Related papers: A Dynamic Programming Approach to the Parisi Funct…
We report large-scale simulations of the three-dimensional Edwards-Anderson Ising spin glass system using the recently introduced multi-overlap Monte Carlo algorithm. In this approach the temperature is fixed and two replica are coupled…
We propose a method of approximating multivariate Gaussian probabilities using dynamic programming. We show that solving the optimization problem associated with a class of discrete-time finite horizon Markov decision processes with…
We prove the dynamic programming principle (DPP) in a class of problems where an agent controls a $d$-dimensional diffusive dynamics via both classical and singular controls and, moreover, is able to terminate the optimisation at a time of…
The super-parametric density estimators and its related algorism were suggested by Y. -S. Tsai et al [7]. The number of parameters is unlimited in the super- parametric estimators and it is a general theory in sense of unifying or…
We introduce a simple two-dimensional spin model with short-range interactions which shows glassy behavior despite a Hamiltonian which is completely homogeneous and possesses no randomness. We solve exactly for both the static partition…
This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use…
We consider stochastic dynamic programming problems with high-dimensional, discrete state-spaces and finite, discrete-time horizons that prohibit direct computation of the value function from a given Bellman equation for all states and time…
This paper develops a comprehensive probabilistic setup to compute approximating functions in active subspaces. Constantine et al. proposed the active subspace method in (Constantine et al., 2014) to reduce the dimension of computational…
Mechanistic knowledge about the physical world is virtually always expressed via partial differential equations (PDEs). Recently, there has been a surge of interest in probabilistic PDE solvers -- Bayesian statistical models mostly based on…
The concepts of sparsity, and regularised estimation, have proven useful in many high-dimensional statistical applications. Dynamic factor models (DFMs) provide a parsimonious approach to modelling high-dimensional time series, however, it…
We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…
A general formulation of the equilibrium state of a many-electron system in terms of a (mixed-state, ensemble) density matrix operator in the Fock space, based on the maximum entropy principle, is introduced. Various characteristic…
We study the problem of algorithmically optimizing the Hamiltonian $H_N$ of a spherical or Ising mixed $p$-spin glass. The maximum asymptotic value $\mathsf{OPT}$ of $H_N/N$ is characterized by a variational principle known as the Parisi…
Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft…
The aim of this paper is to address optimality of stochastic control strategies via dynamic programming subject to total variation distance ambiguity on the conditional distribution of the controlled process. We formulate the stochastic…
The modeling of dynamical systems is essential in many fields, but applying machine learning techniques is often challenging due to incomplete or noisy data. This study introduces a variant of stochastic interpolation (SI) for probabilistic…
It was proved by Michel Talagrand in [10] that the Parisi formula for the free energy in the Sherrington-Kirkpatrick model is differentiable with respect to inverse temperature parameter. We present a simpler proof of this result by using…
Since its development, Stokesian Dynamics has been a leading approach for the dynamic simulation of suspensions of particles at arbitrary concentrations with full hydrodynamic interactions. Although originally developed for the simulation…
We develop a quenched thermodynamic formalism for random dynamical systems generated by countably branched, piecewise-monotone mappings of the interval that satisfy a random covering condition. Given a random contracting potential $\varphi$…
In this paper we study optimal control problems in Wasserstein spaces, which are suitable to describe macroscopic dynamics of multi-particle systems. The dynamics is described by a parametrized continuity equation, in which the Eulerian…