Since their inception, computational homogenization methods based on the fast Fourier
transform (FFT) have grown in popularity, establishing themselves as a powerful tool …

Optimization is a critical component in deep learning. We think optimization for neural
networks is an interesting topic for theoretical research due to various reasons. First, its …

In many optimization problems arising from scientific, engineering and artificial intelligence
applications, objective and constraint functions are available only as the output of a black …

Gradient-based planners are widely used for quadrotor local planning, in which a Euclidean
Signed Distance Field (ESDF) is crucial for evaluating gradient magnitude and direction …

The success of first-principles electronic-structure calculation for predictive modeling in
chemistry, solid-state physics, and materials science is constrained by the limitations on …

This paper presents the input convex neural network architecture. These are scalar-valued
(potentially deep) neural networks with constraints on the network parameters such that the …

The atomic cluster expansion is a general polynomial expansion of the atomic energy in
multi-atom basis functions. Here we implement the atomic cluster expansion in the …

Matrix theory is one of the most fundamental tools of mathematics and science, and a
number of classical books on matrix analysis have been written to explore this theory. As a …

Adaptive gradient methods such as AdaGrad and its variants update the stepsize in
stochastic gradient descent on the fly according to the gradients received along the way; …

When and why can a neural network be successfully trained? This article provides an
overview of optimization algorithms and theory for training neural networks. First, we discuss …