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本文提出 BeTINH 结构化条件神经求解器，通过多方向时间-参数调制与联合残差路径提升 Heston 随机波动率 PDE 参数化族的求解精度与导数保真度，强调下游敏感度指标需导数感知的评估。
A University of Amsterdam paper proposes enriched holomorphic neural networks that are harmonic by construction, combining trainable singular functions derived from local geometry with boundary-only fitting to solve 2D and 3D Laplace problems. The enriched model outperforms all tested methods, with orders-of-magnitude gains where singularities are captured exactly.
该论文提出 Gen-PINNs，一种将生成对抗网络与物理信息神经网络结合的确定性残差-对抗框架，用于求解具有尖锐波前和刚性特征的偏微分方程，在 Burgers、Allen-Cahn 和 Kuramoto-Sivashinsky 方程上相较标准 PINNs 显著提升了精度和收敛性。
This paper introduces Staged Depth Training (SDT), a representation curriculum for Physics-Informed Neural Networks (PINNs) that explicitly learns and transfers hidden representations to improve training performance.
This paper presents an Insurance Reserve Intelligence Platform using Physics-Informed and Knowledge-Informed Neural Networks for accurate and efficient term-life insurance reserve prediction, achieving high accuracy and 119.53 times faster inference than classical solvers.
This paper evaluates a physics-informed neural network for short-horizon atmospheric temperature forecasting with sparse observations, demonstrating performance improvements in specific regions but identifying limitations over complex terrain.
PINNForge is an LLM-driven evolutionary framework for automating the design of Physics-Informed Neural Networks (PINNs) for solving partial differential equations (PDEs), achieving state-of-the-art performance through execution feedback.
This paper develops an adaptive physics-informed neural network framework for solving the Blasius boundary-layer equation, achieving high accuracy with reduced wall-shear error through adaptive loss weighting and residual-based collocation.
This paper introduces a layerwise decoupling approach for structured sparsification of fully connected layers in neural networks, demonstrating improved robustness and reduced over-pruning compared to joint methods.
This paper proposes using graph hypernetworks to explicitly represent relationships in PDEs for amortizing physics-informed neural networks, showing improved accuracy in solving coupled systems.
These lecture notes introduce Physics Informed Neural Networks (PINNs) and Neural Operators, covering their implementation in PyTorch and open-source libraries like NVIDIA PhysicsNeMo, with applications in engineering and physics.
This paper identifies a failure mode in physics-informed neural networks where derivative fidelity is compromised during function-value training and provides strengthened benchmark evidence.
Anima Anandkumar describes a guest post on Terence Tao's blog detailing a method using Physics-Informed Neural Networks to find singular solutions for the Euler equations in fluid dynamics, highlighting its earlier release and broader applications in scientific computing.
A physics-informed graph attention network is proposed as a surrogate for TCAD simulation, enabling faster design space exploration by predicting mesh-node values and incorporating carrier-transport physics.
This paper compares Fourier spectral differentiation and spatial automatic differentiation in periodic physics-informed neural networks, finding that Fourier methods achieve significant training speedups and memory reductions without compromising accuracy.
DeSyR is a decoupled symbolic recovery framework that combines PINN-guided structure search with physics-informed coefficient refinement to accurately recover symbolic solutions for differential equations.
This paper proposes a Physics-Informed Error Field Learning (PIEFL) framework for Physics-Informed Neural Networks, introducing an auxiliary error network to improve solution accuracy in solving partial differential equations under computational constraints.
This study investigates the benefits of frequency decomposition for Physics-Informed Neural Networks (PINNs) by proposing a dual-branch, spectrally-gated architecture (DBSG-PINN). Ablation experiments on 1D PDE benchmarks indicate that frequency decomposition is most effective on spectrally complex problems, reducing error by up to 59.2%.
This study systematically evaluates physics-informed neural network techniques for fluid dynamics, showing that combining periodic activations with causal weighting improves performance on the Navier-Stokes vortex shedding benchmark, while further additions cause degradation due to nonlinear interactions.
The paper introduces a reference-free instrument to detect and discriminate operator misspecification in hybrid PDE-parameter learning from a single fit, demonstrating its effectiveness on a parabolic inverse problem while separating it from parameter unidentifiability.