Related papers: Moment Estimates and DeepRitz Methods on Learning …

Diffusion models are powerful generative models that achieve state-of-the-art performance in image synthesis. However, training them demands substantial amounts of data and computational resources. Continual learning would allow for…

Linear stationary reaction-convection-diffusion equations with Dirichlet boundary conditions are approximated using a simple finite difference method corresponding to central differences and the addition of a high-order stabilization term…

We study the rheology of a suspension of soft deformable droplets subjected to a pressure-driven flow. Through computer simulations, we measure the apparent viscosity as a function of droplet concentration and pressure gradient, and provide…

This study challenges strictly guaranteeing ``dissipativity'' of a dynamical system represented by neural networks learned from given time-series data. Dissipativity is a crucial indicator for dynamical systems that generalizes stability…

Earth system forecasting has traditionally relied on complex physical models that are computationally expensive and require significant domain expertise. In the past decade, the unprecedented increase in spatiotemporal Earth observation…

Probabilistic forecasting is crucial for real-world spatiotemporal systems, such as climate, energy, and urban environments, where quantifying uncertainty is essential for informed, risk-aware decision-making. While diffusion models have…

Foundation models enable prompt-based classifiers for zero-shot and few-shot learning. Nonetheless, the conventional method of employing fixed prompts suffers from distributional shifts that negatively impact generalizability to unseen…

Aerial manipulators undergo rapid, configuration-dependent changes in inertial coupling forces and aerodynamic forces, making accurate dynamics modeling a core challenge for reliable control. Analytical models lose fidelity under these…

In this work, we propose a novel phase-field model for the simulation of two-phase flows that is accurate, conservative, bounded, and robust. The proposed model conserves the mass of each of the phases, and results in bounded transport of…

Recent work has framed decision-making as a sequence modeling problem using generative models such as diffusion models. Although promising, these approaches often overlook latent factors that exhibit evolving dynamics, elements that are…

Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws are dissipative due to fluid viscosity or plasma collisions.…

With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing…

Deformable image registration aims to precisely align medical images from different modalities or times. Traditional deep learning methods, while effective, often lack interpretability, real-time observability and adjustment capacity during…

Continuous-time long-term event prediction plays an important role in many application scenarios. Most existing works rely on autoregressive frameworks to predict event sequences, which suffer from error accumulation, thus compromising…

Diffusion models have established themselves as state-of-the-art generative models across various data modalities, including images and videos, due to their ability to accurately approximate complex data distributions. Unlike traditional…

Diffusion models are renowned for their generative capabilities, yet their pretraining processes exhibit distinct phases of learning speed that have been entirely overlooked in prior post-training acceleration efforts in the community. In…

In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…

Dataset distillation enables the training of deep neural networks with comparable performance in significantly reduced time by compressing large datasets into small and representative ones. Although the introduction of generative models has…

In Multiple Object Tracking, objects often exhibit non-linear motion of acceleration and deceleration, with irregular direction changes. Tacking-by-detection (TBD) trackers with Kalman Filter motion prediction work well in…

Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…