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: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: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: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:2607. 07718v1 Announce Type: cross Abstract: Neural operators have become a common approach for learning PDE solution maps and accelerating numerical simulations.
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.
arXiv:2607. 01128v1 Announce Type: new Abstract: Operator learning for partial differential equations (PDEs) on arbitrary geometries builds fast neural surrogates for large-scale simulation.
M-plicits introduces a multiscale framework for neural implicit surfaces that models a surface as a residual sum of MLPs trained on nested neighborhoods. By localizing supervision to narrow bands around previous zero-level sets, the method achieves robustness to noisy input, avoids costly mesh extraction, and enables a multiscale sphere-tracing algorithm with analytical normal computation. Experiments on Stanford and Thingi32 show superior Chamfer distance and IoU metrics compared to existing methods while using far fewer parameters.
Mesh subdivision is a fundamental operation for converting coarse, editable meshes into high-resolution surfaces, with broad applications in digital asset creation. Classical rule-based schemes rely on fixed local refinement rules and often produce over-smoothed surfaces.
arXiv:2608. 04051v1 Announce Type: new Abstract: Real-world time series are often governed by recurring patterns, but their dominant periods may vary across datasets, forecasting settings, and individual input windows.
The paper introduces the Function‑Space Transformer (FST), a neural framework that learns from functions by using a spatially adaptive continuous latent representation. FST places features at anchors whose positions are predicted from input samples and refines these anchors through recursive function‑space interactions, allowing the representation to adapt to each input rather than relying on a fixed grid. Experiments on PDEBench (Burgers and Darcy flow) and ImageNet‑1K show that FST outperforms or matches state‑of‑the‑art baselines such as Perceiver IO and the Vision Transformer while using fewer parameters.
arXiv:2608.27883v1 Announce Type: new Abstract: Physical systems are often modeled by solution operators that map input fields, parameters, geometries, or past states to steady or future physical sta...