Related papers: Deterministic diffusion models for Lagrangian turb…
Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, bio-fluids, atmosphere, oceans, and astrophysics. Despite exceptional theoretical,…
Recent advances in data-driven modeling have shown that diffusion models can successfully generate synthetic Lagrangian trajectories in turbulent flows. Building on this progress, we extend the method to the joint generation of pairs of…
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…
Turbulence is prevalent in nature and industry, from large-scale wave dynamics to small-scale combustion nozzle sprays. In addition to the multi-scale nonlinear complexity and both randomness and coherent structures in its dynamics,…
Velocity-model building is a fundamental component of seismic imaging, yet it remains a challenging inverse problem due to limited data coverage, nonlinearity, and the need to integrate heterogeneous information such as well logs. We…
Computational imaging is crucial in many disciplines from autonomous driving to life sciences. However, traditional model-driven and iterative methods consume large computational power and lack scalability for imaging. Deep learning (DL) is…
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,…
We revisit the issue of Lagrangian irreversibility in the context of recent results [Xu, et al., PNAS, 111, 7558 (2014)] on flight-crash events in turbulent flows and show how extreme events in the Eulerian dissipation statistics are…
Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehesion necessitates an understanding of the space of turbulent fluid flow…
Decision-making stands as a pivotal component in the realm of autonomous vehicles (AVs), playing a crucial role in navigating the intricacies of autonomous driving. Amidst the evolving landscape of data-driven methodologies, enhancing…
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…
Diffusion Probabilistic Models stand as a critical tool in generative modelling, enabling the generation of complex data distributions. This family of generative models yields record-breaking performance in tasks such as image synthesis,…
We make a comparative analysis of some recent one-dimensional Langevin models of the acceleration of a Lagrangian fluid particle in developed turbulent flow. The class of models characterized by random intensities of noises (RIN models)…
Many real-world machine learning tasks require outputs that satisfy hard constraints, such as physical conservation laws, structured dependencies in graphs, or column-level relationships in tabular data. Existing approaches rely either on…
The local statistical and geometric structure of three-dimensional turbulent flow can be described by properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the…
Image generative models, particularly diffusion-based models, have surged in popularity due to their remarkable ability to synthesize highly realistic images. However, since these models are data-driven, they inherit biases from the…
Diffusion models show promise for dynamic scene deblurring; however, existing studies often fail to leverage the intrinsic nature of the blurring process within diffusion models, limiting their full potential. To address it, we present a…
A deterministic multi-scale dynamical system is introduced and discussed as prototype model for relative dispersion in stationary, homogeneous and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and…
Latent diffusion models achieve state-of-the-art performance on a variety of generative tasks, such as image synthesis and image editing. However, the robustness of latent diffusion models is not well studied. Previous works only focus on…
The diffusion model has recently emerged as a potent approach in computer vision, demonstrating remarkable performances in the field of generative artificial intelligence. Capable of producing high-quality synthetic images, diffusion models…