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Machine learning methods have been successful in many areas, like image classification and natural language processing. However, it still needs to be determined how to apply ML to areas with mathematical constraints, like solving PDEs.…
Despite their ubiquity throughout science and engineering, only a handful of partial differential equations (PDEs) have analytical, or closed-form solutions. This motivates a vast amount of classical work on numerical simulation of PDEs and…
Machine Learning (ML) is increasingly used across many disciplines with impressive reported results. However, recent studies suggest published performance of ML models are often overoptimistic. Validity concerns are underscored by findings…
As further progress in the accurate and efficient computation of coupled partial differential equations (PDEs) becomes increasingly difficult, it has become highly desired to develop new methods for such computation. In deviation from…
Machine Learning (ML) research has increased substantially in recent years, due to the success of predictive modeling across diverse application domains. However, well-known barriers exist when attempting to deploy ML models in high-stakes,…
Predicting the outcome of liquid droplet collisions is an extensively studied phenomenon but the current physics based models for predicting the outcomes are poor (accuracy $\approx 43\%$). The key weakness of these models is their limited…
Deep metric learning (DML) enables learning with less supervision through its emphasis on the similarity structure of representations. There has been much work on improving generalization of DML in settings like zero-shot retrieval, but…
Machine learning (ML) models have emerged as a promising approach for solving partial differential equations (PDEs) in science and engineering. Previous ML models typically cannot generalize outside the training data; for example, a trained…
Material scientists are increasingly adopting the use of machine learning (ML) for making potentially important decisions, such as, discovery, development, optimization, synthesis and characterization of materials. However, despite ML's…
A significant level of stigma and inequality exists in mental healthcare, especially in under-served populations. Inequalities are reflected in the data collected for scientific purposes. When not properly accounted for, machine learning…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…
The recent development of machine learning (ML) and Deep Learning (DL) increases the opportunities in all the sectors. ML is a significant tool that can be applied across many disciplines, but its direct application to civil engineering…
Context: Machine Learning (ML) significantly impacts Software Engineering (SE), but studies mainly focus on practitioners, neglecting researchers. This overlooks practices and challenges in teaching, researching, or reviewing ML…
Machine learning (ML) provides powerful tools for predictive modeling. ML's popularity stems from the promise of sample-level prediction with applications across a variety of fields from physics and marketing to healthcare. However, if not…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…