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Tensor Factor Models (TFM) are appealing dimension reduction tools for high-order large-dimensional tensor time series, and have wide applications in economics, finance and medical imaging. In this paper, we propose a projection estimator…
We present an implementation of algorithms for the symbolic integration of hyperlogarithms multiplied by rational functions in the computer algebra system FORM. This implementation encompasses cases where hyperlogarithms have rational…
Current challenges in developing foundational models for volumetric imaging data, such as magnetic resonance imaging (MRI), stem from the computational complexity of training state-of-the-art architectures in high dimensions and curating…
We present a fully non-intrusive parametric reduced-order modeling (PROM) framework for geometrically nonlinear structures subject to geometric variations. The method builds upon equation-driven Galerkin ROMs constructed from vibration…
Machine learning has been widely used for predicting material properties. However, efficient prediction of lattice thermal conductivity ($\kappa_\mathrm{L}$) remains a long-standing challenge, primarily due to the scarcity of high-quality…
This work explores an unexpected application of Implicit Computational Complexity (ICC) to parallelize loops in imperative programs. Thanks to a lightweight dependency analysis, our algorithm allows splitting a loop into multiple loops that…
Reinforcement learning has been successfully applied to the problem of tuning PID controllers in several applications. The existing methods often utilize function approximation, such as neural networks, to update the controller parameters…
We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…
Recently, the transformer architecture has enabled substantial progress in many areas of pattern recognition and machine learning. However, as with other neural network models, there is currently no general method available to explain their…
We introduce and explore an approach for constructing force fields for small molecules, which combines intuitive low body order empirical force field terms with the concepts of data driven statistical fits of recent machine learned…
Factor graph is a graph representing the factorization of a probability distribution function, and has been utilized in many autonomous machine computing tasks, such as localization, tracking, planning and control etc. We are developing an…
To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…
Tensor analysis has been a widely studied in physics applications including circuit theory and electric machines. This paper reviews some of the main features of this type of representation for unbalanced power distribution systems and…
Accelerating magnetic resonance image (MRI) reconstruction process is a challenging ill-posed inverse problem due to the excessive under-sampling operation in k-space. In this paper, we propose a recurrent transformer model, namely…
State-of-the-art probabilistic model checkers perform verification on explicit-state Markov models defined in a high-level programming formalism like the PRISM modeling language. Typically, the low-level models resulting from such…
We present an alternative technique for evaluating multiloop Feynman diagrams, using the integration by fractional expansion method. Here we consider generic diagrams that contain propagators with radiative corrections which topologically…
Large-scale integration of distributed energy resources into residential distribution feeders necessitates careful control of their operation through power flow analysis. While the knowledge of the distribution system model is crucial for…
The massless one-loop box integral with arbitrary indices in arbitrary space-time dimension $d$ is shown to reduce to a sum over three generalised hypergeometric functions. This result follows from the solution to the third order…
The renewable energy proliferation calls upon the grid operators and planners to systematically evaluate the potential impacts of distributed energy resources (DERs). Considering the significant differences between various inverter-based…
We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular low displacement rank) for integrating tensor fields defined on weighted trees. Several applications of the resulting fast…