Loc Nguyen

We study an inverse initial-data problem for a nonlinear Schr\"odinger equation in which the initial wave field is reconstructed from lateral measurements. Our approach combines a Legendre-polynomial-exponential-time dimensional reduction…

Generative diffusion models are increasingly used for medical imaging data augmentation, but text prompting cannot produce causal training data. Re-prompting rerolls the entire generation trajectory, altering anatomy, texture, and…

Large Language Models (LLMs) have shown remarkable capabilities, but their inherent probabilistic nature often leads to inconsistency and inaccuracy in complex problem-solving tasks. This paper introduces DANA (Domain-Aware Neurosymbolic…

We propose to combine the Carleman estimate and the Newton method to solve an inverse source problem for nonlinear parabolic equations from lateral boundary data. The stability of this inverse source problem is conditionally logarithmic.…

We develop an efficient and convergent numerical method for solving the inverse problem of determining the potential of nonlinear hyperbolic equations from lateral Cauchy data. In our numerical method we construct a sequence of linear…

Collaborative filtering (CF) is an important approach for recommendation system which is widely used in a great number of aspects of our life, heavily in the online-based commercial systems. One popular algorithms in CF is the K-nearest…

This paper aims to mathematically advance the field of quantitative thermo-acoustic imaging. Given several electromagnetic data sets, we establish for the first time an analytical formula for reconstructing the absorption coefficient from…