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.
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.
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.
PASTIS selects minimal models from stochastic dynamics data.
problem Overfitting in model selection for stochastic dynamics.
method Combining likelihood-estimation statistics with extreme value theory.
result PASTIS reliably identifies minimal models, even with low sampling rates or error.
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.
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.
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.
Study on test risk dynamics in learning theory with stochastic gradient flow.
problem Understanding test risk in stochastic gradient flow dynamics.
method Path integral formulation for small learning rates, explicit computation for weak features.
result Explicit corrections due to stochastic term in dynamics, good agreement with simulations.
Improved noise estimation in latent neural SDEs enhances model accuracy.
problem Latent neural SDEs underestimate noise, limiting their stochastic dynamics modeling.
method Explicit additional noise regularization in the loss function.
result Model accurately captures diffusion component of stochastic time series 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.
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.
Improves model accuracy for neural nets in stochastic dynamics with partial prior knowledge.
problem Stability and accuracy in neural nets modeling stochastic dynamics with many parameters.
method Three steps: probabilistic weights, partial knowledge incorporation, and PAC-Bayesian training.
result Improved model fit with partial and noisy prior knowledge.
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.
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.
Neural Processes combine the strengths of neural networks and Gaussian processes to achieve both flexible learning and fast prediction in stochastic processes. However, a large class of problems comprises underlying temporal dependency structures in a sequence of stochastic processes that Neural Processes (NP) do not e…
A framework learns multiscale dynamics from single trajectories using normalizing flows.
problem Learning effective stochastic dynamics from single observed paths of slow variables.
method Data-driven approach based on coupled multiscale SDEs, stochastic averaging, and normalizing flows for density modeling.
result Scalable approach to capturing epistemic uncertainty in multiscale systems.
Paper models Bitcoin market dynamics using 1+1D field theory.
problem Understanding stylized facts in Bitcoin markets.
method Collects order-book datasets, applies KPZ-like stochastic equations.
result Predicts order book dynamics with high precision.
In this paper we study how to learn stochastic, multimodal transition dynamics in reinforcement learning (RL) tasks. We focus on evaluating transition function estimation, while we defer planning over this model to future work. Stochasticity is a fundamental property of many task environments. However, discriminative f…
SGD in DLNs reveals feature learning dynamics.
problem Understanding SGD dynamics in DLNs during saddle-to-saddle training.
method Stochastic Langevin dynamics with anisotropic, state-dependent noise; one-dimensional per-mode SDEs; Boltzmann distribution approximation.
result SGD noise encodes feature learning progression but does not alter saddle-to-saddle dynamics.
The paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jump in logarithm of VIX, we derive a linear relation between the stochastic volatility factor and VVIX index. We detect the exist…
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…
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.
Analyzes high-dimensional SGD dynamics using DMFT.
problem Understanding the high-dimensional behavior of multi-pass SGD with small batch sizes.
method Derives DMFT equations for high-dimensional SGD dynamics.
result Proves DMFT equations characterize the asymptotic distribution of SGF parameters.
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.
Study models forest transitions with deep learning for parameter estimation.
problem Complex dynamics of forest, agricultural, and abandoned lands.
method Developed a stochastic differential equation model and used deep learning for parameter estimation.
result Deep learning approach estimates model parameters from time-series data.
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.
New model predicts dynamic tax evasion with audits and imitation.
problem Static treatment of tax compliance and evasion in Bertotti and Modanese model.
method Piecewise Deterministic Markov Processes (PDMPs) for audits and imitation mechanisms.
result Model shows persistent fluctuations and stationary distribution, not extreme equilibrium.
We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do…
New dynamics for SGD in small learning rate regime.
problem Improving stochastic gradient descent in small learning rate regime.
method Introducing stochastic modified flows and distribution dependent stochastic modified flows.
result Captures fluctuating dynamics of SGD in small learning rate - infinite width scaling regime.
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.
Stochastic stability is a popular solution concept for stochastic learning dynamics in games. However, a critical limitation of this solution concept is its inability to distinguish between different learning rules that lead to the same steady-state behavior. We address this limitation for the first time and develop a …
Modeling stochastic arbitrage bubbles in Black-Scholes framework.
problem Analyzing arbitrage bubbles in financial markets.
method Developed a generalized Black-Scholes equation with stochastic arbitrage bubbles.
result The Black-Scholes model is a low-energy limit of a stochastic model.
One of the challenges in model-based control of stochastic dynamical systems is that the state transition dynamics are involved, and it is not easy or efficient to make good-quality predictions of the states. Moreover, there are not many representational models for the majority of autonomous systems, as it is not easy …
Foundational brain dynamics model using stochastic optimal control.
problem Complex and noisy fMRI signals in brain dynamics.
method Continuous-discrete state space model with amortized inference and locally linear approximations.
result State-of-the-art results across various downstream tasks.
Deep learning solves complex stochastic control with jumps.
problem Solving high-dimensional stochastic control tasks with jumps.
method Model-based approach using two neural networks, iteratively trained with objectives derived from the Hamilton-Jacobi-Bellman equation.
result Demonstrates effectiveness in solving complex high-dimensional stochastic control tasks.
Improved sampling efficiency with Random Reshuffling for Langevin dynamics.
problem Sampling efficiency in stochastic gradient algorithms.
method Random Reshuffling for Stochastic Gradient Langevin Dynamics (SGLD).
result Random Reshuffling leads to improved performance in sampling.
Paper introduces a new volatility model for natural gas markets and discusses swing option pricing.
problem Modeling price and storage dynamics in natural gas markets with path-dependent volatility.
method Developed a novel stochastic path-dependent volatility model and used deep learning for swing option pricing.
result Proposed a deep learning method for numerical approximations of swing option pricing.
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.
Improved privacy analysis for stochastic gradient descent.
problem Analyzing privacy leakage in noisy stochastic gradient descent.
method Modeling Rényi divergence dynamics with Langevin diffusions, proving exponential privacy loss convergence for smooth and strongly convex objectives.
result Privacy loss converges exponentially fast for smooth and strongly convex objectives under constant step size.
In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid. Active traders are characterised by the decision to buy, (+1), or sell, (-1), a …
We propose an analytically tractable class of models for the dynamics of a limit order book, described through a stochastic partial differential equation (SPDE) with multiplicative noise for the order book centered at the mid-price, along with stochastic dynamics for the mid-price which is consistent with the order flo…
Neural SVEs model complex systems with memory, outperforming traditional methods.
problem Modeling systems with memory effects and irregular behavior.
method Introducing neural stochastic Volterra equations as a physics-inspired architecture.
result Neural SVEs outperform neural SDEs and DeepONets in various applications.
Model for valuing options on epidemic spread.
problem Valuation of options on epidemic spread during an outbreak.
method Stochastic differential SIR model for epidemic dynamics.
result Parsimonious model for option valuation on epidemic spread.
In this paper, we propose a novel technique to implement stochastic gradient methods, which are beneficial for learning from large datasets, through accelerated stochastic dynamics. A stochastic gradient method is based on mini-batch learning for reducing the computational cost when the amount of data is large. The sto…
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…
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.
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.
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.