Neural Eigenfluid Bases: Spectral Objectives, Gauge, and Topology
19d
- Publicado
- Recolectado
Reduced-order models simplify fluid simulation by representing complex flows with a small number of spatial modes. Building on Laplacian Eigenfluids, we introduce Neural Eigenfluid Bases (NEB), a neural representation whose basis functions can be evaluated anywhere in space. We enforce incompressibility and impermeable boundaries directly through differential lifts and potential boundary conditions. Geometry-local orthogonalization and Rayleigh minimization then learn an ordered basis. We connect learning in potential and velocity spaces, and derive a spectral-variance relation explaining why these objectives weight approximate modes differently, even though their exact positive spectra agree. Gauge fixing reduces the number of spatial derivatives needed for potential learning, while a Dirichlet energy loss learns independent circulation fields around obstacles. With 1024 modes, both objectives keep velocity errors below 1% in periodic vortex merger. For random flows around obstacles, potential-based learning captures more initial energy and gives lower final errors than numerical Laplacian bases of the same size. The reduced state is about a thousand times smaller than the full reference model. Three-dimensional tests separate spatial reconstruction errors from errors in coefficient evolution. Precomputed Galerkin operators allow millisecond-scale updates when the same basis is reused across simulations. This provides a physically constrained basis for continuous flow reconstruction and efficient reduced-order simulation.
Autores
Baiming Zhang, Shiying Xiong, Zhecheng Wang
Categorías
overfeed.news indexa y enlaza. Publicamos un extracto breve; el artículo completo sigue en arXiv AI Papers.
Más de arXiv AI Papers
Inicia sesión para seguir esta fuente
Medical Image Segmentation: Foundation Model Adaptation versus Task-Specific Training
Foundation models pretrained on large natural-image collections are increasingly adapted for medical image segmentation, in the expectation that they will replace models trained for each task. Most comparisons, however, use data from the training distribution and a single task-specific baseline whose configuration is rarely justified, and therefore provide limited evidence of performance at new clinical sites. It also remains unclear how much of a foundation model must be adapted, and what determines this. We adapted a foundation model, DINOv2, with strategies ranging from tuning only its bias terms to full fine-tuning, and compared it with U-Nets and ResU-Nets trained from scratch. Experiments covered colonoscopy, breast ultrasound and dermoscopy, with testing on held-out data from the training source and on independent datasets from other institutions. The adapted foundation model generalised better on every external dataset. Within the training distribution, the task-specific models remained competitive when training data were abundant, and delineated boundaries more precisely, while the foundation model more often missed small lesions. Only a small fraction of the foundation model required adaptation, and the capacity needed was determined by the imaging domain rather than by the adaptation method. A widely used polyp test set was also found to duplicate images from another benchmark. Foundation-model adaptation is therefore warranted where models must work across sites, with capacity selected on the target domain.
Toward Foundation Detection Models via Example-Based Grounding in EM-DETR
DeepLearning (DL)-based Computer-Aided Diagnostic (CAD) systems have shown great promise in supporting clinicians, but their performance heavily depends on the availability of large, well-annotated datasets. In medical lesion detection, the scarcity of comprehensive, stan dardized annotations and the heterogeneity of existing datasets limit the development of robust foundation models. In this work, we introduce a novel approach to building a multi-domain foundation model for le sion detection by integrating diverse medical image datasets annotated for both anatomical structures and abnormalities. We first propose a student-teacher training strategy to effectively combine datasets with heterogeneous label spaces, mitigating catastrophic forgetting, and im proving feature learning. In addition, building on our previously pro posed example-based EM-DETR framework, we adapt it to jointly learn from multiple domain-specific datasets, enabling fine-grained, example driven detection across modalities. Our model achieves state-of-the-art (SOTA) results, with image-level AUC scores exceeding previous SOTA by 1% point on four key findings in CXRs. We achieve a leading mAP50 in CXRs and mammography, surpassing EM-DETR trained on a single dataset by 2-3% points. This approach paves the way for scalable foundation models in medical imaging that leverage heterogeneous data while maintaining robust and generalizable performance.
TorchCurves: Differentiable Parametric Curves
We present TorchCurves, a PyTorch library that treats vector-valued parametric curves as learnable primitives. Its central operation maps batches of scalar inputs to points on curves represented in B-spline or Legendre polynomial bases, with differentiation through both inputs and coefficients. Curve coefficients can be optimized jointly with the surrounding model or produced by another network. The library provides trainable modules, reusable basis modules, and a functional interface, supporting applications ranging from continuous feature embeddings to Kolmogorov-Arnold networks and functional regression. Its implementation combines classical evaluation algorithms with vectorized PyTorch operations, emphasizing readability and maintainability without custom hardware kernels. Timing experiments compare curve evaluation against NumPy and SciPy and KAN training against EfficientKAN across a range of problem sizes. The results illustrate where this generality remains computationally practical and where overhead is substantial. Library is available on GitHub at https://github.com/alexshtf/torchcurves.
AutoScaffold: AI-Guided Scaffolding for Reinforcement Learning of Language Models
Reinforcement learning with verifiable rewards (RLVR) produces rich training experience, yet outcome rewards reduce each attempt to a single number and leave most of this information unused. Training-time scaffolds, such as strategies or hints added to the prompt during training, offer a natural way to turn this information into guidance, but their design and adaptation are largely left to humans and tailored to specific domains. We introduce AutoScaffold, a unified AI-for-AI framework that turns a student's training experience into adaptive scaffolds, with minimal domain-specific information and no human intervention during training. A frozen teacher periodically examines this experience, diagnoses bottlenecks, and designs scaffolds in two forms: (i) strategies shared across a class of tasks and (ii) hints for individual hard tasks, adjusting the content and amount of support as the student learns. The scaffolds are removed at evaluation. We apply the same framework to ALFWorld, search-based QA, mathematical reasoning, and GPU kernel generation. When evaluated without scaffolds, students trained with AutoScaffold outperform those trained with the corresponding RL baselines in all four domains, with gains of 7.2 points in ALFWorld success and 4.0 points in average QA exact match. On GPU kernel generation, AutoScaffold increases the fraction of tasks with a correct kernel that runs faster than the PyTorch reference by up to 5.0 points. On math, our student surpasses QuestA's reported accuracy using approximately one-third as many student training steps. Analyses show that the teacher identifies a different failure in each task class and shifts its scaffolds from step-by-step workflows to targeted fixes as the student improves, and that its revised scaffolds help the student learn more than keeping the previous scaffold or using no scaffold.