Related papers: High-Dimensional Dependency Structure Learning for…

To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we proposes an Adaptive Multi-Scale Manifold Embedding (AMSME)…

Physics-based Earth system models (ESMs) are essential for attributing climate change and generating scenario projections, yet their reliance on high-resolution numerical integration makes multi-decadal experiments expensive. In parallel,…

We introduce Hindsight-Guided Momentum (HGM), a first-order optimization algorithm that adaptively scales learning rates based on the directional consistency of recent updates. Traditional adaptive methods, such as Adam or RMSprop , adapt…

We present an efficient alternating direction method of multipliers (ADMM) algorithm for segmenting a multivariate non-stationary time series with structural breaks into stationary regions. We draw from recent work where the series is…

We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the…

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…

Generalizing across disparate physical laws remains a fundamental challenge for artificial intelligence in science. Existing deep-learning solvers are largely confined to single-equation settings, limiting transfer across physical regimes…

Adaptive gradient methods such as Adam have been shown to be very effective for training deep neural networks (DNNs) by tracking the second moment of gradients to compute the individual learning rates. Differently from existing methods, we…

An inexact accelerated stochastic Alternating Direction Method of Multipliers (AS-ADMM) scheme is developed for solving structured separable convex optimization problems with linear constraints. The objective function is the sum of a…

This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…

Collaborative transportation of heavy payloads via loco-manipulation is a challenging yet essential capability for legged robots operating in complex, unstructured environments. Centralized planning methods, e.g., holistic trajectory…

We study the combination of the alternating direction method of multipliers (ADMM) with physics-informed neural networks (PINNs) for a general class of nonsmooth partial differential equation (PDE)-constrained optimization problems, where…

Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…

Many modern computer vision and machine learning applications rely on solving difficult optimization problems that involve non-differentiable objective functions and constraints. The alternating direction method of multipliers (ADMM) is a…

Imperfections and uncertainties in forecast models are often represented in ensemble prediction systems by stochastic perturbations of model equations. In this article, we present a new technique to generate model perturbations. The…

Recent advances in neural-network architecture allow for seamless integration of convex optimization problems as differentiable layers in an end-to-end trainable neural network. Integrating medium and large scale quadratic programs into a…

Several structural learning algorithms for staged tree models, an asymmetric extension of Bayesian networks, have been defined. However, they do not scale efficiently as the number of variables considered increases. Here we introduce the…

The combination of reduced basis and collocation methods enables efficient and accurate evaluation of the solutions to parameterized PDEs. In this paper, we study the stochastic collocation methods that can be combined with reduced basis…

Mesh generation is essential for accurate and efficient computational fluid dynamics simulations. To resolve critical features in the flow, adaptive mesh refinement (AMR) is routinely employed in certain regions of the computational domain,…