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, nine 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 nine 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/.

Diffusion-based generative models have reformed generative AI, and have enabled new capabilities in the science domain, for example, generating 3D structures of molecules. Due to the intrinsic problem structure of certain tasks, there is often a symmetry in the system, which identifies objects that can be converted by a group action as equivalent, hence the target distribution is essentially defined on the quotient space with respect to the group. In this work, we establish a formal framework for diffusion modeling on a general quotient space, and apply it to molecular structure generation which follows the special Euclidean group SE(3) symmetry. The framework reduces the necessity of learning the component corresponding to the group action, hence simplifies learning difficulty over conventional group-equivariant diffusion models, and the sampler guarantees recovering the target distribution, while heuristic alignment strategies lack proper samplers. The arguments are empirically validated on structure generation for small molecules and proteins, indicating that the principled quotient-space diffusion model provides a new framework that outperforms previous symmetry treatments.

AlphaFold3 introduces a diffusion-based architecture that elevates protein structure prediction to all-atom resolution with improved accuracy. This state-of-the-art performance has established AlphaFold3 as a foundation model for diverse generation and design tasks. However, its iterative design substantially increases inference time, limiting practical deployment in downstream settings such as virtual screening and protein design. We propose DCFold, a single-step generative model that attains AlphaFold3-level accuracy. Our Dual Consistency training framework, which incorporates a novel Temporal Geodesic Matching (TGM) scheduler, enables DCFold to achieve a 15× acceleration in inference while maintaining predictive fidelity. We validate its effectiveness across both structure prediction and binder design benchmarks.

Protein interaction modeling is central to protein design, which has been transformed by machine learning with applications in drug discovery and beyond. In this landscape, structure-based de novo binder design is cast as either conditional generative modeling or sequence optimization via structure predictors (``hallucination''). We argue that this is a false dichotomy and propose Proteina-Complexa, a novel fully atomistic binder generation method unifying both paradigms. We extend recent flow-based latent protein generation architectures and leverage the domain-domain interactions of monomeric computationally predicted protein structures to construct Teddymer, a new large-scale dataset of synthetic binder-target pairs for pretraining. Combined with high-quality experimental multimers, this enables training a strong base model. We then perform inference-time optimization with this generative prior, unifying the strengths of previously distinct generative and hallucination methods. Proteina-Complexa sets a new state of the art in computational binder design benchmarks: it delivers markedly higher in-silico success rates than existing generative approaches, and our novel test-time optimization strategies greatly outperform previous hallucination methods under normalized compute budgets. We also demonstrate interface hydrogen bond optimization, fold class-guided binder generation, and extensions to small molecule targets and enzyme design tasks, again surpassing prior methods. Code, models and new data will be publicly released.

Scalable sampling of molecular states in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann Generators tackle this problem by pairing a generative model, capable of exact likelihood computation, with importance sampling to obtain consistent samples under the target distribution. Current Boltzmann Generators primarily use continuous normalizing flows (CNFs) trained with flow matching for efficient training of powerful models. However, likelihood calculation for these models is extremely costly, requiring thousands of function evaluations per sample, severely limiting their adoption. In this work, we propose Few-Step Accurate Likelihoods for Continuous Flows (FALCON), a method which allows for few-step sampling with a likelihood accurate enough for importance sampling applications by introducing a hybrid training objective that encourages invertibility. We show FALCON outperforms state-of-the-art normalizing flow models for molecular Boltzmann sampling and is two orders of magnitude faster than the equivalently performing CNF model. FALCON code is available at: https://github.com/danyalrehman/FALCON.

Solving time-dependent Partial Differential Equations (PDEs) is one of the most critical problems in computational science. While Physics-Informed Neural Networks (PINNs) offer a promising framework for approximating PDE solutions, their accuracy and training speed are limited by two core barriers: gradient-descent-based iterative optimization over complex loss landscapes and non-causal treatment of time as an extra spatial dimension. We present Frozen-PINN, a novel PINN based on the principle of space-time separation that leverages random features instead of training with gradient descent, and incorporates temporal causality by construction. On nine PDE benchmarks, including challenges like extreme advection speeds, shocks, and high-dimensionality, Frozen-PINNs achieve superior training efficiency and accuracy over state-of-the-art PINNs, often by several orders of magnitude. Our work addresses longstanding training and accuracy bottlenecks of PINNs, delivering quickly trainable, highly accurate, and inherently causal PDE solvers, a combination that prior methods could not realize. Our approach challenges the reliance of PINNs on stochastic gradient-descent-based methods and specialized hardware, leading to a paradigm shift in PINN training and providing a challenging benchmark for the community.