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Recent studies have significantly enhanced the performance of single-image super-resolution (SR) using convolutional neural networks (CNNs). While there can be many high-resolution (HR) solutions for a given input, most existing CNN-based…

Dynamic DNN optimization techniques such as layer-skipping offer increased adaptability and efficiency gains but can lead to i) a larger memory footprint as in decision gates, ii) increased training complexity (e.g., with non-differentiable…

The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…

Neural networks have been very successful in many applications; we often, however, lack a theoretical understanding of what the neural networks are actually learning. This problem emerges when trying to generalise to new data sets. The…

Optimization lies at the heart of machine learning and signal processing. Contemporary approaches based on the stochastic gradient method are non-adaptive in the sense that their implementation employs prescribed parameter values that need…

The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…

We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…

Personalized models are essential in digital health because individuals exhibit substantial physiological and behavioral heterogeneity. Yet personalization is limited by scarce and noisy user-specific data. Most existing methods rely on…

Adaptive optimization methods are well known to achieve superior convergence relative to vanilla gradient methods. The traditional viewpoint in optimization, particularly in convex optimization, explains this improved performance by arguing…

We introduce adaptive sampling methods for stochastic programs with deterministic constraints. First, we propose and analyze a variant of the stochastic projected gradient method where the sample size used to approximate the reduced…

This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…

Building on the successes of local kernel methods for approximating the solutions to partial differential equations (PDE) and the evaluation of definite integrals (quadrature/cubature), a local estimate of the error in such approximations…

We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…

Modern retrieval systems are often driven by an underlying machine learning model. The goal of such systems is to identify and possibly rank the few most relevant items for a given query or context. Thus, such systems are typically…

Predictive models that generalize well under distributional shift are often desirable and sometimes crucial to building robust and reliable machine learning applications. We focus on distributional shift that arises in causal inference from…

We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…

With the continuous improvement of the performance of object detectors via advanced model architectures, imbalance problems in the training process have received more attention. It is a common paradigm in object detection frameworks to…

Adaptive learning aims to stimulate and meet the needs of individual learners, which requires sophisticated system-level coordination of diverse tasks, including modeling learning resources, estimating student states, and making…

A novel solve-training framework is proposed to train neural network in representing low dimensional solution maps of physical models. Solve-training framework uses the neural network as the ansatz of the solution map and train the network…

Neural differential equations offer a powerful framework for modeling continuous-time dynamics, but forecasting stiff biophysical systems remains unreliable. Standard Neural ODEs and physics informed variants often require orders of…