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Computational fluid dynamics (CFD) analysis is widely used in engineering. Although CFD calculations are accurate, the computational cost associated with complex systems makes it difficult to obtain empirical equations between system…
Motivated by risk assessment of coastal flooding, we consider time-consuming simulators with a spatial output. The aim is to perform sensitivity analysis (SA), quantifying the influence of input parameters on the output. There are three…
The development of advanced software tools for power system analysis requires extensive programming expertise. Even when using open-source tools, programming skills are essential to modify built-in models. This can be particularly…
Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found. In this paper, we…
Time domain simulation is the basis of dynamic security assessment for power systems. Traditionally, numerical integration methods are adopted by simulation software to solve nonlinear power system differential-algebraic equations about any…
Causal discovery amounts to unearthing causal relationships amongst features in data. It is a crucial companion to causal inference, necessary to build scientific knowledge without resorting to expensive or impossible randomised control…
Representational similarity analysis (RSA) is a multivariate technique to investigate cortical representations of objects or constructs. While avoiding ill-posed matrix inversions that plague multivariate approaches in the presence of many…
Mathematical reasoning in large language models (LMs) has garnered significant attention in recent work, but there is a limited understanding of how these models process and store information related to arithmetic tasks within their…
In this paper, we present SCALAR (Symbolic Conjecture and LLM-Assisted Reasoning), a neurosymbolic framework for automated conjecture generation in quantum circuit analysis built on top of the CUDA-Q open source framework. The system…
Symbolic regression (SR) aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, is a powerful paradigm for scientific discovery. Recent advances have expanded SR to describe related phenomena using a…
Simulated Annealing (SA) is a widely used stochastic optimization algorithm, yet much of its theoretical understanding is limited to asymptotic convergence guarantees or general spectral bounds. In this paper, we develop a finite-time…
The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic…
Combining abstract, symbolic reasoning with continuous neural reasoning is a grand challenge of representation learning. As a step in this direction, we propose a new architecture, called neural equivalence networks, for the problem of…
The development of next-generation molecular simulation models requires moving beyond pre-defined functional forms toward machine learning (ML) techniques that directly capture multiscale physics. Here, we demonstrate such an approach using…
Structural equation modeling (SEM) is a popular tool in the social and behavioural sciences, where it is being applied to ever more complex data types. The high-dimensional data produced by modern sensors, brain images, or (epi)genetic…
A critical question about Large Language Models (LLMs) is whether their apparent deficiency in mathematical reasoning is inherent, or merely a result of insufficient exposure to high-quality mathematical data. To explore this, we developed…
In many applications, such as physiology and finance, large time series data bases are to be analyzed requiring the computation of linear, nonlinear and other measures. Such measures have been developed and implemented in commercial and…
Machine-learning technologies for learning dynamical systems from data play an important role in engineering design. This research focuses on learning continuous linear models from data. Stability, a key feature of dynamic systems, is…
Nonlinear dynamics and pattern formation in the systems with quadratic nonlinearity is computed symbolically by specially developed MATHEMATICA package. A Web interface for the presented methods is developed, which turns the implementations…
This paper presents a technique for reduced-order Markov modeling for compact representation of time-series data. In this work, symbolic dynamics-based tools have been used to infer an approximate generative Markov model. The time-series…