Data assimilation (DA) and uncertainty quantification (UQ) are extensively used in analysing
and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical …

The two fields of machine learning and graphical causality arose and are developed
separately. However, there is, now, cross-pollination and increasing interest in both fields to …

We introduce a new family of deep neural network models. Instead of specifying a discrete
sequence of hidden layers, we parameterize the derivative of the hidden state using a …

Over the last 20 years Machine Learning (ML) has been applied to a wide variety of
applications in the fields of engineering and computer science. In the field of material …

Mesh-based simulations are central to modeling complex physical systems in many
disciplines across science and engineering. Mesh representations support powerful …

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 …

Here we present a machine learning framework and model implementation that can learn to
simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and …

Partial differential equations (PDEs) are commonly derived based on empirical
observations. However, recent advances of technology enable us to collect and store …

Learning to optimize (L2O) is an emerging approach that leverages machine learning to
develop optimization methods, aiming at reducing the laborious iterations of hand …

While deep learning has shown tremendous success in a wide range of domains, it remains
a grand challenge to incorporate physical principles in a systematic manner to the design …