arXiv Machine Learning
Dynamic Quadtree Tokenization and Transformer for Adaptive Mesh PDE Forecasting
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arXiv Machine Learning
Jun 4
MeshTok: Efficient Multi-Scale Tokenization for Scalable PDE Transformers
arXiv:2606. 04366v1 Announce Type: new Abstract: Conventional patchified Transformers operate on uniform spatial partitions, distributing computational effort evenly across the domain irrespective of local features.
arXiv AI
Sep 1
APPSolver: Adaptive Patch Partitioning for Point-Wise Ship Flow Prediction on Unstructured Meshes
arXiv:2608.29355v1 Announce Type: new Abstract: Large non-uniform point sets make direct attention-based surrogate modeling costly for ship hydrodynamics. We introduce APPSolver, a point-wise flow-pr...
arXiv Machine Learning
Jun 30
Transolver-3: Scaling Up Transformer Solvers to Industrial-Scale Geometries
arXiv:2602. 04940v2 Announce Type: replace Abstract: Deep learning has emerged as a transformative tool for the neural surrogate modeling of partial differential equations (PDEs), known as neural PDE solvers.
arXiv AI
Aug 17
ArGEnT: Arbitrary Geometry-encoded Transformer for Operator Learning
arXiv:2602. 11626v3 Announce Type: replace-cross Abstract: Learning solution operators on arbitrary geometries remains a central challenge in scientific machine learning, especially for many-query simulation, physics-informed learning, and evolving geometries requiring accurate, geometry-aware predictions at arbitrary spatial locations.
arXiv AI
Jul 10
LLT: Local Linear Transformer for PDE Operator Learning
arXiv:2607. 07718v1 Announce Type: cross Abstract: Neural operators have become a common approach for learning PDE solution maps and accelerating numerical simulations.
arXiv AI
Aug 28
Successive Capacity Growth: Task-Complexity-Driven Width and Depth Expansion for Vision Transformer Encoders in JEPA World Models
The paper introduces Successive Capacity Growth (SCG), a method for adaptively expanding Vision Transformer encoders in Joint-Embedding Predictive Architectures (JEPAs). SCG starts with a minimal encoder and incrementally increases width or depth based on a task‑agnostic test‑and‑verify mechanism, while a Sketched Isotropic Gaussian Regularizer (SIGReg) keeps learned semantic dimensions independent. Experiments on multi‑object dynamics and 2D navigation tasks show that SCG achieves up to 20.3% better prediction loss than fixed small baselines and 23% better than fixed large models, with far greater parameter efficiency and no false‑positive expansions.