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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…
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…
Normalizing flows are a powerful class of generative models for continuous random variables, showing both strong model flexibility and the potential for non-autoregressive generation. These benefits are also desired when modeling discrete…
Synthesizing fully developed three-dimensional turbulent velocity fields remains a long-standing problem in fluid mechanics and an open challenge for generative modeling. The difficulty arises from the coexistence of extreme dimensionality,…
Reconstructing near-wall turbulence from wall-based measurements is a critical yet inherently ill-posed problem in wall-bounded flows, where limited sensing and spatially heterogeneous flow-wall coupling challenge deterministic estimation…
Reynolds-averaged Navier-Stokes (RANS) equations are widely used in engineering turbulent flow simulations. However, RANS predictions may have large discrepancies due to the uncertainties in modeled Reynolds stresses. Recently, Wang et al.…
Modern reinforcement learning (RL) algorithms have found success by using powerful probabilistic models, such as transformers, energy-based models, and diffusion/flow-based models. To this end, RL researchers often choose to pay the price…
We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…
A modeling paradigm is developed to augment predictive models of turbulence by effectively utilizing limited data generated from physical experiments. The key components of our approach involve inverse modeling to infer the spatial…
Extreme floods pose escalating risks in a changing climate, yet forecasting remains challenging due to peak flow underestimation and high uncertainty. We introduce DRUM, a diffusion-based probabilistic deep learning approach that advances…
Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…
Diffusion models have become the de facto framework for generating new datasets. The core of these models lies in the ability to reverse a diffusion process in time. The goal of this manuscript is to explain, from a PDE perspective, how…
Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…
Diffusion models surpass previous generative models in sample quality and training stability. Recent works have shown the advantages of diffusion models in improving reinforcement learning (RL) solutions. This survey aims to provide an…
Generative policies based on diffusion models and flow matching have shown strong promise for offline reinforcement learning (RL), but their applicability remains largely confined to continuous action spaces. To address a broader range of…
Weather forecasting remains a crucial yet challenging domain, where recently developed models based on deep learning (DL) have approached the performance of traditional numerical weather prediction (NWP) models. However, these DL models,…
Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic…
We propose a framework for developing wall models for large-eddy simulation that is able to capture pressure-gradient effects using multi-agent reinforcement learning. Within this framework, the distributed reinforcement learning agents…
Leveraging neural networks as surrogate models for turbulence simulation is a topic of growing interest. At the same time, embodying the inherent uncertainty of simulations in the predictions of surrogate models remains very challenging.…
Forecasting high-dimensional, PDE-governed dynamics remains a core challenge for generative modeling. Existing autoregressive and diffusion-based approaches often suffer cumulative errors and discretisation artifacts that limit long,…