Related papers: Physics-Constrained Fine-Tuning of Flow-Matching M…

We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…

Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty…

Flow-based generative modeling is a powerful tool for solving inverse problems in physical sciences that can be used for sampling and likelihood evaluation with much lower inference times than traditional methods. We propose to refine flows…

Integrating physics models within machine learning models holds considerable promise toward learning robust models with improved interpretability and abilities to extrapolate. In this work, we focus on the integration of incomplete physics…

In scientific and engineering domains, modeling high-dimensional complex systems governed by partial differential equations (PDEs) remains challenging in terms of physical consistency and numerical stability. However, existing approaches,…

Despite recent advances, goal-directed generation of structured discrete data remains challenging. For problems such as program synthesis (generating source code) and materials design (generating molecules), finding examples which satisfy…

Constrained generative modeling is fundamental to applications such as robotic control and autonomous driving, where models must respect physical laws and safety-critical constraints. In real-world settings, these constraints rarely take…

Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…

We present a generative modeling framework for synthesizing physically feasible two-dimensional incompressible flows under arbitrary obstacle geometries and boundary conditions. Whereas existing diffusion-based flow generators either ignore…

Inferring physical fields from sparse observations while strictly satisfying partial differential equations (PDEs) is a fundamental challenge in computational physics. Recently, deep generative models offer powerful data-driven priors for…

We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…

Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes. While neural networks have recently been explored for surrogate and reduced order modeling of PDE…

Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…

Granular flows govern many natural and industrial processes, yet their interior kinematics and mechanics remain largely unobservable, as experiments access only boundaries or free surfaces. Conventional numerical simulations are…

Flow matching is a recent framework to train generative models that exhibits impressive empirical performance while being relatively easier to train compared with diffusion-based models. Despite its advantageous properties, prior methods…

Precipitation results from complex processes across many scales, making its accurate simulation in Earth system models (ESMs) challenging. Existing post-processing methods can improve ESM simulations locally, but cannot correct errors in…

Diffusion models have demonstrated strong generative capabilities across scientific domains, but often produce outputs that violate physical laws. We propose a new perspective by framing physics-informed generation as a sparse reward…

Fine-tuning flow matching models is a central challenge in settings with limited data, evolving distributions, or strict efficiency demands, where unconstrained fine-tuning can erode the accuracy and efficiency gains learned during…

Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…

Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions,…