Time series with non-uniform intervals occur in many applications, and are difficult to model using standard recurrent neural networks (RNNs). We generalize RNNs to have continuous-time hidden dynamics defined by ordinary differential equations (ODEs), a model we call ODE-RNNs. Furthermore, we use ODE-RNNs to replace t…
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48 results for “latent ODE”
We present Ordinary Differential Equation Variational Auto-Encoder (ODEVAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODEVAE can simultaneously learn the embedding of high dimensional trajectories and infer arbitrarily complex conti…
The paper provides convergence guarantees for ODE-based generative models using transformers.
problem Theoretical guarantees for ODE-based generative models.
method A pre-trained autoencoder maps inputs to a latent space, and a transformer predicts the velocity field.
result The distribution of samples generated via estimated ODE flow converges to the target distribution in Wasserstein-2 distance.
Statistical approach uses ODEs for modeling individual health trajectories.
problem Challenges in applying ODEs to longitudinal cohort data, especially noise and parameter sensitivity.
method Combines ODEs with neural networks to model individual health trajectories using each observation as initial value.
result Demonstrates improved modeling of individual health trajectories compared to global regression.
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.
Balanced Neural ODEs combine VAEs and Neural ODEs for efficient time series modeling.
problem Efficiently modeling systems with time-varying inputs and varying complexity.
method Combines VAEs for dimensionality reduction and Neural ODEs for dynamics, using variational parameters to adaptively learn.
result Balanced Neural ODEs (B-NODE) efficiently approximate Koopman operator without predefined dimensionality.
New method combines ODE solvers with Bayesian inference for efficient model training.
problem Combining ODE solvers with Bayesian inference for efficient model training.
method Probabilistic state space model using extended Kalman filter for joint inference from differential equations and data.
result Efficient approximate Bayesian inference on latent force and ODE solution.
SurvLatent ODE predicts VTE risk for cancer patients, outperforming current methods.
problem Predicting clinical outcomes from irregularly sampled EHR data with competing events.
method Neural ODE-based Recurrent Neural Networks (ODE-RNN) for flexible survival time estimation.
result SurvLatent ODE outperforms Khorana Risk scores for VTE risk prediction.
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.
LHM integrates expert ODEs with neural ODEs for disease progression prediction.
problem Predicting disease progression under medications using limited data.
method Integrating expert-designed ODEs with machine-learned Neural ODEs.
result LHM consistently outperforms previous methods, especially in small sample regimes.
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.
Novel deep learning model improves AUC prediction for tacrolimus dosing.
problem Model misspecification in current pharmacokinetic models.
method Latent Neural-ODE for learning individualized pharmacokinetic dynamics.
result Latent ODE model outperforms standard methods in AUC prediction accuracy.
Gradient matching with Gaussian processes is a promising tool for learning parameters of ordinary differential equations (ODE's). The essence of gradient matching is to model the prior over state variables as a Gaussian process which implies that the joint distribution given the ODE's and GP kernels is also Gaussian di…
Gradient flow autoencoder improves data efficiency over traditional autoencoders.
problem Sub-optimal latent space representations in autoencoders.
method Gradient flow through ODE with adaptive step size for optimization.
result Gradient flow autoencoder achieves higher data efficiency.
LiLaN uses linear latent networks to solve stiff ODEs efficiently.
problem Solving stiff ordinary differential equations (StODEs) requires expensive methods.
method LiLaN integrates latent dynamics analytically, avoiding explicit/implicit integration.
result LiLaN can approximate stiff nonlinear systems to any accuracy epsilon.
LS4 models time-series with latent states, outperforming previous methods.
problem Learning sharp transitions in time-series data.
method State space ODE with convolutional representation to bypass hidden states.
result LS4 significantly outperforms previous models in various metrics.
New method sparsifies hybrid neural ODEs for better performance and stability.
problem Excessive latent states and interactions from mechanistic models lead to training inefficiency and over-fitting.
method Automatic state selection and structure optimization combining domain-informed graph modifications with data-driven regularization.
result Improved predictive performance and robustness with desired sparsity.
DDPM encoder matches optimal transport for natural images.
problem Understanding theoretical properties of DDPM latent space.
method Showed DDPM encoder matches optimal transport for common distributions.
result DDPM encoder map coincides with optimal transport map for natural images.
A new method directly encodes data into latent space using gradient flow.
problem Suboptimal representations in physical sciences due to encoder inversion.
method Decoder-only approach using gradient flow and ODEs, avoiding integrals.
result Superior data efficiency and explicit encoding compared to traditional autoencoders.
New method identifies physical constants from video data alone.
problem Identifying physical constants from video data.
method Proves level-set slope-coverage condition ensures local affine mapping to true physical state, enabling exact parameter recovery.
result Underdamped systems identifiable from a single video clip, other regimes require three diverse trajectories.
This paper uses ODE to improve RNN models for time series data.
problem Improving RNN models for irregularly sampled time series data.
method Extending RNNs with Neural Ordinary Differential Equations (ODEs).
result New ODE-based RNN models reduce training and evaluation time.
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.
New model predicts banana disease risk from climate data.
problem Managing Black Sigatoka disease under climate change.
method Latent Neural ODEs to model infection dynamics.
result Superior generalization performance up to one month ahead.
MSLs use parallelizable root-finding for efficient ODE and PDE solutions.
problem Efficiently solving initial value problems for ODEs and PDEs.
method Leveraging time-parallel methods, MSLs use parallelizable root-finding algorithms.
result MSLs offer significant speedups in NFEs and inference time.
Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Modelscs.LG
Enhances generative models by improving expressivity without high computational cost.
problem Improving expressivity in generative models without increasing computational complexity.
method Proposes a new family of generative flows on an augmented data space, proving they can approximate a Hamiltonian ODE as a universal transport map.
result Demonstrates state-of-the-art performance on flow-based generative modeling benchmarks.
Improved meta-learning for dynamics using additional structured knowledge.
problem Meta-learning for dynamics with limited raw observations.
method Extended Neural ODE Process model to use privileged information.
result Improved accuracy and calibration on simulated dynamics tasks.
TGNN4I model forecasts irregularly observed graph data using ODEs.
problem Forecasting graph-structured data with irregular time steps and partial observations.
method Introduces a time-continuous latent state in each node using ODEs and GRUs, integrating graph neural network layers.
result Validated usefulness of graph structure and time-continuous dynamics in irregular observation settings.
AdjointDEIS simplifies diffusion model optimization.
problem Optimizing diffusion models with respect to a differentiable metric.
method Novel bespoke ODE solvers for continuous adjoint equations.
result Continuous adjoint equations simplify to a simple ODE, improving efficiency.
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.
Model predicts trading strategies based on latent demand and price impact.
problem Predicting strategic trading behavior of investors with private targets.
method Equilibrium model of dynamic trading, learning, and pricing by strategic investors.
result Trading strategies are a combination of target following, liquidity provision, and front-running based on latent demand and price pressure.
New estimators reduce variance in training variational autoencoders with discrete latent variables.
problem Training variational autoencoders with discrete latent variables requires efficient gradient estimation.
method Introduce ReinMax-Rao and ReinMax-CV estimators using Rao-Blackwellisation and control variates.
result Demonstrate superior performance on training variational autoencoders with discrete latent spaces.
Like many numerical methods, solvers for initial value problems (IVPs) on ordinary differential equations estimate an analytically intractable quantity, using the results of tractable computations as inputs. This structure is closely connected to the notion of inference on latent variables in statistics. We describe a …
We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constan…
DLFM models complex systems with uncertainty, outperforming traditional methods.
problem Modeling highly nonlinear dynamical systems with robust uncertainty quantification.
method Deep latent force model (DLFM) using physics-informed kernels derived from ODEs.
result DLFM achieves comparable performance to non-physics-informed models on univariate tasks and captures dynamics in real-world data.
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…
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.
Probabilistic Numeric SMC Sampling for Bayesian Nonlinear System Identification in Continuous Timestat.ML
This paper tackles Bayesian system identification with probabilistic numerical methods.
problem Accurately modeling nonlinear dynamic systems from noisy data.
method Probabilistic Sequential Monte Carlo (SMC) combined with probabilistic numerical integration.
result Efficient identification of latent states and system parameters from noisy measurements.
Proposes a new method for efficient model reconstruction with uncertain parameters.
problem Reconstructing models with latent variables or parameters of unknown distribution.
method Local squared Wasserstein-2 (W_2) method.
result Efficiently reconstructs output distributions from observation data.
Deep learning for integrating diverse clinical measurements.
problem Combining data from different measurement instruments in longitudinal clinical registries.
method Domain adaptation using deep learning for mapping items from different instruments.
result Domain adaptation can recover latent trajectories even with limited data and misalignment.
PFM generates novel samples on data manifolds using pullback geometry.
problem Generating novel samples on complex data manifolds.
method Pullback Flow Matching framework leveraging pullback geometry and isometric learning.
result PFM achieves improved manifold learning and generative performance.
This study shows why training Neural ODEs is hard and proposes a new method.
problem Training Neural ODEs is challenging, especially in practice.
method Proposed a new stabilization method and provided an analytical convergence analysis.
result Insights and techniques for researchers starting work on Neural ODEs.
Inflationary flows use DBMs for accurate Bayesian inference.
problem Calibrated uncertainty quantification in Bayesian inference.
method Inflationary flows leverage DBMs to map data to a Gaussian latent space.
result Inflationary flows produce accurate, identifiable posterior distributions.
Minimal surfaces in third-order ODEs identified for linear second-order ODEs.
problem Characterizing minimal surfaces in third-order ODEs.
method Analyzing submanifolds of third-order ODEs as Riemannian manifolds.
result Linear second-order ODEs with are the only minimal surfaces and totally geodesic.
DALTON improves ODE parameter estimation by learning from noisy data.
problem High sensitivity to parameters in ODEs produces unreliable parameter estimates.
method Data-adaptive probabilistic likelihood approximation for ODEs.
result DALTON produces more accurate parameter estimates than existing methods.
Proposes a new tensor decomposition method for functional temporal data with adaptive complexity.
problem Challenges in temporal tensor decomposition for general tensor data with continuous indexes.
method Encodes continuous spatial indexes as learnable Fourier features and uses neural ODEs for temporal trajectories. Introduces a sparsity-inducing prior for complexity adaptation.
result Significantly outperforms existing methods in prediction performance and robustness against noise.
Improved neural-ODE for faster convergence and stability.
problem Stability, consistency, and convergence issues in neural-ODE solvers.
method Proposed a first-order Nesterov's accelerated gradient (NAG) based ODE-solver.
result Efficacy demonstrated in three tasks: supervised classification, density estimation, and time-series modelling.
New method uses Gaussian ODE filtering to approximate likelihoods for fast ODE inverse problems.
problem Intractable forward models in likelihood-free inference, especially for ODEs.
method Gaussian ODE filtering to construct local Gaussian likelihood approximations.
result New solvers outperform standard likelihood-free approaches on benchmark systems.
Faster training of neural ODEs using Gauß-Legendre quadrature.
problem Training neural ODEs is slow due to solving ODEs numerically.
method Use Gauß-Legendre quadrature to solve integrals faster than ODE-based methods.
result Faster training of neural ODEs, especially for large models.