相关论文: Towards Reliable Neural Optimizers: Permutation-Eq…

Recent developments in applying machine learning to address Alternating Current Optimal Power Flow (AC OPF) problems have demonstrated significant potential in providing close to optimal solutions for generator dispatch in near real-time.…

In deep learning, different kinds of deep networks typically need different optimizers, which have to be chosen after multiple trials, making the training process inefficient. To relieve this issue and consistently improve the model…

Routing configurations of a network should constantly adapt to traffic variations to achieve good network performance. Adaptive routing faces two main challenges: 1) how to accurately measure/estimate time-varying traffic matrices? 2) how…

Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of…

We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…

In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solutions of the partial differential equation…

In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In…

In this paper, we consider approximating the parameter-to-solution maps of parametric partial differential equations (PPDEs) using deep neural networks (DNNs). We propose an efficient approach combining reduced collocation methods (RCMs)…

Pretraining methods gain increasing attraction recently for solving PDEs with neural operators. It alleviates the data scarcity problem encountered by neural operator learning when solving single PDE via training on large-scale datasets…

The ever-increasing integration of stochastic renewable energy sources into power systems operation is making the supply-demand balance more challenging. While joint chance-constrained methods are equipped to model these complexities and…

We present a stochastic first-order optimization method specialized for deep neural networks (DNNs), ECCO-DNN. This method models the optimization variable trajectory as a dynamical system and develops a discretization algorithm that…

Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many…

Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

The main feature of the Dynamic Multi-objective Optimization Problems (DMOPs) is that optimization objective functions will change with times or environments. One of the promising approaches for solving the DMOPs is reusing the obtained…

Modern scientific data acquisition generates petabytes of data that must be transferred to geographically distant computing clusters. Conventional tools either rely on preconfigured sessions, which are difficult to tune for users without…

Operator learning for time-dependent partial differential equations (PDEs) has seen rapid progress in recent years, enabling efficient approximation of complex spatiotemporal dynamics. However, most existing methods rely on fixed time step…

This paper deals with the identification of linear stochastic dynamical systems, where the unknowns include system coefficients and noise variances. Conventional approaches that rely on the maximum likelihood estimation (MLE) require…

Existing architectures for operator learning require that the number and locations of sensors (where the input functions are evaluated) remain the same across all training and test samples, significantly restricting the range of their…

In recent years, pre-trained visual-linguistic models have demonstrated tremendous potential, becoming a crucial foundational framework for numerous downstream tasks. However, the information density between text and images is not uniformly…