Differential equations have proven to be a powerful mathematical tool in science and
engineering, leading to better understanding, prediction, and control of dynamic processes …

Recent advances in molecular biology and fluorescence microscopy imaging have made
possible the inference of the dynamics of molecules in living cells. Such inference allows us …

The weak form is a ubiquitous, well-studied, and widely-utilized mathematical tool in modern
computational and applied mathematics. In this work we provide a survey of both the history …

Accurate modeling of a thermal field is one of the fundamental requirements in engineering
thermal management in numerous industries. Existing studies have shown that using …

Multi-dimensional stochastic differential equations (SDEs) are a powerful tool to describe
dynamics of phenomena that change over time. We focus on the parametric estimation of …

Quantum superoperator learning is a pivotal task in quantum information science, enabling
accurate reconstruction of unknown quantum operations from measurement data. We …

Performing Markov chain Monte Carlo parameter estimation on complex mathematical
models can quickly lead to endless searching through highly multimodal parameter spaces …

In this paper, we study application of Le Cam's one‐step method to parameter estimation in
ordinary differential equation models. This computationally simple technique can serve as …

The computation and modeling of extents has been proposed to handle the complexity of
large-scale model identification tasks. Unfortunately, the existing extent-based framework …

We address the problem of parameter estimation for partially observed linear Ordinary
Differential Equations. Estimation from time series with standard estimators can give …