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Recently, Deng et al. (2026) proposed Generative Modeling via Drifting (GMD), a novel framework for generative tasks. This note presents an analysis of GMD through the lens of Wasserstein Gradient Flows (WGF), i.e., the path of steepest…

Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…

Recently, deep clustering methods have gained momentum because of the high representational power of deep neural networks (DNNs) such as autoencoder. The key idea is that representation learning and clustering can reinforce each other: Good…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

Attention-based neural networks have achieved state-of-the-art results on a wide range of tasks. Most such models use deterministic attention while stochastic attention is less explored due to the optimization difficulties or complicated…

Turbulent flows are of central importance across applications in science and engineering problems. For design and analysis, scientists and engineers use Computational Fluid Dynamics (CFD) simulations using turbulence models. Turbulent…

Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…

In hierarchal order of molecular geometry, we compare the performances of Geometric Quantum Machine Learning models. Two molecular datasets are considered: the simplistic linear shaped LiH-molecule and the trigonal pyramidal molecule NH3.…

A key question for machine learning approaches in particle physics is how to best represent and learn from collider events. As an event is intrinsically a variable-length unordered set of particles, we build upon recent machine learning…

We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an interacting particle method (IPM). We utilize the expressiveness…

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…

In this paper, we propose a simple yet effective method to represent point clouds as sets of samples drawn from a cloud-specific probability distribution. This interpretation matches intrinsic characteristics of point clouds: the number of…

With the rapidly growing model complexity and data volume, training deep generative models (DGMs) for better performance has becoming an increasingly more important challenge. Previous research on this problem has mainly focused on…

We introduce the framework of continuous--depth graph neural networks (GNNs). Graph neural ordinary differential equations (GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of…

We present a Machine Learning approach to solve electronic quantum transport equations of one-dimensional nanostructures. The transmission coefficients of disordered systems were computed to provide training and test datasets to the…

Diffusion models have emerged as preeminent contenders in the realm of generative models. Distinguished by their distinctive sequential generative processes, characterized by hundreds or even thousands of timesteps, diffusion models…

Deep Gaussian Processes (DGPs) compose GP layers to warp inputs, enabling improved emulation of computer models with nonstationary input-output behavior compared with ordinary GPs. In contrast to GPs, the predictive uncertainty for DGP…

Recommendation system algorithm based on multi-task learning (MTL) is the major method for Internet operators to understand users and predict their behaviors in the multi-behavior scenario of platform. Task correlation is an important…

Uncertainty Quantification (UQ) presents a pivotal challenge in the field of Artificial Intelligence (AI), profoundly impacting decision-making, risk assessment and model reliability. In this paper, we introduce Credal and Interval Deep…

The diffusive transport distance, a novel pseudo-metric between probability measures on the real line, is introduced. It generalizes Martingale optimal transport, and forms a hierarchy with the Hellinger and the Wasserstein metrics. We…