The paper introduces pcNN‑SN, a physics‑enhanced predictor‑corrector neural network algorithm that couples with the discrete ordinates (SN) method for neutron transport equations. By using high‑ and low‑accuracy data, the network predicts correction factors for coarse‑grid solutions, incorporating local physical features and dimensionless transformations to reduce input dimensionality. The algorithm maintains conservation properties and, when coupled with SN sweeps, achieves fine‑grid accuracy while reducing computation time by over 60% on a three‑dimensional test problem.
Efficient determination of the effective multiplication factor (keff) is an important computational task in reactor core neutronics analysis. Physics-informed neural networks (PINNs) incorporate neutr...
The paper introduces JI-PINN, a joint initialization strategy for physics-informed neural networks that simultaneously initializes neutron flux and the effective multiplication factor (keff) using a low-resolution approximate solution. By jointly optimizing both quantities under physical constraints, the method achieves significant reductions in computational time—up to nearly 50%—across various benchmark neutron diffusion problems while maintaining accuracy. It also reduces anomalous keff deviations, offering a more robust approach to solving K‑eigenvalue problems with PINNs.
arXiv:2606. 29874v1 Announce Type: cross Abstract: Data-driven material modeling techniques have gained significant attention due to their ability to capture complex constitutive behaviors beyond the limitations of classical material models.
arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.
arXiv:2606. 07982v1 Announce Type: new Abstract: High-dimensional transient heat diffusion under noisy boundary conditions exposes a fundamental limitation of classical numerical methods: accuracy degrades catastrophically where physical noise is unavoidable.
This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations. Such systems, found in applications like turbidity currents and thermal convection, feature strong nonlinear coupling and multiscale behavior that make high-fidelity simulations computationally expensive.
arXiv:2502. 07209v4 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) seek to solve partial differential equations (PDEs) with deep learning.
arXiv:2606. 19562v1 Announce Type: new Abstract: This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations.
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:2610.20525v1 Announce Type: new Abstract: Neural emulation need not require learning a substitute for known physics. We investigate PolyNets that couple a continuous-time neural representation...
arXiv:2606. 28519v1 Announce Type: new Abstract: Training operator-learning models for large-scale problems governed by partial differential equations (PDEs) is challenging due to the curse of dimensionality, memory constraints, and limited training data.
The paper introduces a method to amortize physics-informed neural networks (PINNs) across related partial differential equations (PDEs) by explicitly modeling equation relationships in an operator graph. Coefficient vectors encode numerical parameters, while the graph hypernetwork generates diagonal codes that initialize a meta‑trained factorized PINN for each target equation. Experiments on scalar convection‑diffusion‑reaction, two‑field Fisher‑KPP, and a capacitively coupled plasma model show that term‑based descriptors and graph conditioning improve solution accuracy compared to coefficient‑vector conditioning, especially for high‑reaction and coupled systems.