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We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, mechatronic systems. We derive the equations of motion for some typical mechatronic systems using deterministic principles…
This paper develops some mathematical models arising in behavioral sciences, particularly in psychology, which are formalized via general preferences with variable ordering structures. Our considerations are based on the recent variational…
The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…
We consider one-step methods for integrating stochastic differential equations and prove pathwise convergence using ideas from rough path theory. In contrast to alternative theories of pathwise convergence, no knowledge is required of…
Global dynamics in nonlinear stochastic systems is often difficult to analyze rigorously. Yet, many excellent numerical methods exist to approximate these systems. In this work, we propose a method to bridge the gap between computation and…
We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…
We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…
Stochastic quantization provides an alternate approach to the computation of quantum observables, by stochastically sampling phase space in a path integral. Furthermore, the stochastic variational method can provide analytical control over…
Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes…
Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…
In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…
Stochastic systems are used to model a variety of phenomena in which noise plays an essential role. In these models, one potential goal is to determine if noise can induce transitions between states, and if so, to calculate the most…
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…
The Euler-Maclaurin formula which relates a discrete sum with an integral, is generalised to the setting of Riemann-Stieltjes sums and integrals on stochastic processes whose paths are a.s. rectifiable, namely, continuous and with bounded…
We introduce a variational method for approximating distribution functions of dynamics with a ``Liouville operator'' $\hL,$ in terms of a {\em nonequilibrium action functional} for two independent (left and right) trial states. The method…
Stochastic dominance is an important concept in probability theory, econometrics and social choice theory for robustly modeling agents' preferences between random outcomes. While many works have been dedicated to the univariate case, little…
We review the application of Statistical Mechanics methods to the study of online learning of a drifting concept in the limit of large systems. The model where a feed-forward network learns from examples generated by a time dependent…
Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process…
We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…
Non-canonical equations of motion are derived from a variational principle written in symplectic form. The invariant measure of phase space and the covariant expression for the entropy are derived from non-canonical transformations of…