Related papers: Adaptive Probability Flow Residual Minimization fo…

Fractional-order stochastic gradient descent (FOSGD) leverages fractional exponents to capture long-memory effects in optimization. However, its utility is often limited by the difficulty of tuning and stabilizing these exponents. We…

We present a reduced order modeling (ROM) technique for subsurface multi-phase flow problems building on the recently introduced deep residual recurrent neural network (DR-RNN) [1]. DR-RNN is a physics aware recurrent neural network for…

Optimal Power Flow (OPF) is a fundamental problem in power systems. It is computationally challenging and a recent line of research has proposed the use of Deep Neural Networks (DNNs) to find OPF approximations at vastly reduced runtimes…

We derive a new adaptive leverage score sampling strategy for solving the Column Subset Selection Problem (CSSP). The resulting algorithm, called Adaptive Randomized Pivoting, can be viewed as a randomization of Osinsky's recently proposed…

The AC Optimal Power Flow (AC-OPF) problem is a core building block in electrical transmission system. It seeks the most economical active and reactive generation dispatch to meet demands while satisfying transmission operational limits. It…

Dimensionality reduction (DR) algorithms, which reduce the dimensionality of a given data set while preserving the information of the original data set as well as possible, play an important role in machine learning and data mining. Duan…

Modern GPUs are equipped with large amounts of high-bandwidth memory, enabling them to support mini-batch sizes of up to tens of thousands of training samples. However, most existing optimizers struggle to perform effectively at such a…

We extend the Weak Adversarial Neural Pushforward Method (WANPM) to fractional Fokker-Planck equations, in which the classical Laplacian diffusion operator is replaced by the fractional Laplacian of order alpha in (0, 2]. The solution…

We present a quantum computing formulation to address a challenging problem in the development of probabilistic learning on manifolds (PLoM). It involves solving the spectral problem of the high-dimensional Fokker-Planck (FKP) operator,…

Efficiently solving the Fokker-Planck equation (FPE) is central to analyzing complex parameterized stochastic systems. However, current numerical methods lack parallel computation capabilities across varying conditions, severely limiting…

We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansions, operator splitting time integration, and a new…

The optimal power flow (OPF) problem is fundamental in power system operations and planning. Large-scale renewable penetration in distribution networks calls for real-time feedback control, and hence the need for fast and distributed…

Computational Fluid Dynamics (CFD) is an important approach for analyzing flow phenomena and predicting engineering-relevant quantities. The governing physics is formulated as partial differential equations(PDEs) and solved numerically on…

Balancing policy expressiveness with the exploration-exploitation trade-off is a core challenge in online Reinforcement Learning (RL). While Stochastic Differential Equation (SDE)-based diffusion policies can represent complex, multimodal…

We introduce PF-AGD, the first parameter-free, deterministic, accelerated first-order method to achieve $O(\epsilon^{-5/3}\log(1/\epsilon))$ oracle complexity bound when minimizing sufficiently smooth, non-convex functions; this is the…

This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…

We propose to optimize neural networks with a uniformly-distributed random learning rate. The associated stochastic gradient descent algorithm can be approximated by continuous stochastic equations and analyzed within the Fokker-Planck…

Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and…

Flow matching has emerged as a powerful framework for generative modeling, offering computational advantages over diffusion models by leveraging deterministic Ordinary Differential Equations (ODEs) instead of stochastic dynamics. While…

Existing customization methods require access to multiple reference examples to align pre-trained diffusion probabilistic models (DPMs) with user-provided concepts. This paper aims to address the challenge of DPM customization when the only…