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In this paper, we present recent efforts to develop reduced order modeling (ROM) capabilities for spectral element methods (SEM). Namely, we detail the implementation of ROM for both continuous Galerkin and discontinuous Galerkin methods in…
As language models have grown in parameters and layers, it has become much harder to train and infer with them on single GPUs. This is severely restricting the availability of large language models such as GPT-3, BERT-Large, and many…
We describe an iterative method to optimize the multi-scale entanglement renormalization ansatz (MERA) for the low-energy subspace of local Hamiltonians on a D-dimensional lattice. For translation invariant systems the cost of this…
The efficient optimization of actuated soft structures, particularly under complex nonlinear forces, remains a critical challenge in advancing robotics. Simulations of nonlinear structures, such as soft-bodied robots modeled using the…
Current inference scaling methods, such as Self-consistency and Best-of-N, have proven effective in improving the accuracy of LLMs on complex reasoning tasks. However, these methods rely heavily on the quality of candidate responses and are…
In this paper, we explored the opportunity to enhance power grid robustness after routing stage, and propose a linear programming based algorithm that maximizes the improvement of power grid strengthening with given available routing…
This paper presents a novel approach for performing computations using Look-Up Tables (LUTs) tailored specifically for Compute-in-Memory applications. The aim is to address the scalability challenges associated with LUT-based computation by…
Tensor networks are a powerful tool to simulate a variety of different physical models, including those that suffer from the sign problem in Monte Carlo simulations. The Hubbard model on the honeycomb lattice with non-zero chemical…
Subspace identification methods (SIMs) have proven very powerful for estimating linear state-space models. To overcome the deficiencies of classical SIMs, a significant number of algorithms has appeared over the last two decades, where most…
Transformer-based pre-trained language models (PLMs) mostly suffer from excessive overhead despite their advanced capacity. For resource-constrained devices, there is an urgent need for a spatially and temporally efficient model which…
We prove an algorithmic hardness result for finding low-energy states in the so-called \emph{continuous random energy model (CREM)}, introduced by Bovier and Kurkova in 2004 as an extension of Derrida's \emph{generalized random energy…
Parameter-Efficient Tuning (PETuning) methods have been deemed by many as the new paradigm for using pretrained language models (PLMs). By tuning just a fraction amount of parameters comparing to full model finetuning, PETuning methods…
Expectation-maximization (EM) is a popular and well-established method for image reconstruction in positron emission tomography (PET) but it often suffers from slow convergence. Ordered subset EM (OSEM) is an effective reconstruction…
This work proposes a novel adaptive linearized alternating direction multiplier method (LADMM) to convex optimization, which improves the convergence rate of the LADMM-based algorithm by adjusting step-size iteratively.The innovation of…
In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks…
In this work we present a new method of black-box optimization and constraint satisfaction. Existing algorithms that have attempted to solve this problem are unable to consider multiple modes, and are not able to adapt to changes in…
In this paper we have proposed a semi-heuristic optimization algorithm for designing optimal plant layouts in process-focused manufacturing/service facilities. Being a semi-heuristic search, our algorithm is likely to be more efficient in…
The exponential growth of large language models (LLMs) like ChatGPT has revolutionized artificial intelligence, offering unprecedented capabilities in natural language processing. However, the extensive computational resources required for…
By means of the multicomponent Shan-Chen lattice Boltzmann method (LBM), we investigate the multiphase flow through porous media. Despite the excellent accuracy of the LBM, large domains result in unaffordable computational expenses. The…
We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which the constraint is given by mass conservation. Our approach…