Haixu Wu
Famous AuthorPublications
Latent Generative Solvers for Generalizable Long-Term Physics Simulation
We study long-horizon surrogate simulation across heterogeneous PDE systems. We introduce Latent Generative Solvers (LGS), a two-stage framework that (i) maps diverse PDE states into a shared latent physics space with a pretrained VAE, and (ii) learns probabilistic latent dynamics with a Transformer trained by flow matching. Our key mechanism is an uncertainty knob that perturbs latent inputs during training and inference, teaching the solver to correct off-manifold rollout drift and stabilizing autoregressive prediction. We further use flow forcing to update a system descriptor (context) from model-generated trajectories, aligning train/test conditioning and improving long-term stability. We pretrain on a curated corpus of $\sim$2.5M trajectories at $128^2$ resolution spanning 12 PDE families. LGS matches strong deterministic neural-operator baselines on short horizons while substantially reducing rollout drift on long horizons. Learning in latent space plus efficient architectural choices yields up to \textbf{70$\times$} lower FLOPs than non-generative baselines, enabling scalable pretraining. We also show efficient adaptation to an out-of-distribution $256^2$ Kolmogorov flow dataset under limited finetuning budgets. Overall, LGS provides a practical route toward generalizable, uncertainty-aware neural PDE solvers that are more reliable for long-term forecasting and downstream scientific workflows.
Brep2Shape: Boundary and Shape Representation Alignment via Self-Supervised Transformers
Boundary representation (B-rep) is the industry standard for computer-aided design (CAD). While deep learning shows promise in processing B-rep models, existing methods suffer from a representation gap: continuous approaches offer analytical precision but are visually abstract, whereas discrete methods provide intuitive clarity at the expense of geometric precision. To bridge this gap, we introduce Brep2Shape, a novel self-supervised pre-training method designed to align abstract boundary representations with intuitive shape representations. Our method employs a geometry-aware task where the model learns to predict dense spatial points from parametric Bézier control points, enabling the network to better understand physical manifolds derived from abstract coefficients. To enhance this alignment, we propose a Dual Transformer backbone with parallel streams that independently encode surface and curve tokens to capture their distinct geometric properties. Moreover, the topology attention is integrated to model the interdependencies between surfaces and curves, thereby maintaining topological consistency. Experimental results demonstrate that Brep2Shape offers significant scalability, achieving state-of-the-art accuracy and faster convergence across various downstream tasks.