Progress in combustion science and engineering has led to the generation of large amounts
of data from large-scale simulations, high-resolution experiments, and sensors. This corpus …

Innovative approaches and tools play an important role in shaping design, characterization
and optimization for the field of photonics. As a subset of machine learning that learns …

It is widely known that neural networks (NNs) are universal approximators of continuous
functions. However, a less known but powerful result is that a NN with a single hidden layer …

The conjoining of dynamical systems and deep learning has become a topic of great
interest. In particular, neural differential equations (NDEs) demonstrate that neural networks …

Interpretability in machine learning (ML) is crucial for high stakes decisions and
troubleshooting. In this work, we provide fundamental principles for interpretable ML, and …

Sparse model identification enables the discovery of nonlinear dynamical systems purely
from data; however, this approach is sensitive to noise, especially in the low-data limit. In this …

We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward
and inverse nonlinear problems described by partial differential equations (PDEs) and noisy …

For centuries, flow visualization has been the art of making fluid motion visible in physical
and biological systems. Although such flow patterns can be, in principle, described by the …

Digital twin can be defined as a virtual representation of a physical asset enabled through
data and simulators for real-time prediction, optimization, monitoring, controlling, and …

In the context of science, the well-known adage" a picture is worth a thousand words" might
well be" a model is worth a thousand datasets." In this manuscript we introduce the SciML …