The paper introduces BeTINN, a structured conditional neural network architecture that extends time‑induced modulation with multi‑directional time‑parameter conditioning and a joint residual pathway. BeTINN is evaluated on the Heston stochastic‑volatility PDE, showing improved accuracy for both option values and key sensitivity metrics compared to baseline models. Ablation studies highlight the contributions of each architectural component, and the authors observe that physics‑based validation loss does not fully capture derivative fidelity, underscoring the need for derivative‑aware evaluation when sensitivities are important.
By Jose Miguel Lara Rangel, Mixtli Vazquez Mendoza
The paper introduces an end‑to‑end equivariant surrogate model for three‑dimensional Rayleigh‑Bénard convection, combining an equivariant convolutional autoencoder with an equivariant convolutional LSTM that employs $G$‑steerable kernels. The architecture exploits $D_4$‑steerable kernels in vertically stacked layers and partial kernel sharing in the vertical direction to respect the system’s E(2) equivariance in the horizontal plane while handling broken translational symmetry vertically. Experiments show notable improvements in sample and parameter efficiency and better scaling to more complex dynamics.
By Fynn Fromme, Hans Harder, Christine Allen-Blanchette, Sebastian Peitz
The paper introduces the Local Gradient Neural Operator (LGNO), a lightweight and interpretable neural operator designed for field temporal evolution prediction and source identification in mechanical problems. LGNO leverages nonlinear gradient discretization priors and multilayer perceptron convolutional layers to learn translation‑invariant local kernels resembling discrete stencils, with a zero‑consistent stencil factorization that separates coefficient learning from field reconstruction. Experiments on a range of PDE benchmarks—including linear, nonlinear, static, dynamic, low‑ and high‑dimensional cases—demonstrate that LGNO achieves comparable accuracy to global neural operators while using fewer parameters and maintaining rollout stability across diffusion, flow, and quantum phenomena.
By Baiming Zhang, Jinsong Tang, Ying Xu, Lihua Chen, Shiying Xiong
arXiv:2607. 28762v1 Announce Type: new Abstract: This work embeds feature interaction modules derived from factorization machines (FMs) into physics-informed neural networks (PINNs) and neural operator learning, to enhance model expressiveness for solution manifolds of parameterized partial differential equations (PDEs).
By Quan Gu, Hongxia Liu
Physics-Informed Conformal Prediction (PI‑CP) embeds PDE residuals into the nonconformity score of split conformal prediction, yielding distribution‑free prediction intervals with provable coverage that adapt spatially to physics violations. The method demonstrates consistent 89‑91% coverage across six physics scenarios, outperforming MC Dropout and Deep Ensembles, while Fourier Neural Operators (FNO) achieve superior accuracy over CNN and DeepONet. Additionally, the authors prove that FNO’s translation equivariance limits its ability to solve PDEs with Dirichlet boundary conditions, and show that adding coordinate channels can reduce error by up to 63×.
By Michael Chin
arXiv:2603. 04430v2 Announce Type: replace Abstract: We introduce Flowers, a neural architecture for learning PDE solution operators built entirely from multihead warps.
By Till Muser, Alexandra Spitzer, Matti Lassas, Maarten V. de Hoop, Ivan Dokmani\'c