Process-based modelling offers interpretability and physical consistency in many domains of
geosciences but struggles to leverage large datasets efficiently. Machine-learning methods …

The popularity of machine learning (ML), deep learning (DL) and artificial intelligence (AI)
has risen sharply in recent years. Despite this spike in popularity, the inner workings of ML …

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 …

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 …

We introduce the framework of continuous--depth graph neural networks (GNNs). Graph
neural ordinary differential equations (GDEs) are formalized as the counterpart to GNNs …

We present DiffTaichi, a new differentiable programming language tailored for building high-
performance differentiable physical simulators. Based on an imperative programming …

The adjoint sensitivity method scalably computes gradients of solutions to ordinary
differential equations. We generalize this method to stochastic differential equations …

The original" Seven Motifs" set forth a roadmap of essential methods for the field of scientific
computing, where a motif is an algorithmic method that captures a pattern of computation …

Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal
dynamics. However, a fundamental limitation has been that such models have typically been …

Including prior knowledge is important for effective machine learning models in physics and
is usually achieved by explicitly adding loss terms or constraints on model architectures …