Gerrit Gerhartz, Francesco Alesiani, Jonathan Warrell, Henrik Christiansen, Matheus Ferraz, Mathias Niepert
Guidance and composition of generative models have applications in visual design, chemistry, and biology. Logical guidance composes conditional scores exactly for diffusion models. However, Flow Matching (FM) and Stochastic Interpolants (SI) learn velocity fields. We show that negation and exclusive disjunction admit exact conditional velocity composition on any interpolant, whereas conjunction, and therefore any formula containing one, is exact on Gaussian paths but in general incurs a drift-interaction error, so composed velocities need not sample the logical target. LOGSI solves this by using score-based re-equilibration as our principled mechanism and falling back to the Gaussian-path velocity rule as an approximate transport predictor. In non-Gaussian bridge problems, generation alternates transport steps with score re-equilibration steps. On image trans fer (EMNIST to CMNIST, CelebA) and QM9 source-to-target molecular editing with logical attribute constraints, LOGSI improves rule conformity at the same network-evaluation budget over composed-velocity baselines, while also improving fidelity on the image tasks. More broadly, LOGSI applies wherever stochastic interpolants need guidance and logical combinations of constraints are natural.
Luis Medrano-Navarro, Giacomo Baldan, Qiang Liu, Benjamin Holzschuh, Jan Hagnberger, Mathias Niepert, Nils Thuerey
Neural surrogate models for Partial Differential Equations (PDEs) on unstructured 3D geometries are often limited by poor generalization and the high cost of generating large-scale training datasets. Consequently, pre-training on massive datasets of related PDE dynamics has emerged as a critical alternative to enhance the robustness and scalability of these models. However, this strategy is neither compute- nor data-efficient, as it relies on massive pre-computed data that is very costly to generate. In this work, we introduce a disk-data-free pre-training framework tailored to both steady-state and transient regimes. For steady-state problems, we propose a geometry-driven strategy that leverages intrinsic shape descriptors to learn representations of complex 3D domains. For transient problems, we introduce a physics-driven approach based on online generation of synthetic PDE data, enabling scalable pre-training without reliance on expensive datasets. Across multiple experiments, our approach achieves faster convergence, greater data efficiency, and higher accuracy during fine-tuning, particularly under realistic low-data regimes. This methodology provides a practical pathway toward data-efficient neural emulators for large-scale simulations. Code and models are available at https://github.com/tum-pbs/GMP.