SGLDS models multivariate data with a sparse graph linking latent states.
problem Modeling sequential multivariate data with varying dynamics.
method Nonparametric Bayesian approach using a gamma process and Bernoulli-Poisson link.
result Demonstrates state-of-the-art performance on synthetic and real data.
New method for state inference in state-space models with unknown dynamics.
problem State inference in state-space models with computationally expensive and undefined dynamics.
method Estimate state transition dynamics using a multi-output Gaussian process and Bayesian Neural Network as a surrogate model.
result Significant improvement in accuracy for state inference and prediction in non-stationary user models.
This research improves dynamical systems understanding by identifying latent states and their nonlinear transitions.
problem Previous work on dynamical systems could not identify nonlinear transition dynamics, leading to unreliable predictions.
method Proposes a state-space modeling framework using variational auto-encoders to identify latent states and their nonlinear transition functions.
result Demonstrates high accuracy in recovering latent state dynamics and future prediction accuracy.
ROAD-EnKFs use learned low-dimensional models to improve state reconstruction and forecasting.
problem Reconstructing and forecasting states of unknown or expensive systems.
method Learned low-dimensional surrogate models and ensemble Kalman filter integration.
result ROAD-EnKFs achieve higher accuracy at lower computational cost than existing methods.
This work studies learning dynamics in SSMs, linking them to deep linear networks.
problem Lack of theoretical understanding of SSMs, especially in deep state spaces.
method Analyzes learning dynamics of linear SSMs, focusing on frequency domain, and establishes links to deep linear networks.
result Analytical solutions for SSM learning dynamics under mild assumptions, linking to deep linear networks.
Machine learning aids excited-state molecular dynamics studies.
problem Challenges in studying electronically excited states of molecules.
method Employing machine learning techniques for excited-state molecular dynamics.
result Highlight successes and challenges in machine learning for excited-state processes.
Paper models non-linear dynamics from time series data.
problem Modeling non-linear dynamical systems from time series data.
method Introduces latent state modeling and a novel alternating minimization algorithm.
result LaNoLem achieves competitive performance in dynamics estimation and prediction.
Neural Physicist learns physical dynamics from images.
problem Learning meaningful physical state representations and accurate state transitions from image sequences.
method Neural Physicist uses VAE for state extraction, NP for parameters, and SSM for dynamics.
result Achieves long-term predictions and identifies system degrees of freedom.
Reduces nonlinear electromechanical dynamics through quasi-steady state hypothesis.
problem Nonlinear dynamics of electromechanical systems.
method Quasi-steady state hypothesis, non-dimensionalization, scaling.
result Physical justification and characteristic time scales of dynamics.
dynestyx: A library for probabilistic programming of dynamical systems
problem integrating state-space models into probabilistic programming languages
method a unified interface for specifying priors and performing inference
result principled uncertainty quantification for state and parameters
New method clusters ab initio dynamics to predict excited state properties.
problem Complex excited state dynamics in polyatomic systems.
method Time series guided clustering algorithm to generate meta-stable patterns.
result Accurate prediction of ground and excited state properties.
GDM models time series with smoother transitions and interpretable states.
problem Capturing smooth, variable-speed transitions and stochastic mixtures of states.
method Introduces a continuous relaxation of discrete states and a Gumbel noise model.
result Models real-world datasets more faithfully with smoother dynamics and interpretable states.
Proposes a novel approach for RUL estimation of aero-engines.
problem Lack of prior knowledge for defining exact failure thresholds in dynamic environments.
method Simultaneous and dynamic prediction of continuous and discrete states within a single learning framework.
result Improves RUL estimation for aero-engines by reducing complexity.
New framework analyzes temporal features in state space models.
problem Understanding temporal dependencies in data streams.
method Proposes a framework for rigorous analysis of state representations in ESNs, using temporal feature spaces and kernel machines.
result Phase transition in kernel richness for cycle reservoir topology.
Study of SGD with state-dependent noise, improving escape from local minima.
problem Understanding and improving the dynamics of SGD in non-convex optimization.
method Formal study on SGD with state-dependent noise, proposing power-law dynamic with state-dependent diffusion.
result Power-law dynamic can escape from sharp minima exponentially faster than flat minima.
This study uses persistent homology to analyze complex transitional networks from time series data.
problem Lack of effective tools to summarize complex topology in transitional networks.
method Persistent homology from topological data analysis applied to coarse-grained state-space networks (CGSSN).
result CGSSN improves dynamic state detection and noise robustness compared to other methods.
Review of algorithms for linear system approximations.
problem Linear approximation of high-dimensional dynamical systems.
method State-of-the-art algorithms for low-rank DMD.
result Provides additional details for comprehensive understanding.
Framework models multiscale dynamics with Bayesian learning for regime changes.
problem Analyzing complex interactions between fast and slow processes.
method Hierarchical state-space modeling with Sequential Monte Carlo.
result Bayesian approach accurately tracks state transitions and identifies switching dynamics.
Dynamical-VAE learns causal dynamics from POMDPs using future information.
problem Learning accurate state representations from partial observations in POMDPs.
method Dynamical Variational Auto-Encoder (DVAE) with hindsight framework.
result DVAE uncovers causal graph more effectively than history-based methods.
A new method learns complex dynamical systems from data efficiently.
problem Learning complex dynamical systems from large-scale data efficiently.
method Low-rank structured variational autoencoding framework for nonlinear Gaussian state-space models.
result Consistently demonstrates better predictive capabilities compared to other models.
Online learning improves state estimation of nonlinear systems.
problem Online learning of nonlinear state dynamics in Gaussian state space models.
method Stochastic variational sparse Gaussian process embedded in a particle filter framework, with model updating using stochastic gradient descent.
result State estimation performance significantly improves with online learning of state dynamics.
Meta-causal states group equivalent qualitative causal dynamics, useful for analyzing system changes.
problem Qualitative changes in causal relationships due to agent actions or environmental tipping points.
method Propose meta-causal states to group causal models based on equivalent qualitative behavior and parameterize specific mechanisms.
result Meta-causal states can be inferred from observed agent behavior and disentangled from unlabeled data.
DeepGenMSM models complex dynamical systems for accurate trajectory prediction.
problem Inference and prediction of metastable dynamical systems.
method Deep learning framework with probabilistic encoder, Markov chain, and generative part.
result Accurate long-time kinetics estimation and generation of realistic structures.
Method learns low-dim. state vars from noisy high-dim. data.
problem Discovering dynamical models from noisy high-dimensional data.
method Stochastic Variational Deep Kernel Learning with encoder and latent model.
result Effective denoising, compact state representation, and uncertainty quantification.
New framework compares two stochastic learning dynamics in games.
problem Inability to distinguish between different learning rules leading to the same steady-state behavior.
method Developed a framework for comparative analysis of stochastic learning dynamics with different update rules.
result Identified distinct behaviors in the paths to stochastically stable states for LLL and ML.
Proposes a non-parametric model for dynamic fMRI connectivity.
problem Dynamic functional connectivity in fMRI data.
method Bayesian statistical modeling using predictive likelihood.
result Dynamic states are driven by subject variability and preprocessing differences, not by task or rest.
Flexible online learning framework for neural dynamics.
problem Learning latent neural state and dynamics from complex neural recordings.
method Stochastic gradient variational Bayes approach for joint optimization.
result Framework can optimize nonlinear dynamical system, observation model, and recognition model.
Empirical mode modeling improves state-space analysis of noisy data.
problem Analyzing nonlinear systems with noisy data.
method Combining empirical mode decomposition with empirical dynamic modeling.
result Empirical mode modeling enhances state-space representations in noisy data.
The paper proposes autoregressive models for better offline RL.
problem Offline RL policy evaluation and optimization challenges.
method Autoregressive dynamics models for sequential state and reward prediction.
result Autoregressive models outperform standard methods in log-likelihood and RL tasks.
KalmanNet uses neural networks to improve state estimation in systems with unknown dynamics.
problem State estimation of systems with non-linear dynamics and partial information.
method KalmanNet integrates a recurrent neural network with the Kalman filter to handle non-linearities and model mismatches.
result KalmanNet outperforms classic filtering methods in systems with both mismatched and accurate domain knowledge.
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gauss…
The paper explores states of financial markets using correlation matrices and their dynamics.
problem Understanding the states of financial markets based on correlations.
method Revisits previous work and introduces recent developments in practical applications.
result Analysis of trajectories and symbolic dynamics in correlation matrix space.
Develops a dynamic mean field theory for reinforcement learning.
problem Finite state and action Bayesian reinforcement learning in large state spaces.
method Analogies with statistical physics, interpreting probabilities as couplings and values as spins, solving mean field equations.
result State-action values are statistically independent in the asymptotic state space limit, with exact or approximate equations for computation.
Study on state dynamics in Deep Echo State Networks, revealing the importance of inter-reservoir connections.
problem Understanding state dynamics in multi-layered RNNs.
method Tools from information theory and numerical analysis.
result Inter-reservoir connections enrich representations in higher layers of DeepESNs.
The paper simplifies multi-agent RL dynamics in finite-state Markov games using homogenization.
problem Approximating complex multi-agent reinforcement learning dynamics in finite-state Markov games.
method Rescaling learning process by reducing learning rate and increasing update frequency, proving convergence to an ODE.
result The rescaled process converges to an ODE that approximates the agent's learning dynamics.
Herding uses edge-of-chaos dynamics to generate model states and parameters.
problem Learning from data with deterministic dynamics.
method Alternating parameter perturbations with state maximizations, using edge-of-chaos dynamics.
result Herding achieves fast convergence of moments, generalizing to models with latent variables.
Active learning selects inputs for GPSSM to learn latent states.
problem Optimally learn latent states of a GPSSM through active selection of inputs.
method Use mutual information to select informative inputs; approximate mutual information for GPSSM.
result Effective active learning of GPSSM dynamics in physical systems.
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights in the linear combination is modelled by another linear Gaussian dynamical model…
ETGPSSM efficiently models high-dimensional, non-stationary systems with reduced complexity.
problem Prohibitive computational and parametric complexity in high-dimensional, non-stationary dynamical systems.
method ETGPSSM integrates a single shared GP with input-dependent normalizing flows for scalable and flexible modeling.
result ETGPSSM outperforms existing models in computational efficiency and accuracy.
Developed a method to estimate PLRNNs from neural data, revealing dynamics of working memory.
problem Reconstructing neural dynamics from experimental data for computational analysis.
method Semi-analytical maximum-likelihood estimation using state space models.
result 5-state PLRNN model captures essential working memory dynamics.
New method aligns states for better imitation learning.
problem Different dynamics models between imitator and expert.
method State alignment-based reinforcement learning.
result Superior performance on various imitation learning settings.
New model captures state-dependent variability in partially observed systems.
problem Structured stochasticity not captured by constant-variance models.
method State-coupled stochastic volatility framework with particle expectation-maximization.
result Model consistently reduces recovery bias under partial observation.
Paper introduces OMD for ordered state transitions in SSMs.
problem Modeling ordered latent states in dynamic systems.
method Ordered Matrix Dirichlet (OMD) prior over ordered stochastic matrices.
result OMD models recover interpretable ordered latent structure without sacrificing predictive performance.
Bayesian method synthesizes barrier certificates for unknown systems with latent states.
problem Certifying safety in systems with unknown dynamics and latent states.
method Bayesian inference with Metropolis-Hastings sampler and sum-of-squares program.
result Probabilistic validity of barrier certificates for unknown systems.
Combines deep state space models with diffusion models for better forecasting and capturing latent dynamics
problem Forecasting and capturing latent dynamics in time series
method DDSSM: Diffusion-driven state space model
result Empirically outperforms state-of-the-art deep SSM
This paper develops nudging algorithms using learned surrogates for state estimation in dynamical systems.
problem Estimating the state of a dynamical system from partial observations when dynamics are unknown or expensive to simulate.
method Unified finite-dimensional analysis of nudging algorithms employing learned surrogate models of the dynamics.
result Nudging algorithms with surrogate models retain exponential convergence up to an explicit error floor.
DCRNN improves LSTM for chaotic dynamical system forecasting.
problem Modeling chaotic dynamical systems with recurrent neural networks.
method DCRNN incorporates learnable skip-connections and a Lyapunov stability regularization term.
result DCRNN outperforms LSTM in 100 out of 100 experiments, reducing mean squared error by 80.0%.
Develops a method to model neural dynamics with flexible yet interpretable latent states.
problem Capturing complex nonlinear dynamics in neural time series while maintaining interpretability.
method Gaussian Process Switching Linear Dynamical System (gpSLDS) that balances expressiveness and interpretability.
result Favorable performance in comparison to rSLDS on synthetic and real neuroscience data.