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This study presents incremental correction methods for refining neural network parameters or control functions entering into a continuous-time dynamic system to achieve improved solution accuracy in satisfying the interim point constraints…
Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of…
This is a technical report that extends and clarifies the results presented in [1]. The model identification problem for asymptotically stable linear time invariant systems is considered. The system output is affected by an additive noise…
Recent Monte Carlo simulations of the critical point of the restricted primitive model for ionic solutions are reported. Only the continuum version of the model is considered. A finite size scaling analysis based in the Bruce-Wilding…
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…
We prove a bound on the finite sample error of sequential Monte Carlo (SMC) on static spaces using the $L_2$ distance between interpolating distributions and the mixing times of Markov kernels. This result is unique in that it is the first…
Diffusion processes arise in many fields, and so simulating the path of a diffusion is an important problem. It is usually necessary to make some sort of approximation via model-discretization, but a recently introduced class of algorithms,…
We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test…
Practical model building processes are often time-consuming because many different models must be trained and validated. In this paper, we introduce a novel algorithm that can be used for computing the lower and the upper bounds of model…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
Simulation is a fundamental research tool in the computer architecture field. These kinds of tools enable the exploration and evaluation of architectural proposals capturing the most relevant aspects of the highly complex systems under…
Neural networks, a central tool in machine learning, have demonstrated remarkable, high fidelity performance on image recognition and classification tasks. These successes evince an ability to accurately represent high dimensional…
The EM algorithm is a powerful tool for maximum likelihood estimation with missing data. In practice, the calculations required for the EM algorithm are often intractable. We review numerous methods to circumvent this intractability, all of…
Combinatorial optimization problems are ubiquitous in industrial applications. However, finding optimal or close-to-optimal solutions can often be extremely hard. Because some of these problems can be mapped to the ground-state search of…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…
Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the…
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…