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Accurate and efficient power flow (PF) analysis is crucial in modern electrical networks' operation and planning. Therefore, there is a need for scalable algorithms that can provide accurate and fast solutions for both small and large scale…

Deep Neural Networks (DNNs) are very popular because of their high performance in various cognitive tasks in Machine Learning (ML). Recent advancements in DNNs have brought beyond human accuracy in many tasks, but at the cost of high…

An adaptive modeling method (AMM) that couples a deep neural network potential and a classical force field is introduced to address the accuracy-efficiency dilemma faced by the molecular simulation community. The AMM simulated system is…

Diffusion Models (DMs), also referred to as score-based diffusion models, utilize neural networks to specify score functions. Unlike most other probabilistic models, DMs directly model the score functions, which makes them more flexible to…

Enforcing state and input constraints during reinforcement learning (RL) in continuous state spaces is an open but crucial problem which remains a roadblock to using RL in safety-critical applications. This paper leverages invariant sets to…

To close the moment model deduced from kinetic equations, the canonical approach is to provide an approximation to the flux function not able to be depicted by the moments in the reduced model. In this paper, we propose a brand new closure…

Dynamic programming is a mathematical optimization method and a computer programming method as well. In this paper, the notion of sheaf programming in topological spaces is introduced and it is demonstrated that it relates very well to the…

We review several of the most widely used techniques for training recurrent neural networks to approximate dynamical systems, then describe a novel algorithm for this task. The algorithm is based on an earlier theoretical result that…

Cells control fluid flows with a spatial and temporal precision that far exceeds the capabilities of current microfluidic technologies. Cells achieve this superior spatio-temporal control by harnessing dynamic networks of cytoskeleton and…

The use of guidance to steer sampling toward desired outcomes has been widely explored within diffusion models, especially in applications such as image and trajectory generation. However, incorporating guidance during training remains…

Diffusion Models (DMs) have demonstrated state-of-the-art performance in content generation without requiring adversarial training. These models are trained using a two-step process. First, a forward - diffusion - process gradually adds…

This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…

Optical flow provides information on relative motion that is an important component in many computer vision pipelines. Neural networks provide high accuracy optical flow, yet their complexity is often prohibitive for application at the edge…

Differentiable programming, enabled by automatic differentiation (AD), provides a robust framework for gradient-based optimization in computational plasma physics. While optimization is often only used towards design, we demonstrate that it…

Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…

In a world made of atoms, the computer simulation of molecular systems, such as proteins in water, plays an enormous role in science. Software packages that perform these computations have been developed for decades. In molecular…

This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…

Humans can easily describe, imagine, and, crucially, predict a wide variety of behaviors of liquids--splashing, squirting, gushing, sloshing, soaking, dripping, draining, trickling, pooling, and pouring--despite tremendous variability in…

We show how to adjust the parameters of a thermodynamic computer by gradient descent in order to perform a desired computation at a specified observation time. Within a digital simulation of a thermodynamic computer, training proceeds by…

Molecular modeling is an important topic in drug discovery. Decades of research have led to the development of high quality scalable molecular force fields. In this paper, we show that neural networks can be used to train a universal…