Maricela Best McKay

Maricela Best McKay, Nathan P. Lawrence, Brian Wetton et al.

The Gauss-Newton matrix is widely viewed as a positive semidefinite approximation of the Hessian, yet mounting empirical evidence shows that Gauss-Newton descent outperforms Newton's method. We adopt a function space perspective to analyze this phenomenon. We show that the generalized Gauss-Newton (GGN) matrix projects the Newton direction in function space onto the model's tangent space, while a Jacobian-only variant obtained by applying the least squares Gauss-Newton matrix to non-least squares losses projects the function space loss gradient onto this same tangent space. Both projections eliminate distortions from the model's parameterization. Specifically, the evolution of the prediction-target mismatch depends on the model's parameterization through the matrix $JJ^\top$ where $J$ is the Jacobian of the model with respect to its parameters. The projections effectively replace $JJ^\top$ with the identity. We call this effect error whitening. Once the parameterization is removed, the prediction-target mismatch evolves according to dynamics dictated by the structure of the loss and the projection produced by the optimizer. Error whitening is a special property of Gauss-Newton descent that rigorously distinguishes it from Newton's method. We empirically demonstrate that Gauss-Newton optimizers follow the theoretically predicted function space dynamics and outperforms Newton's method, Adam, and Muon across case studies spanning supervised learning, physics-informed deep learning, and approximate dynamic programming.

Maricela Best McKay, Bhushan Gopaluni, Brian Wetton

Lithium ion batteries are widely used in many applications. Battery management systems control their optimal use and charging and predict when the battery will cease to deliver the required output on a planned duty or driving cycle. Such systems use a simulation of a mathematical model of battery performance. These models can be electrochemical or data-driven. Electrochemical models for batteries running at high currents are mathematically and computationally complex. In this work, we show that a well-regarded electrochemical model, the Pseudo Two Dimensional (P2D) model, can be replaced by a computationally efficient Convolutional Neural Network (CNN) surrogate model fit to accurately simulated data from a class of random driving cycles. We demonstrate that a CNN is an ideal choice for accurately capturing Lithium ion concentration profiles. Additionally, we show how the neural network model can be adjusted to correspond to battery changes in State of Health (SOH).