arXiv Machine Learning
Amortizing Physics-Informed Neural Solvers via Graph Hypernetworks
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Hugging Face Trending Papers
2d ago
Amortizing Physics-Informed Neural Solvers via Graph Hypernetworks
Amortizing physics-informed neural networks (PINNs) across related PDEs requires describing each equation to a reusable solver. Coefficient vectors encode numerical parameters in predefined slots, lea...
arXiv Machine Learning
4d ago
Architecture--Optimization Co-Design for Physics-Informed Neural Networks via Layer-wise Coordinate Adaptation and Gradient Conflict Resolution
arXiv:2601.12971v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) can be limited by coordinate representations and conflicting gradients from heterogeneous physical constra...
Hugging Face Trending Papers
Jul 13
SPARC-Net: A Spectral, Causality-Aware, and Hard-Constrained Physics-Informed Architecture for Stiff and Shock-Dominated Partial Differential Equations
Physics-Informed Neural Networks (PINNs) provide a meshless approach for solving partial differential equations (PDEs), but suffer severe degradation in stiff and shock-dominated problems, where small PDE residuals can correspond to globally inaccurate solutions. We show these failures are multi-causal, arising from the concurrent interplay of (i) spectral bias against sharp features, (ii) imbalanced multi-term optimization and loss-weight collapse, (iii) violation of temporal causality, and (iv) under-resolved collocation.
arXiv Machine Learning
Aug 27
Physics-Informed Error Field Learning: A Post-Training Optimization Framework for Physics-Informed Neural Networks
Physics-Informed Error Field Learning (PIEFL) is a post‑training optimization framework for Physics‑Informed Neural Networks (PINNs). After a primary network reaches satisfactory accuracy, PIEFL introduces an auxiliary error network that learns the discrepancy between the current approximation and the exact solution by deriving error control equations under physical constraints. The learned error correction is then combined with the primary prediction, improving solution accuracy without modifying the primary network architecture and focusing computational resources on correcting existing prediction errors.
arXiv Machine Learning
Jul 14
SPARC-Net: A Spectral, Causality-Aware, and Hard-Constrained Physics-Informed Architecture for Stiff and Shock-Dominated Partial Differential Equations
arXiv:2607. 11310v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) provide a meshless approach for solving partial differential equations (PDEs), but suffer severe degradation in stiff and shock-dominated problems, where small PDE residuals can correspond to globally inaccurate solutions.
arXiv Machine Learning
Sep 7
Disentangling Attention in Deep Operator Learning: A Controlled Study of Data-Driven and Physics-Informed Architectures
The paper investigates how different attention mechanisms affect the performance of DeepONet neural operators. Five variants—varying in cross‑attention, self‑attention, tokenization, and attention depth—are trained in both data‑driven and physics‑informed settings on one‑ and two‑dimensional PDE benchmarks. Results show that per‑sensor tokenization with cross‑attention consistently reduces error, while branch self‑attention helps only in complex spatial problems, and deeper cross‑attention yields diminishing returns with higher cost.