Related papers: Stochastic Flow Matching for Resolving Small-Scale…
Hydrodynamics provides a universal description of the emergent collective dynamics of vastly different many-body systems, based solely on their symmetries and conservation laws. Here we harness this universality, encoded in the…
This paper collects the efforts done in our previous works [P. Degond, S. Jin, L. Mieussens, A Smooth Transition Between Kinetic and Hydrodynamic Equations, J. Comp. Phys., 209 (2005) 665--694.],[P.Degond, G. Dimarco, L. Mieussens, A Moving…
The stochastic variational approach for geophysical fluid dynamics was introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parameterisations for unresolved scales. This paper applies the variational stochastic…
Accurate and efficient prediction of multi-scale flows remains a formidable challenge. Constructing theoretical models and numerical methods often involves the design and optimization of parameters. While gradient descent methods have been…
Many problems in stellar astrophysics feature flows at low Mach numbers. Conventional compressible hydrodynamics schemes frequently used in the field have been developed for the transonic regime and exhibit excessive numerical dissipation…
The convective Brinkman-Forchheimer (CBF) equations characterize the motion of incompressible fluid flows in a saturated porous medium. The small noise asymptotic for the two-time-scale stochastic convective Brinkman-Forchheimer (SCBF)…
In this work, we introduce a new method to prove the existence and uniqueness of a variational solution to the stochastic nonlinear diffusion equation $dX(t)={\rm div} [\frac{\nabla X(t)}{|\nabla X(t)|}]dt+X(t)dW(t) in…
Uncertainty quantification techniques such as the time-dependent generalized polynomial chaos (TD-gPC) use an adaptive orthogonal basis to better represent the stochastic part of the solution space (aka random function space) in time.…
A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to…
We present a framework for solving time-dependent partial differential equations (PDEs) in the spirit of the random feature method. The numerical solution is constructed using a space-time partition of unity and random feature functions.…
We propose a machine learning framework based on Flow Matching (FM) to identify critical properties in many-body systems efficiently. Using the 2D XY model as a benchmark, we demonstrate that a single network, trained only on configurations…
Flow matching as a paradigm of generative model achieves notable success across various domains. However, existing methods use either multi-round training or knowledge within minibatches, posing challenges in finding a favorable coupling…
Flow matching (FM) is a family of training algorithms for fitting continuous normalizing flows (CNFs). Conditional flow matching (CFM) exploits the fact that the marginal vector field of a CNF can be learned by fitting least-squares…
Normalizing flow-based generative models have been widely used in applications where the exact density estimation is of major importance. Recent research proposes numerous methods to improve their expressivity. However, conditioning on a…
In this article, we introduce the notion of stochastic symmetry of a differential equation. It consists in a stochastic flow that acts over a solution of a differential equation and produces another solution of the same equation. In the…
Flow Matching has limited ability in achieving one-step generation due to its reliance on learned curved trajectories. Previous studies have attempted to address this limitation by either modifying the coupling distribution to prevent…
In this paper, we propose a deep learning based reduced order modeling method for stochastic underground flow problems in highly heterogeneous media. We aim to utilize supervised learning to build a reduced surrogate model from the…
Visually-guided acoustic highlighting seeks to rebalance audio in alignment with the accompanying video, creating a coherent audio-visual experience. While visual saliency and enhancement have been widely studied, acoustic highlighting…
Predicting low-energy molecular conformations given a molecular graph is an important but challenging task in computational drug discovery. Existing state-of-the-art approaches either resort to large scale transformer-based models that…
In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…