Ground-penetrating radar (GPR) B-scan image synthesis is important for data augmentation, algorithm validation, and simulation acceleration, yet generating radargrams with both visual realism and physical consistency remains challenging. Existing learning-based generative models often emphasize visual appearance but provide limited control over response geometry. In this paper, we propose PCFlow, a physics-conditioned flow matching framework for fast GPR B-scan image synthesis. The core of PCFlow is a Maxwell-informed dense physical condition field constructed from the parameterized physical model used for electromagnetic simulation, including material properties, target geometry, propagation cues, and response-domain priors. This condition field provides an interpretable interface between physical scene parameters and radar response geometry, and guides conditional flow matching in the VAE latent space toward physically feasible generation paths. We evaluate PCFlow on a gprMax-based buried-pipeline dataset with both in-distribution and out-of-distribution test cases. Experimental results show that PCFlow generates images with more accurate response geometry and high visual fidelity, demonstrating its effectiveness for controllable and physically faithful radar image synthesis.
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 quantification. Generative models, by learning distributions over spatiotemporal fields, can better handle sparsity and uncertainty. However, existing generative approaches enforce data consistency and PDE constraints simultaneously via sampling-time gradient guidance, resulting in slow and unstable inference. To this end, we propose PerFlow, a Physics-embedded rectified Flow for efficient sparse reconstruction and uncertainty quantification of spatiotemporal dynamics. PerFlow decouples observation conditioning from physics enforcement, performing guidance-free conditioning by feeding observations into rectified-flow dynamics while embedding hard physics via a constraint-preserving projection (e.g., incompressibility or conservation). Theoretically, we establish invariance guarantees to ensure that trajectories remain on the physics-consistent manifold throughout sampling. Experiments on various PDE systems demonstrate competitive reconstruction accuracy with sound physics consistency, while enabling efficient conditional sampling (e.g., 50 steps) and up to 320x faster inference than 2000-step guided diffusion baselines.
We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a differentiable post-training procedure that minimizes weak-form residuals of governing partial differential equations (PDEs), promoting physical consistency and adherence to boundary conditions without distorting the underlying learned distribution. To infer unknown physical inputs, such as source terms, material parameters, or boundary data, we augment the generative process with a learnable latent parameter predictor and propose a joint optimization strategy. The resulting model produces physically valid field solutions alongside plausible estimates of hidden parameters, effectively addressing ill-posed inverse problems in a data-driven yet physicsaware manner. We validate our method on canonical PDE benchmarks, demonstrating improved satisfaction of PDE constraints and accurate recovery of latent coefficients. Our approach bridges generative modelling and scientific inference, opening new avenues for simulation-augmented discovery and data-efficient modelling of physical systems.
Jan Tauberschmidt, Sophie Fellenz, Sebastian J. Vollmer +1
Video generation models have recently attracted substantial attention for their ability to generate visually compelling videos, yet ensuring physically consistent and plausible dynamics still remains a fundamental challenge, driving a growing line of research on physical realism in video generation. To address this challenge, motivated by the fact that physical regularities are primarily encoded in motion patterns, we propose PhysFlow, a novel two-stage framework for improving the physical plausibility of generated videos by decomposing video generation into motion-aware optical flow generation followed by motion-conditioned appearance synthesis. Specifically, PhysFlow consists of a physics-aware optical-flow video generator called PA-Flow and a flow-guided video generator called FlowRender. During the first stage, PA-Flow employs a physics-aware attention module to model how motion attributes and material properties influence global motion and local deformation, respectively, and generates an optical flow video as an explicit representation of motion. In the second stage, FlowRender leverages the decoupled motion representation as guidance to synthesize realistic textures and appearances, ultimately producing the final physically plausible video. To further support model training with explicit physical supervision, we construct PhysVideo, a physics-based video dataset generated with a physics engine and 3D-GS rendering, containing 10K foreground objects and 50K realistic video sequences with annotations of motion and material properties. Extensive experiments demonstrate that our proposed PhysFlow generates videos with superior physical plausibility while maintaining high visual fidelity compared with existing methods.