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Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately…
In this work, we initiate the study of Hamiltonian learning for positive temperature bosonic Gaussian states, the quantum generalization of the widely studied problem of learning Gaussian graphical models. We obtain efficient protocols,…
We extend the worldline instanton technique to compute the vacuum pair production rate for spatially inhomogeneous electric background fields, with the spatial inhomogeneity being genuinely two or three dimensional, both for the magnitude…
We develop a general approach to Stein's method for approximating a random process in the path space $D([0,T]\to R^d)$ by a real continuous Gaussian process. We then use the approach in the context of processes that have a representation as…
Gradient-based meta-learning approaches have been successful in few-shot learning, transfer learning, and a wide range of other domains. Despite its efficacy and simplicity, the burden of calculating the Hessian matrix with large memory…
High-speed railway tunnel communication systems require reliable radio wave propagation prediction to ensure operational safety. However, conventional simulation methods face challenges of high computational complexity and inability to…
Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In…
The high-order hybridizable discontinuous Galerkin (HDG) method combining with an implicit iterative scheme is used to find the steady-state solution of the Boltzmann equation with full collision integral on two-dimensional triangular…
Markov chain Monte Carlo methods for exponential family models with intractable normalizing constant, such as the exchange algorithm, require simulations of the sufficient statistics at every iteration of the Markov chain, which often…
The phase-integral and worldline-instanton methods are two widely used methods to calculate Schwinger pair-production densities in electric fields of fixed direction that depend on just one time or space coordinate in the same fixed plane…
Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-investigated problem, especially when…
We prove new convergence rates for a generalized version of stochastic Nesterov acceleration under interpolation conditions. Unlike previous analyses, our approach accelerates any stochastic gradient method which makes sufficient progress…
We study meson decays using instanton methods in two string models. The first model is the old string model in flat space which combines strings and massive particles and the second is the holographic, Sakai-Sugimoto model. Using the the…
Graphon models provide a flexible nonparametric framework for estimating latent connectivity probabilities in networks, enabling a range of downstream applications such as link prediction and data augmentation. However, accurate graphon…
Numerical and anaytical studies of the instanton liquid model have allowed the determination of many hadronic parameters during the last 13 years. Most part of this thesis is devoted to the extension of the analytical methods. The meson…
Estimation of probability density function from samples is one of the central problems in statistics and machine learning. Modern neural network-based models can learn high dimensional distributions but have problems with hyperparameter…
Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94,PF95]. One difficulty in dealing with…
We present the first unified framework for rate-distortion-optimized compression and segmentation of 3D Gaussian Splatting (3DGS). While 3DGS has proven effective for both real-time rendering and semantic scene understanding, prior works…
Machine learning is rapidly finding its way into the field of computational quantum physics. One of the most popular and widely studied approaches in this direction is to use neural networks to model quantum states (NQS) in the Hamiltonian…
A fast and spectrally accurate Ewald summation method for the evaluation of stokeslet, stresslet and rotlet potentials of three-dimensional Stokes flow is presented. This work extends the previously developed Spectral Ewald method for…