# Complementary First and Second Derivative Methods for Ansatz Optimization in Variational Monte Carlo

## TL;DR

This paper compares first and second derivative optimization methods in variational Monte Carlo, showing their complementary strengths and proposing a hybrid approach for efficient wave function optimization.

## Contribution

It introduces a hybrid optimization method combining linear and accelerated descent techniques for improved variational Monte Carlo wave function optimization.

## Key findings

- Low-memory linear methods efficiently approach the energy minimum.
- Accelerated descent methods precisely locate the minimum with less bias.
- Hybrid approach combines advantages for large, complex wave functions.

## Abstract

We present a comparison between a number of recently introduced low-memory wave function optimization methods for variational Monte Carlo in which we find that first and second derivative methods possess strongly complementary relative advantages. While we find that low-memory variants of the linear method are vastly more efficient at bringing wave functions with disparate types of nonlinear parameters to the vicinity of the energy minimum, accelerated descent approaches are then able to locate the precise minimum with less bias and lower statistical uncertainty. By constructing a simple hybrid approach that combines these methodologies, we show that all of these advantages can be had at once when simultaneously optimizing large determinant expansions, molecular orbital shapes, traditional Jastrow correlation factors, and more nonlinear many-electron Jastrow factors.