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An essential tool in data-driven modeling of dynamical systems from frequency response measurements is the barycentric form of the underlying rational transfer function. In this work, we propose structured barycentric forms for modeling…
In this paper, we introduce the Interpretable Cross-Examination Technique (ICE-T), a novel approach that leverages structured multi-prompt techniques with Large Language Models (LLMs) to improve classification performance over zero-shot and…
A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…
Master-field simulations offer an approach to lattice QCD in which calculations are performed on a small number of large-volume gauge-field configurations. The latter is advantageous for simulations in which the global topological charge is…
We conduct a thorough study of different forms of horizontally explicit and vertically implicit (HEVI) time-integration strategies for the compressible Euler equations on spherical domains typical of nonhydrostatic global atmospheric…
The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile…
Time series forecasting at scale presents significant challenges for modern prediction systems, particularly when dealing with large sets of synchronized series, such as in a global payment network. In such systems, three key challenges…
There has been a recent surge of interest in time series modeling using the Transformer architecture. However, forecasting multivariate time series with Transformer presents a unique challenge as it requires modeling both temporal…
Unconditionally stable time stepping schemes are useful and often practically necessary for advancing parabolic operators in multi-scale systems. However, serious accuracy problems may emerge when taking time steps that far exceed the…
The adaptation of large language models (LLMs) to time series forecasting poses unique challenges, as time series data is continuous in nature, while LLMs operate on discrete tokens. Despite the success of LLMs in natural language…
Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear…
Prompt tuning is a parameter-efficient tuning (PETuning) method for utilizing pre-trained models (PTMs) that simply prepends a soft prompt to the input and only optimizes the prompt to adapt PTMs to downstream tasks. Although it is…
Parameter estimation and associated uncertainty quantification is an important problem in dynamical systems characterized by ordinary differential equation (ODE) models that are often nonlinear. Typically, such models have analytically…
An interpolation method for discretising continuous-time Linear Time Invariant (LTI) models is proposed in this paper. It consists first in using the Loewner interpolation framework on a specific set of frequency data and secondly to…
Recently, there has been a surge of Transformer-based solutions for the long-term time series forecasting (LTSF) task. Despite the growing performance over the past few years, we question the validity of this line of research in this work.…
In this paper, we present a new approach to time series forecasting. Time series data are prevalent in many scientific and engineering disciplines. Time series forecasting is a crucial task in modeling time series data, and is an important…
In recent years, numerous Transformer-based models have been applied to long-term time-series forecasting (LTSF) tasks. However, recent studies with linear models have questioned their effectiveness, demonstrating that simple linear layers…
In this work, we explore LLM's internal representation space to identify attention heads that contain the most truthful and accurate information. We further developed the Inference Time Intervention (ITI) framework, which lets bias LLM…
We derive the partial differential equation (PDE) to which the pseudo-potential lattice Boltzmann method (P-LBM) converges under diffusive scaling, providing a rigorous basis for its consistency analysis. By establishing a direct link…
Large language models (LLMs) exhibit in-context learning abilities which enable the same model to perform several tasks without any task-specific training. In contrast, traditional adaptation approaches, such as fine-tuning, modify the…