arXiv subjects

Ishna Satyarth

Publications and source records attributed to Ishna Satyarth.

2 recordsLinked to original sources

arXiv2026

Performant Tridiagonal Factorization of Skew-Symmetric Matrices

The factorization of skew-symmetric matrices is a critically understudied area of dense linear algebra, particularly in comparison to that of general and symmetric matrices. While some algorithms can be adapted from the symmetric case, the cost of algorithms can be reduced by exploiting skew-symmetry. This work examines the factorization of a skew-symmetric matrix $X$ into its $LTL^T$ decomposition, where $L$ is unit lower triangular and $T$ is tridiagonal. This is also known as a triangular tridiagonalization. This operation is a means for computing the determinant of $X$ as the square of the (cheaply-computed) Pfaffian of the skew-symmetric tridiagonal matrix $T$ as well as for solving systems of equations, across fields such as quantum electronic structure and machine learning. Its application also often requires pivoting in order to improve numerical stability. We compare and contrast previously-published algorithms with those systematically derived using the FLAME methodology. Performant parallel CPU implementations are achieved by fusing operations at multiple levels in order to reduce memory traffic overhead. A key factor is the employment of new capabilities of the BLAS-like Library Instantion Software (BLIS) framework, which now supports casting level-2 and level-3 BLAS-like operations by leveraging its gemm and other kernels, hierarchical parallelism, and cache blocking. A prototype, concise C++ API facilitates the translation of correct-by-construction algorithms into correct code. Experiments verify that the resulting implementations greatly exceed the performance of previous work.

cs.MS↗

arXiv2026

Tensor Hypercontraction Error Correction Using Regression

Wavefunction-based quantum methods are some of the most accurate tools for predicting and analyzing the electronic structure of molecules, in particular for accounting for dynamical electron correlation. However, most methods of including dynamical correlation beyond the simple second-order Møller-Plesset perturbation theory (MP2) level are too computationally expensive to apply to large molecules. Approximations which reduce scaling with system size are a potential remedy, such as the tensor hyper-contraction (THC) technique of Hohenstein et al., but also result in additional sources of error. In this work, we correct errors in THC-approximated methods using machine learning. Specifically, we apply THC to third-order Møller-Plesset theory (MP3) as a simplified model for coupled cluster with single and double excitations (CCSD), and train several regression models on observed THC errors from the Main Group Chemistry Database (MGCDB84). We compare performance of multiple linear regression models and non-linear Kernel Ridge regression models. We also investigate correlation procedures using absolute and relative corrections and evaluate the corrections for both molecule and reaction energies. We discuss the potential for using regression techniques to correct THC-MP3 errors by comparing it to the "canonical" MP3 reference values and find the optimum technique based on accuracy. We find that non-linear regression models reduced root mean squared errors between THC- and canonical MP3 by a factor of 6-9$\times$ for total molecular energies and 2-3$\times$ for reaction energies.

physics.chem-ph↗