Related papers: Optimal-Transport-Guided Functional Flow Matching …
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…
Modeling complex systems that evolve toward equilibrium distributions is important in various physical applications, including molecular dynamics and robotic control. These systems often follow the stochastic gradient descent of an…
The AC Optimal Power Flow (AC-OPF) is a key building block in many power system applications. It determines generator setpoints at minimal cost that meet the power demands while satisfying the underlying physical and operational…
The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost…
Generative policies based on diffusion and flow matching achieve strong performance in robotic manipulation by modeling multi-modal human demonstrations. However, their reliance on iterative Ordinary Differential Equation (ODE) integration…
Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for learning stochastic process priors on function spaces. OFM…
Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for…
While text-to-video diffusion models have made significant strides, many still face challenges in generating videos with temporal consistency. Within diffusion frameworks, guidance techniques have proven effective in enhancing output…
Physics-constrained generative modeling aims to produce high-dimensional samples that are both physically consistent and distributionally accurate, a task that remains challenging due to often conflicting optimization objectives. Recent…
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…
Denoising Diffusion Probabilistic Models (DDPMs) have established a new state-of-the-art in generative image synthesis, yet their deployment is hindered by significant computational overhead during inference, often requiring up to 1,000…
Modeling transition-continuum hypersonic flows poses significant challenges due to thermodynamic nonequilibrium and the associated breakdown of the continuum assumption. Standard continuum models such as the Navier-Stokes equations are…
Synthetic data generation is an important tool for privacy-preserving data sharing. Although diffusion models have set recent benchmarks, flow matching (FM) offers a promising alternative. This paper presents different ways to implement FM…
This work introduces a data-driven, non-intrusive reduced-order modeling (ROM) framework that leverages Optimal Transport (OT) for multi-fidelity and parametric problems in two-phase flows modelling. Building upon the success of…
Deep generative models, particularly diffusion and flow matching models, have recently shown remarkable potential in learning complex policies through imitation learning. However, the safety of generated motions remains overlooked,…
Optimal transport (OT) theory provides a principled framework for modeling mass movement in applications such as mobility, logistics, and economics. Classical formulations, however, generally ignore capacity limits that are intrinsic in…
We provide a theoretical analysis for end-to-end training Discrete Flow Matching (DFM) generative models. DFM is a promising discrete generative modeling framework that learns the underlying generative dynamics by training a neural network…
Flow-based generative models provide strong unconditional priors for inverse problems, but guiding their dynamics for conditional generation remains challenging. Recent work casts training-free conditional generation in flow models as an…
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…
Data-driven emulation of nonlinear dynamics is challenging due to long-range skill decay that often produces physically unrealistic outputs. Recent advances in generative modeling aim to address these issues by providing uncertainty…