Neural operators have emerged as a powerful tool for solving partial differential equations in the context of scientific machine learning. Here, we implement and train a modified Fourier neural operator as a surrogate solver for electromagnetic scattering problems and compare its data efficiency to existing methods. We further demonstrate its application to the gradient-based nanophotonic inverse design of free-form, fully three-dimensional electromagnetic scatterers, an area that has so far eluded the application of deep learning techniques.
PETScML: Second-order solvers for training regression problems in Scientific Machine Learning
Extreme Computing Research Center, King Abdullah University of Science and Technology（阿卜杜拉国王科技大学极端计算研究中心）；Mathematical Institute, University of Oxford（牛津大学数学研究所）
Neural Networks as Surrogate Solvers for Time-Dependent Accretion Disk Dynamics
Department of Physics；Astronomy, Rice University 6100 Main St, Houston, TX 77005, USA；Department of Physics \& Astronomy, University of Victoria 3800 Finnerty Rd, Victoria, BC V8P 5C2, Canada；Institute for Foundations of Data Science, Yale University Kline Tower, 219 Prospect Street, New Haven, CT 06511, USA；Kavli Institute for Astronomy；Astrophysics, Peking University 5 Yiheyuan Road, Haidian District, Beijing 100871, China；Department of Statistics；Data Science, Yale University 219 Prospect Street, New Haven, CT 06511, USA；Department of Computer Science, University of British Columbia 2366 Main Mall, Vancouver, BC V6T 1Z4, Canada；Department of Mechanical Engineering；Applied Mechanics, University of Pennsylvania 220 S 33rd St, Philadelphia, PA 19104, USA；Rice Space Institute, Rice University 6100 Main St, Houston, TX 77005, USA；National Research Council Canada Herzberg Astronomy；Astrophysics Research Centre 5071 West Saanich Rd, Victoria, BC V9E 2E7, Canada
Self-composing neural operators for high-frequency and multiscale PDE surrogates
Yau Mathematical Sciences Center, Tsinghua University（清华大学姚期智数学科学中心）；Ocean University of China（中国海洋大学）；King Abdullah University of Science and Technology（国王 Abdullah 科学与技术大学）
Physics-Informed Neural Network Surrogate for Oxygen Vacancy Dynamics in epitaxial $\mathrm{SrTiO_3}$ on Si memristors via Dynamic Spectral Optimization
When a neural surrogate cannot accelerate a solver: runtime share, closed-loop drift, and the economics of uncertainty gating in a stiff coupled simulation
ETH Zürich（苏黎世联邦理工学院）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（阿尔伯特·爱因斯坦研究所））
Physics Enhanced Deep Surrogates for the Phonon Boltzmann Transport Equation
School of Computational Science and Engineering, Georgia Institute of Technology（计算科学与工程学院，佐治亚理工学院）；Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology（士兵纳米技术研究所，麻省理工学院）
A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Laws
School of Artificial Intelligence；Suzhou Institute for Advanced Research, University of Science；Suzhou Big Data \& AI Research；Engineering Center, China；School of Mathematical Sciences, University of Science；School of Mathematical Sciences
A High-Order Relativistic Two-Fluid Electrodynamic Scheme with Consistent Reconstruction of Electromagnetic Fields and a Multidimensional Riemann Solver for Electromagnetism
