Hong Qin

Alexander S. Glasser, Hong Qin

Yee's finite-difference method preserves two crucial properties of Maxwell's equations -- locality and symplecticity -- and thereby enjoys two computational advantages: scalability on high-performance architectures and long-time numerical accuracy. In this work, we show that Yee's method is a special case of a class of structure-preserving finite element methods -- termed generalized Yee methods (GYMs) -- that are designed to retain both crucial properties. GYMs are built from de Rham-conforming finite elements and achieve locality through sparse mass matrices and their sparse approximate inverses (SPAIs). We prove that the symplectic structure of GYMs is invariant under such sparse approximations, freeing the choice of sparsification strategy. We introduce a novel sparsification strategy, SPAI-OP, which concentrates accuracy at prescribed wave modes by operator probing. We further extend GYMs to structure-preserving electromagnetic particle-in-cell (PIC) methods, whose symplecticity over particle trajectories requires the smooth fields afforded by higher-order finite elements. GYMs therefore retain the computational virtues of Yee's method while enabling unstructured meshes, higher-order accuracy, spectral adaptivity, and symplectic particle coupling.

Jonathan Gorard, Ammar Hakim, Hong Qin et al.

Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional parameter scans and large ensembles of simulations to be performed. Such inverse problems typically involve large uncertainties, both in the measurement parameters being inverted and in the underlying physics models themselves. Monte Carlo sampling, when combined with modern non-linear dimensionality reduction techniques such as autoencoders and manifold learning, can be used to reduce the size of the parameter spaces considerably. However, there is no guarantee that the resulting combinations of parameters will be physically valid, or even mathematically consistent. In this position paper, we advocate adopting a hybrid approach that leverages our recent advances in the development of formal verification methods for numerical algorithms, with the goal of constructing parameter space restrictions with provable mathematical and physical correctness properties, whilst nevertheless respecting both experimental uncertainties and uncertainties in the underlying physical processes.

Megan Doman, Jacob Motley, Hong Qin et al.

COVID-19 related policies were extensively politicized during the 2020 election year of the United States, resulting in polarizing viewpoints. Twitter users were particularly engaged during the 2020 election year. Here we investigated whether COVID-19 related tweets were associated with the overall election results at the state level during the period leading up to the election day. We observed weak correlations between the average sentiment of COVID-19 related tweets and popular votes in two-week intervals, and the trends gradually become opposite. We then compared the average sentiments of COVID-19 related tweets between states called in favor of Republican (red states) or Democratic parties (blue states). We found that at the beginning of lockdowns sentiments in the blue states were much more positive than those in the red states. However, sentiments in the red states gradually become more positive during the summer of 2020 and persisted until the election day.

Hong Qin

A method for machine learning and serving of discrete field theories in physics is developed. The learning algorithm trains a discrete field theory from a set of observational data on a spacetime lattice, and the serving algorithm uses the learned discrete field theory to predict new observations of the field for new boundary and initial conditions. The approach to learn discrete field theories overcomes the difficulties associated with learning continuous theories by artificial intelligence. The serving algorithm of discrete field theories belongs to the family of structure-preserving geometric algorithms, which have been proven to be superior to the conventional algorithms based on discretization of differential equations. The effectiveness of the method and algorithms developed is demonstrated using the examples of nonlinear oscillations and the Kepler problem. In particular, the learning algorithm learns a discrete field theory from a set of data of planetary orbits similar to what Kepler inherited from Tycho Brahe in 1601, and the serving algorithm correctly predicts other planetary orbits, including parabolic and hyperbolic escaping orbits, of the solar system without learning or knowing Newton's laws of motion and universal gravitation. The proposed algorithms are also applicable when effects of special relativity and general relativity are important. The illustrated advantages of discrete field theories relative to continuous theories in terms of machine learning compatibility are consistent with Bostrom's simulation hypothesis.

Jian Liu, Ting Lan, Hong Qin

Traditional data cleaning identifies dirty data by classifying original data sequences, which is a class$-$imbalanced problem since the proportion of incorrect data is much less than the proportion of correct ones for most diagnostic systems in Magnetic Confinement Fusion (MCF) devices. When using machine learning algorithms to classify diagnostic data based on class$-$imbalanced training set, most classifiers are biased towards the major class and show very poor classification rates on the minor class. By transforming the direct classification problem about original data sequences into a classification problem about the physical similarity between data sequences, the class$-$balanced effect of Time$-$Domain Global Similarity (TDGS) method on training set structure is investigated in this paper. Meanwhile, the impact of improved training set structure on data cleaning performance of TDGS method is demonstrated with an application example in EAST POlarimetry$-$INTerferometry (POINT) system.