We present our deep learning framework to solve and accelerate the Time-Dependent partial differential equation's solution of one and two spatial dimensions. We demonstrate DiffusionNet solver by solving the 2D transient heat conduction problem with Dirichlet boundary conditions. The model is trained on solution data calculated using the Alternating direction implicit method. We show the model's ability to predict the solution from any combination of seven variables: the starting time step of the solution, initial condition, four boundary conditions, and a combined variable of the time step size, diffusivity constant, and grid step size. To improve speed, we exploit our model capability to predict the solution of the Time-dependent PDE after multiple time steps at once to improve the speed of solution by dividing the solution into parallelizable chunks. We try to build a flexible architecture capable of solving a wide range of partial differential equations with minimal changes. We demonstrate our model flexibility by applying our model with the same network architecture used to solve the transient heat conduction to solve the Inviscid Burgers equation and Steady-state heat conduction, then compare our model performance against related studies. We show that our model reduces the error of the solution for the investigated problems.
Partial GFlowNet: Accelerating Convergence in Large State Spaces via Strategic Partitioning
University of Science and Technology of China (USTC)（中国科学技术大学）；Suzhou Institute for Advanced Research, USTC（先进研究所）；State Key Laboratory of Precision and Intelligent Chemistry, USTC（精密与智能化学国家重点实验室）
DOF: Accelerating High-order Differential Operators with Forward Propagation
National Key Laboratory of General Artificial Intelligence, Peking University（北京大学通用人工智能国家重点实验室）；California Institute of Technology（加州理工学院）；Stanford University（斯坦福大学）；Center for Machine Learning Research, Peking University（北京大学机器学习研究中心）
Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descent
Department of Statistics and Data Science and Department of Computer Science, University of Central Florida（统计与数据科学系和计算机科学系，中央佛罗里达大学）；Department of Computational Mathematics, Science and Engineering and Department of Mathematics, Michigan State University（计算数学、科学与工程系和数学系，密歇根州立大学）；School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University（数学与统计学系，和湖北计算科学重点实验室，武汉大学）；School of Artificial Intelligence, Wuhan University, National Center for Applied Mathematics in Hubei, and Hubei Key Laboratory of Computational Science, Wuhan, China（人工智能学院，武汉大学，湖北应用数学中心，和湖北计算科学重点实验室，中国武汉）；Institute for Advanced Study, Shenzhen University（先进研究学院，深圳大学）
Accelerating Federated Edge Learning via Optimized Probabilistic Device Scheduling
Shenzhen Research Institute of Big Data（深圳大数据研究院）；Southern University of Science and Technology（南方科技大学）；China Academy of Information and Communications Technology（中国信息通信研究院）；The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；Zhejiang University（浙江大学）
Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone
Sandia National Laboratories（桑迪亚国家实验室）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Berkeley（加州大学伯克利分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
Artificial intelligence for partial differential equations in computational mechanics: A review
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China（清华大学工程力学系）；Simulation Technology, Institute of Photonics, Leibniz University Hannover, Hannover 30167, Germany（汉诺威莱布尼茨大学光子研究所仿真技术部）；Drilling Mechanical Department, CNPC Engineering Technology RD Company Limited, Beijing 102206, China（中石油工程科技研发有限公司钻探机械部）；School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, QLD 4000, Australia（昆士兰科技大学机械、医疗与加工工程学院）；ARC Industrial Transformation Training Centre—Joint Biomechanics, Queensland University of Technology, Brisbane, QLD 4000, Australia（昆士兰科技大学 ARC 工业转型培训中心—联合生物力学）
Cluster Attention Neural Operators for Solving Parametric Partial Differential Equations
University of Chinese Academy of Sciences（中国科学院大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；International School for Advanced Studies (SISSA)（国际高等研究学院（SISSA））；Zhongyuan University of Technology（中原工学院）
