The estimates are reasonably accurate, especially with more than 1,000 data points.
New methods improve solving linear systems and preconditioning with reduced complexity.
problem Efficiently solving linear systems and preconditioning matrices.
method Developed structured semidefinite programming algorithms.
result Improved runtimes for preconditioning and solving linear systems.
A new method learns time-varying autoregressive models from multivariate time series.
problem Learning interpretable spatiotemporal structure in multivariate time series data.
method Windowed low rank tensor approach with non-smooth and non-convex optimization.
result The method can identify the true rank of a switching linear system in noisy data.
This study provides a new mathematical structure for Koopman eigenfunctions.
problem Understanding and representing nonlinear dynamics as linear.
method Theoretical, analytical, and numerical approaches to Koopman eigenfunction space.
result Equivalence of minimal generating set and maximal independent set, defining conditions for independence.
We identify linear dynamical systems under convex constraints with fewer samples.
problem Identifying linear dynamical systems with prior structural information.
method Constrained least squares estimator with error bounds dependent on convex set size.
result Linear dynamical systems can be reliably estimated with fewer samples than unconstrained settings.
Optimal control in changing systems without strong convexity assumptions.
problem Adversarial changes in convex costs for unknown linear systems.
method Non-convex lower confidence bounds and computationally-efficient regret minimization.
result Achieves T \smash{\sqrt{T}} T -regret rate, optimal compared to best stabilizing controller. Geometric framework for dynamic feedback linearization of control systems with symmetry.
problem Dynamic feedback linearization of control systems with symmetry.
method Geometric framework based on Lie symmetry, systematic procedure for all smooth, generic system trajectories.
result Sufficient condition for dynamic feedback linearizability obtained.
AIDEL improves scalability of learned indexes in storage systems.
problem Expensive retraining and heavy inter-model dependency in learned indexes limit scalability.
method Construct different linear regression models based on data distribution, making them independent and easier to partition.
result AIDEL improves insertion performance by about 2x and comparable lookup performance.
Safe RL-based vibration control using LQR guidance.
problem Training risks in RL-based vibration control.
method Hybrid control framework combining LQR and RL.
result LQR controller outperforms uncontrolled scenario.
Solves parameter non-identifiability in Bayesian LTI system identification.
problem Parameter non-identifiability in standard Bayesian approaches for LTI system identification.
method Embedding canonical forms of LTI systems within the Bayesian framework.
result Unlocking the use of meaningful priors and robust uncertainty estimates.
This paper proposes a new method for inferring the latent dimension of linear dynamical systems.
problem Manual specification of latent dimension is impractical and leads to model limitations.
method The paper introduces a minimum description length criterion to infer latent dimension.
result The proposed method effectively infers latent dimension and improves model performance.
We compute symmetry algebras of a system of two equations y^(k)=z^(l)=0, where 2<=k<l. It appears that there are many ways to convert such system of ODEs to an exterior differential system. They lead to different series of finite-dimensional symmetry algebras. For example, for (k,l)=(2,3) we get two non-isomorphic symm…
The paper analyzes identifiability in ODE systems with hidden confounders.
problem Identifiability of ODE systems with hidden confounders.
method Systematic analysis of identifiability in linear ODE systems with hidden confounders, considering both no causal relationships and causal dependencies.
result Comprehensive identifiability analysis of ODE systems with hidden confounders, including causal dependencies.
New method approximates controllability of large networks from coarse summaries.
problem Controlling large-scale linear dynamical systems with incomplete network information.
method Algorithm using stochastic block model to estimate controllability from coarse summaries.
result Average controllability of fine-scale system can be well approximated by coarse-scale system.
Develops a control framework for systemic risk under uncertainty.
problem Systemic risk under model uncertainty.
method Linear-quadratic mean-field control framework with viscosity solutions and verification theorems.
result Explicit feedback controls derived from a coupled Riccati system, preserving analytical tractability.
Improved modeling of chaotic systems using time-delay embeddings and Frenet-Serret frame.
problem Identifying effective coordinate systems for nonlinear dynamical systems.
method Developed a new algorithm to identify more stable and accurate models from less data, leveraging the connection between HAVOK and Frenet-Serret frame.
result The sub- and super-diagonal entries of the linear model correspond to intrinsic curvatures in Frenet-Serret frame.
We develop algorithms to learn non-linear dynamical systems without mixing assumptions.
problem Learning non-linear dynamical systems from dependent data.
method We introduce an offline algorithm and a one-pass streaming method with SGD-RER.
result Our methods achieve optimal or near-optimal performance for learning non-linear systems.
We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the Kähler manifold case. We find conditions for the information geometry of linear systems to be Kähler, and the relation of the Kähler potential to information geometric quantities such …
We show that classical Wilczynski--Se-ashi invariants of linear systems of ordinary differential equations are generalized in a natural way to contact invariants of non-linear ODEs. We explore geometric structures associated with equations that have vanishing generalized Wilczynski invariants and establish relationship…