RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data

Predicting the evolution of complex physical systems remains a central problem in science and engineering. Despite rapid progress in scientific Machine Learning (ML) models, a critical bottleneck is the lack of expensive real-world data, resulting in most current models being trained and validated on simulated data. Beyond limiting the development and evaluation of scientific ML, this gap also hinders research into essential tasks such as sim-to-real transfer. We introduce RealPDEBench, the first benchmark for scientific ML that integrates real-world measurements with paired numerical simulations. RealPDEBench consists of five datasets, three tasks, eight metrics, and ten baselines. We first present five real-world measured datasets with paired simulated datasets across different complex physical systems. We further define three tasks, which allow comparisons between real-world and simulated data, and facilitate the development of methods to bridge the two. Moreover, we design eight evaluation metrics, spanning data-oriented and physics-oriented metrics, and finally benchmark ten representative baselines, including state-of-the-art models, pretrained PDE foundation models, and a traditional method. Experiments reveal significant discrepancies between simulated and real-world data, while showing that pretraining with simulated data consistently improves both accuracy and convergence. In this work, we hope to provide insights from real-world data, advancing scientific ML toward bridging the sim-to-real gap and real-world deployment. Our benchmark, datasets, and instructions are available at https://realpdebench.github.io/.

On the Guidance of Flow Matching

Flow matching has shown state-of-the-art performance in various generative tasks, ranging from image generation to decision-making, where guided generation is pivotal. However, the guidance of flow matching is more general than and thus substantially different from that of its predecessor, diffusion models. Therefore, the challenge in guidance for general flow matching remains largely underexplored. In this paper, we propose the first framework of general guidance for flow matching. From this framework, we derive a family of guidance techniques that can be applied to general flow matching. These include a new training-free asymptotically exact guidance, novel training losses for training-based guidance, and two classes of approximate guidance that cover classical gradient guidance methods as special cases. We theoretically investigate these different methods to give a practical guideline for choosing suitable methods in different scenarios. Experiments on synthetic datasets, image inverse problems, and offline reinforcement learning demonstrate the effectiveness of our proposed guidance methods and verify the correctness of our flow matching guidance framework. Code to reproduce the experiments can be found at https://github.com/AI4Science-WestlakeU/flow_guidance.