Finite element analysis (FEA) has been widely used to generate simulations of complex and nonlinear systems. Despite its strength and accuracy, the limitations of FEA can be summarized into two aspects: a) running high-fidelity FEA often requires significant computational cost and consumes a large amount of time; b) FEA is a deterministic method that is insufficient for uncertainty quantification (UQ) when modeling complex systems with various types of uncertainties. In this paper, a physics-informed data-driven surrogate model, named Neural Process Aided Ordinary Differential Equation (NP-ODE), is proposed to model the FEA simulations and capture both input and output uncertainties. To validate the advantages of the proposed NP-ODE, we conduct experiments on both the simulation data generated from a given ordinary differential equation and the data collected from a real FEA platform for tribocorrosion. The performances of the proposed NP-ODE and several benchmark methods are compared. The results show that the proposed NP-ODE outperforms benchmark methods. The NP-ODE method realizes the smallest predictive error as well as generates the most reasonable confidence interval having the best coverage on testing data points.
Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equations
Division of Applied Mathematics, Brown University（布朗大学应用数学系）；Department of Mathematics, University of California, Riverside（加州大学河滨分校数学系）；Department of Mathematics, University of California, Los Angeles（加州大学洛杉矶分校数学系）；Department of Mathematics and Statistics, University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校数学与统计学系）
Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels
The University of Utah（犹他大学）；The University of Sheffield（谢菲尔德大学）；University of California, Berkeley（加利福尼亚大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；International Computer Science Institute（国际计算机科学研究所）
Magnetic Resonance Spectroscopy Quantification Aided by Deep Estimations of Imperfection Factors and Macromolecular Signal
Xiamen University（厦门大学）；Philips（飞利浦）；Shanghai Electric Group CO., LTD（上海电气集团股份有限公司）；Xingaoyi Medical Equipment Company（兴奥仪医疗设备公司）；Zhongshan Hospital affiliated to Xiamen University（厦门大学附属中山医院）；McLean Hospital, Harvard Medical School（哈佛医学院麦克莱恩医院）；Xiamen University of Technology（厦门理工学院）
Out-of-Distribution Detection in Molecular Complexes via Diffusion Models for Irregular Graphs
Seminar for Applied Mathematics, Department of Mathematics and ETH AI Center, ETH Zurich（应用数学研讨会，数学系和ETH人工智能中心，瑞士苏黎世ETH学院）；Institute for Computational Life Sciences, Zurich University of Applied Sciences（计算生命科学研究所，苏黎世应用科学大学）；Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern（化学、生物化学和药学系，伯尔尼大学）
Graph Neural ODE Digital Twins for Control-Oriented Reactor Thermal-Hydraulic Forecasting Under Partial Observability
Department of Nuclear Engineering, Texas A&M University, College Station, TX 77843, USA（德克萨斯A&M大学核工程系，学院站，TX 77843，美国）；Argonne National Laboratory, Nuclear Science and Engineering Division, USA（阿贡国家实验室，核科学与工程部，美国）
