Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.
problem Predicting and capturing long-term behaviors of stochastic dynamical systems.
method Data-driven framework combining Reservoir Computing and Normalizing Flow, integrating error modeling and both approaches virtues.
result Successfully predicts the long-term evolution of stochastic dynamical systems and replicates dynamical behaviors.
This work learns effective dynamics from short-term data of stochastic systems.
problem Learning effective dynamics from short-term data of stochastic systems.
method Proposes a novel algorithm using a neural network (Auto-SDE) to learn invariant slow manifold from data.
result Validated through numerical experiments to be accurate, stable, and effective.
sFML learns stochastic dynamical systems from data.
problem Learning unknown stochastic dynamical systems from measurement data.
method sFML extends FML for deterministic systems, using a stochastic flow map composed of deterministic and stochastic sub-maps.
result sFML constructs a stochastic evolution model approximating unknown stochastic systems.
Method learns dynamics of slow variables from stochastic data.
problem Modeling unknown multiscale stochastic systems with limited data.
method Data-driven approach to learn effective dynamics from bursts of observation data.
result Generative model accurately captures effective dynamics of slow variables.
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.
Generative models for complex stochastic dynamics using adversarial learning.
problem Data-driven modeling of multistep stochastic dynamics.
method Adversarial learning with GANs and MMD for stable model classes.
result Stable generative models for long-time prediction and stochastic systems.
New method learns dynamics from sparse data using geometric constraints.
problem Learning dynamics from sparse, undersampled data.
method Reformulates inference as a stochastic control problem, using geometry-driven path augmentation.
result Accurately recovers stochastic dynamics from extremely undersampled data.
New method infers dynamical systems from population data.
problem Inferring dynamical systems from population data.
method Deducing and estimating Fokker-Planck equation, projecting to test functions, sparse inference.
result Induces driving forces of dynamical systems.
This work extracts stochastic dynamical systems with α \alpha α -stable Lévy noise.
problem Extracting data-driven governing laws of dynamical systems with non-Gaussian noise.
method End-to-end deep learning approach for learning drift and diffusion coefficients for α \alpha α -stable Lévy noise. result Effectiveness of the method confirmed by numerical experiments.
Method extracts stochastic systems with Lévy noise from data.
problem Identifying stochastic dynamical systems with Lévy noise from short data.
method Estimate Lévy jump measure and noise intensity, approximate drift coefficient.
result Accurate and effective method for discovering stochastic laws.
Derives stochastic and dissipative dynamics preserving Gibbs measure.
problem Understanding and deriving structure-preserving stochastic systems.
method Extension of Hamilton-Pontryagin principle, symmetry reduction, and inclusion of dissipation.
result New derivation of double-bracket dissipation.
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…
Develops a new method to discover stochastic systems with non-Gaussian noise.
problem Discovering governing laws from complex systems with non-Gaussian noise.
method Theoretical framework and numerical algorithm to extract stochastic differential equations with Gaussian and non-Gaussian noise.
result Demonstrated the efficacy and accuracy of the approach on various systems.
This research develops an evolutionary approach to discover non-Gaussian stochastic dynamical systems.
problem Discovering explicit governing equations of stochastic dynamical systems with Lévy noise from data.
method ESSR approach using genetic programming, sparse regression, and nonlocal Kramers-Moyal formulas.
result The approach effectively extracts non-Gaussian stochastic dynamical systems from sample path data.
Unified treatment of RC in stochastic and deterministic settings.
problem Understanding and generalizing reservoir computing in both deterministic and stochastic contexts.
method Investigation of state-space systems, analysis of fading memory and solution stability, introduction of stochastic echo states.
result Generality of fading memory and solution stability in state-space systems, even without the echo state property.
DeepONet accelerates reliability analysis of stochastic nonlinear systems.
problem Time-dependent reliability analysis of systems with stochastic forcing.
method DeepONet, a novel operator network, learns function-to-function mappings.
result DeepONet efficiently and accurately predicts system responses.
Method extracts governing laws from non-Gaussian stochastic systems data.
problem Modeling complex dynamics with non-Gaussian Lévy noise.
method Data-driven method to extract stochastic dynamical systems from noisy data.
result Established a theoretical framework and numerical algorithm to compute Lévy jump measure, drift, and diffusion.
Deep learning scheme identifies and reconstructs chaotic and stochastic systems from noisy data.
problem Challenging identification of governing equations from noisy and partial observations.
method Jointly learns inference model and governing laws using variational deep learning.
result Framework generalizes state-of-the-art methods and accounts for stochastic variabilities.
New method learns stochastic thermodynamics from system currents.
problem Understanding entropy production in complex dynamical systems.
method Constructs learning framework using currents and machine learning loss functions.
result Derives loss functions for thermodynamic functions directly from dynamics.
Adaptive neural network approximates stochastic system densities.
problem Approximating high-dimensional stochastic dynamical systems.
method Temporal KRnet (tKRnet) trained with adaptive collocation points and temporal decomposition.
result Improves density approximation for stochastic systems without curse of dimensionality.
This paper contains a summary of mathematical researches of stochastic properties of the long time behavior of a continuously observed (and interactively controlled) quantum--field top. Applications to interactively controlled stochastic computer-graphic dynamical systems are also discussed.
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.
Safe learning of stochastic dynamics with safety constraints.
problem Learning controlled stochastic dynamics with safety constraints.
method Iterative expansion of a safe control set using kernel-based confidence bounds.
result The method ensures safe exploration and efficient estimation of system dynamics.
Efficiently simulates slow dynamics of high-dimensional stochastic systems.
problem Simulating high-dimensional stochastic systems with slow dynamics and fast modes.
method Designs an algorithm to estimate an invariant manifold and its dynamics, averaging out fast modes.
result Efficient simulator of effective dynamics on low-dimensional invariant manifold.
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.
Dynamical systems are widely used in science and engineering to model systems consisting of several interacting components. Often, they can be given a causal interpretation in the sense that they not only model the evolution of the states of the system's components over time, but also describe how their evolution is af…
We propose a method to infer stochastic low-rank RNNs from neural data.
problem Fitting low-rank RNNs to noisy, stochastic neural data.
method Variational sequential Monte Carlo methods for stochastic low-rank RNNs.
result Lower dimensional latent dynamics compared to state-of-the-art methods.
The study analyzes stochastic Lie systems and their applications in various models.
problem Analyzing stochastic differential equations on manifolds.
method Coalgebra method for Hamiltonian stochastic Lie systems.
result New examples of stochastic Lie systems and Hamiltonian stochastic Lie systems are analyzed.
Efficient algorithm for unknown linear systems with convex costs.
problem Controlling an unknown linear system with stochastic convex costs.
method Optimism in the Face of Uncertainty paradigm.
result Achieves optimal T \sqrt{T} T regret-rate. Bayesian algorithm stabilizes unknown continuous-time systems from unstable data.
problem Learning and stabilizing unknown continuous-time systems with uncertain dynamics.
method Bayesian learning algorithm that learns from unstable data to stabilize the system in finite time.
result The algorithm stabilizes unknown continuous-time stochastic linear systems effectively after a short time period.
Algorithm learns stochastic system dynamics from data.
problem Recovering interpretable symbolic expressions for stochastic systems.
method Data-driven, trajectory averaging, drift-informed correction.
result Recover coefficients and densities to within 5% and 0.01 in total variation, respectively.
Machine learning infers time-reversible dynamics from data.
problem Learn time-reversible dynamics constrained by initial and final conditions.
method Machine learning algorithms solve boundary value problems for deterministic and stochastic dynamics.
result Inferred time-reversible dynamics for various types of systems.
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.
With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems…
A new flow-based Bayesian filter tackles high-dimensional nonlinear stochastic systems.
problem Bayesian filtering for high-dimensional nonlinear systems is challenging due to non-Gaussian distributions and computational limitations.
method Integrates normalizing flows to construct a latent linear state-space model with efficient density estimation and sampling.
result Demonstrates superior accuracy and efficiency in numerical experiments.
Novel method estimates complex nonlinear systems with stochastic differential equations.
problem Handling complex nonlinear dynamical systems with strong learning guarantees.
method Estimates drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled stochastic differential equations.
result Strong theoretical guarantees including finite-sample bounds for various metrics.
Surrogate models speed up RL training in dynamic systems.
problem High computational cost of high-fidelity simulations.
method Developed and tested surrogate models for RL training.
result Surrogate models can significantly accelerate RL training.
Study optimizes resource allocation in noisy systems for better control.
problem Limited attention in stochastic systems with multiplicative noise.
method Analytical and numerical methods for optimal attention allocation.
result Effective resource allocation enhances noise estimation and control decisions.
The paper uses machine learning to compute rare event probabilities in stochastic systems.
problem Characterizing rare events in stochastic dynamical systems with weak noise.
method Developed a neural network framework for computing quasipotential, most probable paths, and prefactors.
result Demonstrated higher effectiveness and accuracy of the algorithm in calculating mean exit times.
Method learns dynamics from noisy partial observations.
problem Reconstructing stochastic dynamical systems from indirect noisy data.
method Amortized path generation method for nonlinear stochastic filtering.
result Learned conditional path generator quantifies uncertainty.
This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic dynamics in a distribution-free manner. The new tools enjoy sound theory rooted in f…
New method controls mean exit time in stochastic systems using machine learning and quasipotential.
problem Controlling mean exit time in stochastic dynamical systems with white noise.
method Developed a neural network to compute the quasipotential function and designed an algorithm to calculate the controller.
result Effective and accurate control strategy demonstrated through numerical experiments.
DeepRSCN models nonlinear systems using stochastic configurations.
problem Modeling nonlinear dynamic systems efficiently.
method Incrementally constructed deep reservoir computing framework with random parameters and online weight updates.
result DeepRSCN outperforms single-layer networks in efficiency, learning, and generalization.
Novel F2NARX model improves surrogate modeling for stochastic dynamical systems.
problem Challenges in constructing accurate and efficient surrogate models for stochastic dynamical systems.
method Function-on-Function Nonlinear AutoRegressive model with eXogenous inputs (F2NARX) combining PCA and Gaussian process regression.
result F2NARX outperforms state-of-the-art NARX models in efficiency and accuracy.
Paper derives an error bound for stochastic LTI systems.
problem Stochastic LTI systems with inputs in control engineering and econometrics.
method PAC-Bayesian-Like error bound derivation.
result Derived an error bound for stochastic LTI systems.
Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters governing the properties of this nonparametric representation. The Bayesian formalism e…
VSDN models sporadic time series with neural SDEs.
problem Modeling irregular and sparse time series data.
method Variational Bayesian method and neural SDEs.
result VSDNs outperform state-of-the-art models in prediction and interpolation.
New method improves long-term forecasting of stochastic dynamical systems.
problem Improving long-term forecasting accuracy for stochastic dynamical systems.
method Combining Koopman and transfer operator theory with feature centering.
result Learning bounds ensure uniform performance on future distributions.