Related papers: PDE-regularized Dynamics-informed Diffusion with U…

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained…

Data assimilation (DA) improves prediction of chaotic systems by combining model forecasts with sparse, noisy observations. Many DA methods are inherently probabilistic, but accurate probabilistic DA is often computationally expensive…

In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the…

Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here,…

The application of deep learning for partial differential equation (PDE)-constrained control is gaining increasing attention. However, existing methods rarely consider safety requirements crucial in real-world applications. To address this…

Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…

The data-driven discovery of long-time macroscopic dynamics and thermodynamics of dissipative systems with particle fidelity is hampered by significant obstacles. These include the strong time-scale limitations inherent to particle…

Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…

We propose Diffusion-Informed Model Predictive Control (D-I MPC), a generic framework for uncertainty-aware prediction and decision-making in partially observable stochastic systems by integrating diffusion-based time series forecasting…

Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…

With the great success of diffusion models (DMs) in generating realistic synthetic vision data, many researchers have investigated their potential in decision-making and control. Most of these works utilized DMs to sample directly from the…

High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are…

Diffusion and flow-based models have enabled significant progress in generation tasks across various modalities and have recently found applications in predictive learning. However, unlike typical generation tasks that encourage sample…

Advanced deep learning-based approaches have been actively applied to forecast the spatiotemporal physical dynamics governed by partial differential equations (PDEs), which acts as a critical procedure in tackling many science and…

Scene flow estimation, which aims to predict per-point 3D displacements of dynamic scenes, is a fundamental task in the computer vision field. However, previous works commonly suffer from unreliable correlation caused by locally constrained…

The conditional diffusion model has been demonstrated as an efficient tool for learning robot policies, owing to its advancement to accurately model the conditional distribution of policies. The intricate nature of real-world scenarios,…

Diffusion models have shown promise in forecasting future data from multivariate time series. However, few existing methods account for recurring structures, or patterns, that appear within the data. We present Pattern-Guided Diffusion…

We develop a novel application of hybrid information divergences to analyze uncertainty in steady-state subsurface flow problems. These hybrid information divergences are non-intrusive, goal-oriented uncertainty quantification tools that…

Accurate interpolation of seismic data is crucial for improving the quality of imaging and interpretation. In recent years, deep learning models such as U-Net and generative adversarial networks have been widely applied to seismic data…

We present DEF (\textbf{\ul{D}}iffusion-augmented \textbf{\ul{E}}nsemble \textbf{\ul{F}}orecasting), a novel approach for generating initial condition perturbations. Modern approaches to initial condition perturbations are primarily…