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.
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.
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.
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
Paper introduces TSSDMN for modeling dynamic multilayer networks.
problem Capturing temporal and cross-layer dynamics in multilayer networks.
method Tensor State Space Model (TSSDMN) using symmetric Tucker decomposition.
result TSSDMN uniquely captures temporal dynamics within and across layers.
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.
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.
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.
Latent MoS learns multiple symmetries for efficient dynamic learning.
problem Efficiently learning dynamics from limited system measurements.
method Latent Mixture of Symmetries (Latent MoS) with hierarchical architecture.
result Latent MoS outperforms baselines in interpolation and extrapolation tasks.
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 new neural ODE model for continuous-time sequence generation.
problem Representing and predicting continuous-time sequences with high accuracy.
method A neural emission model and neural ODE define the latent state evolution, with an Energy-based model for prior distribution.
result The model outperforms existing methods in various tasks, including long-horizon predictions.
Auto-regressive models learn latent states from partially observed linear dynamical systems.
problem Understanding how auto-regressive models learn latent representations from partially observed linear dynamical systems.
method Empirical risk minimization on partially observed linear dynamical systems.
result Two-layer linear auto-regressive models learn to approximate Kalman filtering, coinciding with optimal state estimates.
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.
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.
Proposes DLGPD model to learn dynamics from images for planning.
problem Planning in unknown, indirectly observable environments.
method Deep latent Gaussian process dynamics model trained jointly with neural networks.
result Demonstrates improved data efficiency and transfer learning.
Proposes LDIDPs for efficient sequential data generation from latent dynamical models.
problem Challenges in generating high-fidelity sequential samples from latent dynamical models.
method Utilizes implicit diffusion processes to sample from latent dynamical processes.
result Demonstrates accurate learning of dynamics and efficient generation of high-quality sequential data.
Online DEM improves tracking of latent states in dynamic systems.
problem Tracking latent states in dynamic systems with online updates.
method Specializes DEM for online data assimilation, separating temporal scales.
result ODEM can track latent states of a non-linear generative model.
This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications, including long-term asymptotic patterns. Whereas state-of-the-art data-driven approac…
Proposes iVDFM for identifying latent factors in multivariate time series.
problem Identifying latent factors in multivariate time series with structural dynamics.
method Identifiable Variational Dynamic Factor Model (iVDFM) with iVAE-style conditioning.
result Identifiable latent factors up to permutation and component-wise affine transformations.
Novel method learns time series dynamics without reconstruction.
problem Learning nonlinear stochastic dynamics from video data.
method Recognition-parametrized Gaussian state space model (RP-GSSM) using maximum likelihood.
result Outperforms alternatives on nonlinear stochastic dynamics learning.
Representation learning over graph structured data has been mostly studied in static graph settings while efforts for modeling dynamic graphs are still scant. In this paper, we develop a novel hierarchical variational model that introduces additional latent random variables to jointly model the hidden states of a graph…
LatentTrack generates model parameters online for nonstationary data.
problem Online probabilistic prediction under nonstationary dynamics.
method Sequential neural architecture with latent filtering and amortized inference.
result Consistently lower negative log-likelihood and mean squared error than baselines.
Framework simplifies vision-based control and goal discovery.
problem Learning proportional control from visual data.
method Introduces NewtonianVAE for proportional control and goal discovery.
result Dramatic simplification and acceleration of vision-based controllers.
Improved robust latent variable estimation for neural dynamics.
problem Inconsistent results due to noise and nonlinearity in existing models.
method Probabilistic approach to latent variable estimation in decomposed models.
result More accurate latent variable inference in nonlinear systems with diverse noise conditions.
New technologies for recording the activity of large neural populations during complex behavior provide exciting opportunities for investigating the neural computations that underlie perception, cognition, and decision-making. Nonlinear state space models provide an interpretable signal processing framework by combinin…
q-VAE extracts disentangled latent spaces for robot control and dynamic systems.
problem Disentangled representation learning for latent spaces in robotics.
method Proposes q-VAE based on Tsallis statistics, improving disentanglement and latent dynamics.
result Improves disentangled representation while maintaining data reconstruction accuracy.
Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent trajectories. However, simple state transition structures, linear embedding assumpti…
Generative models learn latent process to match target distributions.
problem Training flow-matching models with auxiliary stochastic dynamics.
method Introduces latent process generator matching, treating generative state as a deterministic image of a Markov process.
result Learn generator of a stochastic process with same marginal distributions.
This paper reviews deep learning methods for state space models.
problem Analyzing temporal dynamics in dynamical systems.
method Selective review of deep neural network approaches for state space models.
result Unified perspective on discrete and continuous time SSMs.
A method for learning a context latent vector to improve generalization in model-based RL.
problem Learning a global dynamics model that can generalize across different dynamics.
method Decomposes learning a global dynamics model into two stages: learning a context latent vector and predicting next states.
result Achieves superior generalization across various simulated robotics and control tasks.
Many dynamical systems exhibit similar structure, as often captured by hand-designed simplified models that can be used for analysis and control. We develop a method for learning to correspond pairs of dynamical systems via a learned latent dynamical system. Given trajectory data from two dynamical systems, we learn a …
EnKO combines VI and EnKF for efficient latent dynamics inference.
problem Particle degeneracy and biased gradient estimators in SMC-based methods.
method EnKO: hybrid of VI and EnKF.
result EnKO outperforms SMC-based methods in predictive ability and particle efficiency.
Identifies latent actions and dynamics from offline data with diverse demonstrators.
problem Recovering latent actions and environment dynamics from action-free trajectories.
method Assumes distinct policies for each demonstrator, identifies latent transitions and policies via matrix factorization.
result Identifies latent transitions and demonstrator policies up to permutation.
New model predicts video sequences with latent dynamics.
problem Predicting video sequences with inherent uncertainty.
method Introduces a novel stochastic temporal model with latent dynamics.
result Latent model outperforms prior state-of-the-art methods.
Novel approach detects early warning indicators in complex systems.
problem Detecting abrupt transitions in complex systems.
method Directed anisotropic diffusion map and latent stochastic dynamical systems.
result Early warning indicators can detect tipping points in state transitions.
SING improves state inference in latent SDE models for better drift function estimation.
problem Intractable posterior inference in latent SDE models.
method Natural gradient variational inference.
result SING provides faster and more reliable inference in latent SDE models.
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.
GD-VAEs learn dynamics from observations using geometric and topological information.
problem Learning parsimonious representations of nonlinear dynamics from observations.
method Develops data-driven methods incorporating geometric and topological information using Variational Autoencoders (VAEs).
result GD-VAEs provide methods for learning reduced dimensional representations of nonlinear dynamics.
New algorithm infers trajectories from partial observations using optimal transport.
problem Inferring trajectories from partial observations of coupled systems.
method Extends MFL algorithm to latent SDEs using observable state space models and partial observations.
result Experiments show significant outperformance over latent-free baseline.
Proposes LAE-EnKF for improved nonlinear data assimilation.
problem Performance of EnKF deteriorates for strongly nonlinear dynamics.
method Reformulates assimilation in a learned latent space with linear dynamics.
result LAE-EnKF yields more accurate and stable assimilation.
ACSSM models irregular time series with continuous dynamics.
problem Modeling irregular time series data.
method ACSSM uses a multi-marginal Doob's h-transform and variational inference with stochastic optimal control.
result ACSSM outperforms in tasks like classification, regression, interpolation, and extrapolation.
RNNs and their variants have been widely adopted for image captioning. In RNNs, the production of a caption is driven by a sequence of latent states. Existing captioning models usually represent latent states as vectors, taking this practice for granted. We rethink this choice and study an alternative formulation, name…
Framework infers Langevin dynamics from stochastic observations of latent systems.
problem Inferring non-stationary Langevin dynamics from indirect stochastic observations.
method Non-parametric framework explicitly modeling stochastic observation process and non-stationary latent dynamics.
result Correct inference of non-stationary dynamics requires accounting for non-equilibrium states and observation duration.
Framework predicts responses in misspecified systems using GPLFM and BNNs.
problem Predicting responses in dynamical systems with model misspecification.
method Integrates GPLFM and BNNs for uncertainty-aware inference and prediction.
result Systematic propagation of uncertainty from diagnosis to prediction.
New method for efficient Bayesian inference in GPSSMs.
problem Challenges in inference for Gaussian process state-space models.
method Free-form variational inference with stochastic gradient Hamiltonian Monte Carlo.
result Our method learns transition dynamics and latent states more accurately than competing methods.
Recurrent-DBN models dynamic relational data with interpretable latent structures.
problem Interpreting dynamic relational data with hidden structures.
method Recurrent Dirichlet Belief Network framework with hierarchical latent structures and efficient inference strategy.
result Recurrent-DBN discovers interpretable latent structures and improves link prediction.
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.
New method uncovers small but significant local activities in time-series data.
problem Reconstructing small but important local activities in time-series data.
method Neural state-space models with latent causal-effect disentanglement.
result Demonstrated proof-of-concept on reconstructing ectopic foci in cardiac electrical propagation.