Related papers: Time-Reversible Bridges of Data with Machine Learn…

Time-reversal symmetry arises naturally as a structural property in many dynamical systems of interest. While the importance of hard-wiring symmetry is increasingly recognized in machine learning, to date this has eluded time-reversibility.…

Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…

Statistical divergences are important tools in data analysis, information theory, and statistical physics, and there exist well known inequalities on their bounds. However, in many circumstances involving temporal evolution, one needs…

This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…

Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…

A machine learning technique is proposed for quantifying uncertainty in power system dynamics with spatiotemporally correlated stochastic forcing. We learn one-dimensional linear partial differential equations for the probability density…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

When optimizing problems with uncertain parameter values in a linear objective, decision-focused learning enables end-to-end learning of these values. We are interested in a stochastic scheduling problem, in which processing times are…

Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…

Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…

We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition…

We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…

We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…

The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport…

Despite the striking successes of deep neural networks trained with gradient-based optimization, these methods differ fundamentally from their biological counterparts. This gap raises key questions about how nature achieves robust,…

Many problems in computational science and engineering become one-to-many after coarse graining, partial observation, or inverse reconstruction: a resolved state may not determine a unique subgrid forcing, a structural descriptor may not…

Learning-based control methods typically assume stationary system dynamics, an assumption often violated in real-world systems due to drift, wear, or changing operating conditions. We study reinforcement learning for control under…

This paper is devoted to studying an infinite time horizon stochastic recursive control problem with jumps, where infinite time horizon stochastic differential equation and backward stochastic differential equation with jumps describe the…

It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…

Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…