Related papers: Using Linearized Optimal Transport to Predict the …
The indeterminate nature of human motion requires trajectory prediction systems to use a probabilistic model to formulate the multi-modality phenomenon and infer a finite set of future trajectories. However, the inference processes of most…
Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…
Non-invasive flow measurement techniques, such as particle tracking velocimetry, resolve 3D velocity fields by pairing tracer particle positions in successive time steps. These trajectories are crucial for evaluating physical quantities…
Flocking refers to collective behavior of a large number of interacting entities, where the interactions between discrete individuals produce collective motion on the large scale. We employ an agent-based model to describe the microscopic…
This work investigates variational frameworks for modeling stochastic dynamics in incompressible fluids, focusing on large-scale fluid behavior alongside small-scale stochastic processes. The authors aim to develop a coupled system of…
Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…
For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling…
We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…
The purpose of this paper is to propose a time-step-robust cell-to-cell integration of particle trajectories in 3-D unstructured meshes in particle/mesh Lagrangian stochastic methods. The main idea is to dynamically update the mean fields…
The stochastic motions of a diffusing particle contain information concerning the particle's interactions with binding partners and with its local environment. However, accurate determination of the underlying diffusive properties, beyond…
We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…
We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…
Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…
This paper is concerned with the adaptive numerical treatment of stochastic partial differential equations. Our method of choice is Rothe's method. We use the implicit Euler scheme for the time discretization. Consequently, in each step, an…
The most probable transition paths of a stochastic dynamical system are the global minimizers of the Onsager-Machlup action functional and can be described by a necessary but not sufficient condition, the Euler-Lagrange equation (a…
We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold. We neurally parametrize the metric as a spatially-varying matrix field…
This paper presents mathematical results in support of the methodology of the probabilistic learning on manifolds (PLoM) recently introduced by the authors, which has been used with success for analyzing complex engineering systems. The…
Stochastic gradient methods enable learning probabilistic models from large amounts of data. While large step-sizes (learning rates) have shown to be best for least-squares (e.g., Gaussian noise) once combined with parameter averaging,…