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We introduce variational spectral learning (VSL), a machine learning framework for solving partial differential equations (PDEs) that operates directly in the coefficient space of spectral expansions. VSL offers a principled bridge between…

Sparse variable selection improves interpretability and generalization in high-dimensional learning by selecting a small subset of informative features. Recent advances in Mixed Integer Programming (MIP) have enabled solving large-scale…

Semidefinite programs (SDPs) are a particular class of convex optimization problems with applications in combinatorial optimization, operational research, and quantum information science. Seminal work by Brand\~{a}o and Svore shows that a…

We introduce a data-driven framework for approximating the convex set of $N$-representable two-electron reduced density matrices (2-RDMs). Traditional approaches characterize this set through linear matrix inequalities that define its…

Many existing procedures for detecting multiple change-points in data sequences fail in frequent-change-point scenarios. This article proposes a new change-point detection methodology designed to work well in both infrequent and frequent…

Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…

The two-electron reduced density matrix (2RDM) carries enough information to evaluate the electronic energy of a many-electron system. The variational 2RDM (v2RDM) approach seeks to determine the 2RDM directly, without knowledge of the wave…

In this work, we conduct the first systematic study of stochastic variational inequality (SVI) and stochastic saddle point (SSP) problems under the constraint of differential privacy (DP). We propose two algorithms: Noisy Stochastic…

Scintillator-SiPM Particle Detectors (SSPDs) are compact, low-power devices with applications including particle physics, underground tomography, cosmic-ray studies, and space instrumentation. They are based on a prism-shaped scintillator…

In this paper, the existing Scheduling Dimension Reduction (SDR) methods for Linear Parameter-Varying (LPV) models are reviewed and a Deep Neural Network (DNN) approach is developed that achieves higher model accuracy under scheduling…

Adaptive causal representation learning from observational data is presented, integrated with an efficient sample splitting technique within the semiparametric estimating equation framework. The support points sample splitting (SPSS), a…

There is a huge problem and time-consuming computation to optimize the IMRT treatment plan. Extracting the optimized plan from the predicted 3D3 so-called optimizing the KBP is also involved in this challenge. Some algorithms and methods…

Large language models (LLMs) are increasingly integrated into real-time machine learning applications, where safeguarding user privacy is paramount. Traditional differential privacy mechanisms often struggle to balance privacy and accuracy,…

In this paper, we introduce the Deep Finite Volume Method (DFVM), an innovative deep learning framework tailored for solving high-order (order \(\geq 2\)) partial differential equations (PDEs). Our approach centers on a novel loss function…

Only a few states in high-dimensional systems can be identified as (un)steerable using existing theoretical or experimental methods. We utilize semidefinite programming (SDP) to construct a dataset for steerability detection in…

We develop in this paper a multi-grade deep learning method for solving nonlinear partial differential equations (PDEs). Deep neural networks (DNNs) have received super performance in solving PDEs in addition to their outstanding success in…

In this work, we conduct a systematic study of stochastic saddle point problems (SSP) and stochastic variational inequalities (SVI) under the constraint of $(\epsilon,\delta)$-differential privacy (DP) in both Euclidean and non-Euclidean…

Unsupervised pre-training is a common step in developing computer vision models and large language models. In this setting, the absence of labels requires the use of similarity-based loss functions, such as contrastive loss, that favor…

Solving high-frequency oscillatory partial differential equations (PDEs) is a critical challenge in scientific computing, with applications in fluid mechanics, quantum mechanics, and electromagnetic wave propagation. Traditional…

This paper addresses the problem of domain shifts in electric motor vibration data created by new operating conditions in testing scenarios, focusing on bearing fault detection and diagnosis (FDD). The proposed method combines the Harmonic…