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Found 16 papers, 2 papers with code
Solution of the Probabilistic Lambert Problem: Connections with Optimal Mass Transport, Schrödinger Bridge and Reaction-Diffusion PDEs
We show that the Lambert problem with endpoint joint probability density constraints is a generalized optimal mass transport (OMT) problem, thereby connecting this classical astrodynamics problem with a burgeoning area of research in modern stochastic control and stochastic machine learning.
Path Structured Multimarginal Schrödinger Bridge for Probabilistic Learning of Hardware Resource Usage by Control Software
The solution of the path structured multimarginal Schr\"{o}dinger bridge problem (MSBP) is the most-likely measure-valued trajectory consistent with a sequence of observed probability measures or distributional snapshots.
On the Contraction Coefficient of the Schrödinger Bridge for Stochastic Linear Systems
In this work, we study a priori estimates for the contraction coefficients associated with the convergence of respective Schr\"{o}dinger systems.
Neural Schrödinger Bridge with Sinkhorn Losses: Application to Data-driven Minimum Effort Control of Colloidal Self-assembly
We show that the minimum effort control of colloidal self-assembly can be naturally formulated in the order-parameter space as a generalized Schr\"{o}dinger bridge problem -- a class of fixed-horizon stochastic optimal control problems that originated in the works of Erwin Schr\"{o}dinger in the early 1930s.
Proximal Mean Field Learning in Shallow Neural Networks
We propose a custom learning algorithm for shallow over-parameterized neural networks, i. e., networks with single hidden layer having infinite width.
Convex and Nonconvex Sublinear Regression with Application to Data-driven Learning of Reach Sets
We consider estimating a compact set from finite data by approximating the support function of that set via sublinear regression.
A Physics-informed Deep Learning Approach for Minimum Effort Stochastic Control of Colloidal Self-Assembly
We propose formulating the finite-horizon stochastic optimal control problem for colloidal self-assembly in the space of probability density functions (PDFs) of the underlying state variables (namely, order parameters).
A Distributed Algorithm for Measure-valued Optimization with Additive Objective
We propose a distributed nonparametric algorithm for solving measure-valued optimization problems with additive objectives.
On the Convexity of Discrete Time Covariance Steering in Stochastic Linear Systems with Wasserstein Terminal Cost
In particular, we show that when the terminal state covariance is upper bounded, with respect to the L\"{o}wner partial order, by the covariance matrix of the desired terminal normal distribution, then our problem admits a unique global minimizing state feedback gain.
The Curious Case of Integrator Reach Sets, Part I: Basic Theory
This is the first of a two part paper investigating the geometry of the integrator reach sets, and the applications thereof.
Global Convergence of Second-order Dynamics in Two-layer Neural Networks
Recent results have shown that for two-layer fully connected neural networks, gradient flow converges to a global optimum in the infinite width limit, by making a connection between the mean field dynamics and the Wasserstein gradient flow.
Reflected Schrödinger Bridge: Density Control with Path Constraints
How to steer a given joint state probability density function to another over finite horizon subject to a controlled stochastic dynamics with hard state (sample path) constraints?
Hopfield Neural Network Flow: A Geometric Viewpoint
We provide gradient flow interpretations for the continuous-time continuous-state Hopfield neural network (HNN).
Gradient Flow Algorithms for Density Propagation in Stochastic Systems
The need for computing the transient joint PDFs subject to prior dynamics arises in uncertainty propagation, nonlinear filtering and stochastic control.
DeGroot-Friedkin Map in Opinion Dynamics is Mirror Descent
We provide a variational interpretation of the DeGroot-Friedkin map in opinion dynamics.
Proximal Recursion for Solving the Fokker-Planck Equation
We develop a new method to solve the Fokker-Planck or Kolmogorov's forward equation that governs the time evolution of the joint probability density function of a continuous-time stochastic nonlinear system.
Optimization and Control
