Related papers: A prediction-correction based iterative convolutio…

An emerging line of work has shown that machine-learned predictions are useful to warm-start algorithms for discrete optimization problems, such as bipartite matching. Previous studies have shown time complexity bounds proportional to some…

We present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the coupling of the atomistic and continuum models as a constrained optimization problem with virtual Dirichlet controls on the…

In this paper, we present an impulse response identification scheme that incorporates the internal positivity side-information of the system. The realization theory of positive systems establishes specific criteria for the existence of a…

In this paper, we study the stochastic convergence of regularized solutions for backward heat conduction problems. These problems are recognized as ill-posed due to the exponential decay of eigenvalues associated with the forward problems.…

Iterative Hard Thresholding (IHT) is a class of projected gradient descent methods for optimizing sparsity-constrained minimization models, with the best known efficiency and scalability in practice. As far as we know, the existing…

In applications of climate information, coarse-resolution climate projections commonly need to be downscaled to a finer grid. One challenge of this requirement is the modeling of sub-grid variability and the spatial and temporal dependence…

In this paper a novel method to solve the constant coefficient wave equation, subject to interface jump conditions, is presented. In general, such problems pose issues for standard finite difference solvers, as the inherent discontinuity in…

The Optimized Gradient Method (OGM), its strongly convex extension, the Information Theoretical Exact Method (ITEM), as well as the related Triple Momentum Method (TMM) have superior convergence guarantees when compared to the Fast Gradient…

The transmission matrix (TM) is a representation to describe the light scattering process through a scattering medium. The degree of control elements in TM is correlated with the capacity of evaluating enormous equations with tremendous…

The connectionist temporal classification (CTC) enables end-to-end sequence learning by maximizing the probability of correctly recognizing sequences during training. The outputs of a CTC-trained model tend to form a series of spikes…

We introduce the Closest Point Heat Method (CPHM), a novel approach for solving the surface Eikonal equation on general smooth surfaces. Building on the strengths of the classical heat method, such as simplicity of implementation and…

Transferability estimation identifies the best pre-trained models for downstream tasks without incurring the high computational cost of full fine-tuning. This capability facilitates deployment and advances the pre-training and fine-tuning…

This paper proposes topology optimization for considering shielding and penetrating features. Based on the fictitious physical model, which is a useful approach to control geometric features, the proposed method analyzes fictitious…

To address the problem of combined heat and power economic emission dispatch (CHPEED), a two-stage approach is proposed by combining multi-objective optimization (MOO) with integrated decision making (IDM). First, a practical CHPEED model…

Solving Stefan problems via neural networks is inherently challenged by the nonlinear coupling between the solutions and the free boundary, which results in a non-convex optimization problem. To address this, this work proposes an Operator…

This paper introduces a novel distributed optimization technique for networked systems, which removes the dependency on specific parameter choices, notably the learning rate. Traditional parameter selection strategies in distributed…

A method is developed for solving quasilinear convection diffusion problems starting on a coarse mesh where the data and solution-dependent coefficients are unresolved, the problem is unstable and approximation properties do not hold. The…

This paper explores an iterative coupling approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order…

In this paper, we consider the adaptive Eulerian--Lagrangian method (ELM) for linear convection-diffusion problems. Unlike the classical a posteriori error estimations, we estimate the temporal error along the characteristics and derive a…

Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…