arXiv Machine Learning
Tackling Failure Modes of PINNs and PIKANs Using Conflict-Free Gradients
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arXiv AI
Jul 17
LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks
arXiv:2607. 14233v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE).
arXiv Machine Learning
Oct 16
The importance of tensor handling and implementation of physics-informed DeepONets
The paper presents a modified physics-informed DeepONet (PI-DeepONet) architecture that reduces computational cost by eliminating redundancy in the Branch network’s handling of input functions across collocation points. The new formulation is mathematically equivalent to the original but uses smaller input tensors and fewer network evaluations, leading to faster training while maintaining comparable predictive accuracy on 1D, 2D, and 3D linear advection problems. Experiments show up to a 3.75× speed‑up in 2D and enable feasible training of 3D models on an NVIDIA A100 GPU, where the original architecture fails due to memory limits.
arXiv Machine Learning
Aug 10
Mitigating Gradient Pathology in PINNs through Aligned Constraint
arXiv:2605. 25001v2 Announce Type: replace Abstract: While Physics-Informed Neural Networks (PINNs) are powerful for solving Partial Differential Equations (PDEs), their training is often paralyzed by gradient pathology.
arXiv Machine Learning
Sep 10
Latent-MoE: Domain-Aware Mixture-of-Experts for PDEs with Multi-Regime Physics
arXiv:2609.07814v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) struggle on PDEs whose governing physics varies across the domain. We trace this to a structural property of s...
arXiv Machine Learning
Jul 27
Latent PDE mapping for efficient physics-informed learning across geometries with limited data
arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.
arXiv AI
Oct 5
Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers
The paper presents a data‑efficient pre‑training framework for neural surrogate models solving PDEs on unstructured 3D geometries. It introduces a geometry‑driven strategy for steady‑state problems that uses intrinsic shape descriptors, and a physics‑driven approach for transient problems that generates synthetic PDE data online. Experiments show faster convergence, higher data efficiency, and improved accuracy during fine‑tuning, especially in low‑data settings.