Related papers: A Technical Survey of Sparse Linear Solvers in Ele…
In the field of uncertainty quantification, sparse polynomial chaos (PC) expansions are commonly used by researchers for a variety of purposes, such as surrogate modeling. Ideas from compressed sensing may be employed to exploit this…
Efficient numerical solvers for sparse linear systems are crucial in science and engineering. One of the fastest methods for solving large-scale sparse linear systems is algebraic multigrid (AMG). The main challenge in the construction of…
The stagnation of EDA technologies roots from insufficient knowledge reuse. In practice, very similar simulation or optimization results may need to be repeatedly constructed from scratch. This motivates my research on introducing more…
Despite the growing availability of large datasets, causal structure learning remains computationally prohibitive at scale. We revisit sparsest-permutation learning for linear structural equation models and show that exact Cholesky…
Systems of linear equations arise at the heart of many scientific and engineering applications. Many of these linear systems are sparse; i.e., most of the elements in the coefficient matrix are zero. Direct methods based on matrix…
Ill-conditioning of the system matrix is a well-known complication in immersed finite element methods and trimmed isogeometric analysis. Elements with small intersections with the physical domain yield problematic eigenvalues in the system…
Despite being a key bottleneck in many machine learning tasks, the cost of solving large linear systems has proven challenging to quantify due to problem-dependent quantities such as condition numbers. To tackle this, we consider a…
We examine what is an efficient and scalable nonlinear solver, with low work and memory complexity, for many classes of discretized partial differential equations (PDEs) - matrix-free Full multigrid (FMG) with a Full Approximation Storage…
The demand for substantial increases in the spatial resolution of global weather- and climate- prediction models makes it necessary to use numerically efficient and highly scalable algorithms to solve the equations of large scale…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
The accuracy of a large eddy simulation (LES) is determined by the accuracy of the model used to describe the effect of unresolved scales, the numerical errors of the resolved scales, and the optimality of the length scale that separates…
In the present study, we consider the Extra-Membrane-Intra model (EMI) for the simulation of excitable tissues at the cellular level. We provide the (possibly large) system of partial differential equations (PDEs), equipped with ad hoc…
Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and…
The application of Machine Learning (ML) in Electronic Design Automation (EDA) for Very Large-Scale Integration (VLSI) design has garnered significant research attention. Despite the requirement for extensive datasets to build effective ML…
The Riesz maps of the $L^2$ de Rham complex frequently arise as subproblems in the construction of fast preconditioners for more complicated problems. In this work we present multigrid solvers for high-order finite element discretizations…
Circuit analysis of any certain model behavior is a central task in mechanistic interpretability. We introduce our circuit discovery pipeline with Sparse Autoencoders (SAEs) and a variant called Transcoders. With these two modules inserted…
We present factorization and solution phases for a new linear complexity direct solver designed for concurrent batch operations on fine-grained parallel architectures, for matrices amenable to hierarchical representation. We focus on the…
The increasing complexity of deep learning recommendation models (DLRM) has led to a growing need for large-scale distributed systems that can efficiently train vast amounts of data. In DLRM, the sparse embedding table is a crucial…
Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This…
Electronic Design Automation (EDA) is essential for IC design and has recently benefited from AI-based techniques to improve efficiency. Logic synthesis, a key EDA stage, transforms high-level hardware descriptions into optimized netlists.…