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.
This work extends identifiability analysis to sequential latent variable models, focusing on Switching Dynamical Systems.
problem Identifying latent variables in sequential data models.
method Proved identifiability of Markov Switching Models and established conditions for Switching Dynamical Systems.
result Identifiability of latent variables and non-linear mappings in Switching Dynamical Systems up to affine transformations.
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 …
Model captures system input variations in latent space for actionable dynamics.
problem Learning dynamical systems from data without prescribing a mathematical model.
method Structured latent ODE model with stochastic factors of variation for each input.
result Improves generation of time-series data and inference of system inputs over baselines.
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.
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.
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.
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.
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 identifies latent variables and models from spacecraft data.
problem Learning reliable models from spacecraft data with complex relationships.
method Inductive bias inspired by controllable canonical forms for sparse, input-dependent latent variables.
result Identifies latent variables up to scaling and determines dynamic models up to transformations for linear and affine systems.
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.
Neuroscience is experiencing a data revolution in which many hundreds or thousands of neurons are recorded simultaneously. Currently, there is little consensus on how such data should be analyzed. Here we introduce LFADS (Latent Factor Analysis via Dynamical Systems), a method to infer latent dynamics from simultaneous…
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear stochastic differential equation (SDE) driven by a Wiener process, with a drift evolu…
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.
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.
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.
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.
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.
New methods improve sampling from complex dynamical models.
problem Sampling from high-dimensional, non-linear latent dynamical models is computationally challenging.
method Introduce auxiliary MCMC and Particle Gibbs samplers with improved performance and parallelisation.
result Enhanced samplers maintain performance in high-dimensional latent spaces and support parallelisation.
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.
Paper proposes learning system dynamics from irregularly-sampled partial observations.
problem Capturing dynamics of multi-agent systems with irregular and partial observations.
method LG-ODE, a latent ordinary differential equation model using graph neural networks and neuralODE.
result Demonstrates effectiveness on motion capture, spring system, and charged particle datasets.
This work discovers latent field effects governing interacting dynamical systems.
problem Discovering field effects governing interacting dynamical systems.
method Proposes neural fields to learn latent force fields from observed dynamics, disentangling local object interactions and global field effects.
result Accurately discovers latent field effects in various dynamical systems.
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 linearizes nonlinear coupled oscillators on graphs.
problem Predicting global synchronization in nonlinear coupled oscillators on graphs.
method Latent dynamic filters learned through supervised matrix factorization.
result Latent dynamics filters enable effective prediction of global synchronization.
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.
Physics-guided model improves deep learning for nonlinear systems.
problem Intractable inference of nonlinear dynamical systems from data.
method Physics-guided Deep Markov Model (PgDMM) using neural networks.
result Improved performance on nonlinear systems with structured latent space.
We propose a framework for the completely unsupervised learning of latent object properties from their interactions: the perception-prediction network (PPN). Consisting of a perception module that extracts representations of latent object properties and a prediction module that uses those extracted properties to simula…
Optimally explores dynamical systems with varying properties using context inference.
problem Learning dynamics models for systems with varying properties.
method Formulates dynamics models as stochastic processes conditioned on a latent context variable inferred from system transitions. Uses probabilistic formulation to compute optimal action sequences for exploration.
result Demonstrates effectiveness of the method on non-linear toy-problems and reinforcement learning environments.
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of coupled maps as a synchronous update graph dynamical systems. Specifically, we study …
Model infers latent variables in sparse coding models using Langevin dynamics.
problem Sampling posterior distribution in sparse coding models.
method Langevin dynamics for inference and simultaneous learning of parameters.
result Langevin dynamics efficiently sample from 'L0 sparse' posterior distribution.
Method learns model for unknown stochastic system from data.
problem Modeling unknown stochastic dynamical systems.
method Autoencoder approach using deep neural networks (DNNs).
result Decoder serves as a predictive model for unknown stochastic systems.
Improved SINDy autoencoder for identifying noisy dynamical systems.
problem Robust identification of noisy dynamical systems from data.
method Incorporates noise-separating neural network structures into SINDy autoencoder architecture.
result Accurately recovers latent dynamics and estimates measurement noise from noisy observations.
A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie in the identification of the computational dynamics underlying task processing. …
D2PCCA integrates deep learning and probabilistic modeling for nonlinear dynamical systems.
problem Analyzing nonlinear dynamical systems with probabilistic understanding.
method Combines deep learning and probabilistic modeling, using KL annealing and normalizing flows.
result Captures latent dynamics in sequential datasets with improved convergence and flexibility.
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.
Dynamical system models (including RNNs) often lack the ability to adapt the sequence generation or prediction to a given context, limiting their real-world application. In this paper we show that hierarchical multi-task dynamical systems (MTDSs) provide direct user control over sequence generation, via use of a latent…
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…
Latent force models are systems whereby there is a mechanistic model describing the dynamics of the system state, with some unknown forcing term that is approximated with a Gaussian process. If such dynamics are non-linear, it can be difficult to estimate the posterior state and forcing term jointly, particularly when …
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…
Meta-Dynamic models learn shared neural dynamics across tasks.
problem Learning latent dynamics from neural recordings across different tasks.
method Captures variabilities on a low-dimensional manifold to meta-learn dynamics.
result Meta-Dynamic models can rapidly learn latent dynamics from new recordings.
Develops VAEs for learning complex physical systems from data.
problem Learning low-dimensional representations of nonlinear physical systems.
method Variational Autoencoders with manifold latent spaces.
result Effective in learning nonlinear Burgers equation and constrained mechanical systems.
High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear probabilistic approaches to this data are required. In this paper we introduce the v…
New method uses Diffusion Maps for latent space modeling of dynamical systems.
problem Building reduced dynamical models from time series data.
method Two rounds of Diffusion Maps on latent coordinates, with lifting back to ambient space.
result Approximation of full state functions in reduced coordinates.
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.
Modeling interacting objects with latent Gaussian process ODEs.
problem Time uncertainty-aware modeling of continuous-time dynamics of interacting objects.
method A new model using latent Gaussian process ordinary differential equations to infer independent dynamics and interactions.
result Our model improves long-term predictions and successfully encapsulates independent dynamics and interactions.
We propose an efficient inference method for switching nonlinear dynamical systems. The key idea is to learn an inference network which can be used as a proposal distribution for the continuous latent variables, while performing exact marginalization of the discrete latent variables. This allows us to use the reparamet…
A popular approach for predicting the future of dynamical systems involves mapping them into a lower-dimensional "latent space" where prediction is easier. We show that the information-theoretically optimal approach uses different mappings for present and future, in contrast to state-of-the-art machine-learning approac…
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.