Related papers: Neural Jump Stochastic Differential Equations

We define a new variant of exclusion processes in discrete time that has jump probabilities that depend on the last jump performed. In a particular limit for the jump probabilities and in suitable scaling limits for space and time, we…

We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…

Designing video prediction models that account for the inherent uncertainty of the future is challenging. Most works in the literature are based on stochastic image-autoregressive recurrent networks, which raises several performance and…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…

Neural differential equations have recently emerged as a flexible data-driven/hybrid approach to model time-series data. This work experimentally demonstrates that if the data contains oscillations, then standard fitting of a neural…

In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…

We propose a novel problem formulation of continuous-time information propagation on heterogenous networks based on jump stochastic differential equations (SDE). The structure of the network and activation rates between nodes are naturally…

Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power.…

We demonstrate that the processes underlying on-line auction price bids and many other longitudinal data can be represented by an empirical first order stochastic ordinary differential equation with time-varying coefficients and a smooth…

Continuous-time stochastic systems have attracted a lot of attention recently, due to their wide-spread use in finance for modelling price-dynamics. More recently models taking into accounts shocks have been developed by assuming that the…

We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…

The existing literature on stochastic simulation of chemical reaction networks has a tendency to move as quickly as possible to the abstract formulation of the stochastic dynamics in terms of probabilities based on the concept of the…

In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…

Modeling brain dynamics to better understand and control complex behaviors underlying various cognitive brain functions are of interests to engineers, mathematicians, and physicists from the last several decades. With a motivation of…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

We investigate the convergence of hitting times for jump-diffusion processes. Specifically, we study a sequence of stochastic differential equations with jumps. Under reasonable assumptions, we establish the convergence of solutions to the…

Neural Stochastic Differential Equations (NSDE) have been trained as both Variational Autoencoders, and as GANs. However, the resulting Stochastic Differential Equations can be hard to interpret or analyse due to the generic nature of the…

Numerous models for supervised and reinforcement learning benefit from combinations of discrete and continuous model components. End-to-end learnable discrete-continuous models are compositional, tend to generalize better, and are more…