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Leveraging the Wasserstein distance -- a summation of sample-wise transport distances in data space -- is advantageous in many applications for measuring support differences between two underlying density functions. However, when supports…

Accurate characterization of subsurface heterogeneity is important for the safe and effective implementation of geological carbon storage (GCS) projects. This paper explores how machine learning methods can enhance data assimilation for GCS…

We consider in this paper a challenging problem of simulating fluid flows, in complex multiscale media possessing multi-continuum background. As an effort to handle this obstacle, model reduction is employed. In \cite{rh2}, homogenization…

Existing rectified flow models are based on linear trajectories between data and noise distributions. This linearity enforces zero curvature, which can inadvertently force the image generation process through low-probability regions of the…

Subsurface geomodeling plays a critical role in reservoir characterization, uncertainty quantification, and subsurface flow prediction. However, integrating heterogeneous sources of geological information, including conceptual geological…

We introduce Prior-Informed Flow Matching (PIFM), a conditional flow model for graph reconstruction. Reconstructing graphs from partial observations remains a key challenge; classical embedding methods often lack global consistency, while…

We propose the Vortex Particle Flow Map (VPFM) method to simulate incompressible flow with complex vortical evolution in the presence of dynamic solid boundaries. The core insight of our approach is that vorticity is an ideal quantity for…

The volume of scientific data produced for and by numerical simulation workflows is increasing at an incredible rate. This raises concerns either in computability, interpretability, and sustainability. This is especially noticeable in earth…

Guidance of generative models is typically achieved by modifying the probability flow vector field through the addition of a guidance field. In this paper, we instead propose the Source-Guided Flow Matching (SGFM) framework, which modifies…

Computational Fluid Dynamics (CFD) is widely used in aerospace, energy, and biology to model fluid flow, heat transfer, and chemical reactions. While Large Language Models (LLMs) have transformed various domains, their application in CFD…

Coflow provides a key application-layer abstraction for capturing communication patterns, enabling the efficient coordination of parallel data flows to reduce job completion times in distributed systems. Modern data center networks (DCNs)…

In situ approaches can accelerate the pace of scientific discoveries by allowing scientists to perform data analysis at simulation time. Current in situ workflow systems, however, face challenges in handling the growing complexity and…

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation…

Physical Reservoir Computing (PRC) leverages the intrinsic nonlinear dynamics of physical substrates, mechanical, optical, spintronic, and beyond, as fixed computational reservoirs, offering a compelling paradigm for energy-efficient and…

Functional data, i.e., smooth random functions observed over a continuous domain, are increasingly available in areas such as biomedical research, health informatics, and epidemiology. However, effective statistical analysis for functional…

This paper introduces a Particle Flow Map Level Set (PFM-LS) method for high-fidelity interface tracking. We store level-set values, gradients, and Hessians on particles concentrated in a narrow band around the interface, advecting them via…

The Wasserstein distance is a discrepancy measure between probability distributions, defined by an optimal transport problem. It has been used for various tasks such as retrieving similar items in high-dimensional images or text data. In…

The study of alloys using computational methods has been a difficult task due to the usually unknown stoichiometry and local atomic ordering of the different structures experimentally. In order to combat this, first-principles methods have…

Flow Matching (FM) generative models offer efficient simulation-free training and deterministic sampling, but their practical deployment is challenged by high-precision parameter requirements. We adapt optimal transport (OT)-based…

Simulating trajectories of dynamical systems is a fundamental problem in a wide range of fields such as molecular dynamics, biochemistry, and pedestrian dynamics. Machine learning has become an invaluable tool for scaling physics-based…